Daily Papers

We present JoyAI-Image, a unified multimodal foundation model for visual understanding, text-to-image generation, and instruction-guided image editing. JoyAI-Image couples a spatially enhanced Multimodal Large Language Model (MLLM) with a Multimodal Diffusion Transformer (MMDiT), allowing perception and generation to interact through a shared multimodal interface. Around this architecture, we build a scalable training recipe that combines unified instruction tuning, long-text rendering supervision, spatially grounded data, and both general and spatial editing signals. This design gives the model broad multimodal capability while strengthening geometry-aware reasoning and controllable visual synthesis. Experiments across understanding, generation, long-text rendering, and editing benchmarks show that JoyAI-Image achieves state-of-the-art or highly competitive performance. More importantly, the bidirectional loop between enhanced understanding, controllable spatial editing, and novel-view-assisted reasoning enables the model to move beyond general visual competence toward stronger spatial intelligence. These results suggest a promising path for unified visual models in downstream applications such as vision-language-action systems and world models.

Deep research agents (DRAs) integrate LLM reasoning with external tools. Memory systems enable DRAs to leverage historical experiences, which are essential for efficient reasoning and autonomous evolution. Existing methods rely on retrieving similar trajectories from memory to aid reasoning, while suffering from key limitations of ineffective memory evolution and increasing storage and retrieval costs. To address these problems, we propose a novel Memory Intelligence Agent (MIA) framework, consisting of a Manager-Planner-Executor architecture. Memory Manager is a non-parametric memory system that can store compressed historical search trajectories. Planner is a parametric memory agent that can produce search plans for questions. Executor is another agent that can search and analyze information guided by the search plan. To build the MIA framework, we first adopt an alternating reinforcement learning paradigm to enhance cooperation between the Planner and the Executor. Furthermore, we enable the Planner to continuously evolve during test-time learning, with updates performed on-the-fly alongside inference without interrupting the reasoning process. Additionally, we establish a bidirectional conversion loop between parametric and non-parametric memories to achieve efficient memory evolution. Finally, we incorporate a reflection and an unsupervised judgment mechanisms to boost reasoning and self-evolution in the open world. Extensive experiments across eleven benchmarks demonstrate the superiority of MIA.

From the invention of writing and the printing press, to television and social media, human history is punctuated by major innovations in communication technology, which fundamentally altered how ideas spread and reshaped our culture. Recent chatbots powered by generative artificial intelligence constitute a novel medium that encodes cultural patterns in their neural representations and disseminates them in conversations with hundreds of millions of people. Understanding whether these patterns transmit into human language, and ultimately shape human culture, is a fundamental question. While fully quantifying the causal impact of a chatbot like ChatGPT on human culture is very challenging, lexicographic shift in human spoken communication may offer an early indicator of such broad phenomenon. Here, we apply econometric causal inference techniques to 740,249 hours of human discourse from 360,445 YouTube academic talks and 771,591 conversational podcast episodes across multiple disciplines. We detect a measurable and abrupt increase in the use of words preferentially generated by ChatGPT, such as delve, comprehend, boast, swift, and meticulous, after its release. These findings suggest a scenario where machines, originally trained on human data and subsequently exhibiting their own cultural traits, can, in turn, measurably reshape human culture. This marks the beginning of a closed cultural feedback loop in which cultural traits circulate bidirectionally between humans and machines. Our results motivate further research into the evolution of human-machine culture, and raise concerns over the erosion of linguistic and cultural diversity, and the risks of scalable manipulation.

Precise six-degree-of-freedom (6DoF) head pose estimation is crucial for safety-critical applications and human-computer interaction scenarios, yet existing monocular methods still struggle with robust pose estimation. We revisit this problem by introducing TRGv2, a lightweight extension of our previous Translation, Rotation, and Geometry (TRG) network, which explicitly models the bidirectional interaction between facial geometry and head pose. TRGv2 jointly infers facial landmarks and 6DoF pose through an iterative refinement loop with landmark-to-image projection, ensuring metric consistency among face size, rotation, and depth. To further improve generalization to out-of-distribution data, TRGv2 regresses correction parameters instead of directly predicting translation, combining them with a pinhole camera model for analytic depth estimation. In addition, we identify a previously overlooked source of bias in cross-dataset evaluations due to inconsistent head center definitions across different datasets. To address this, we propose a reference system alignment strategy that quantifies and corrects translation bias, enabling fair comparisons across datasets. Extensive experiments on ARKitFace, BIWI, and the challenging DD-Pose benchmarks demonstrate that TRGv2 outperforms state-of-the-art methods in both accuracy and efficiency. Code and newly annotated landmarks for DD-Pose will be publicly available.

We present HSImul3R, a unified framework for simulation-ready 3D reconstruction of human-scene interactions (HSI) from casual captures, including sparse-view images and monocular videos. Existing methods suffer from a perception-simulation gap: visually plausible reconstructions often violate physical constraints, leading to instability in physics engines and failure in embodied AI applications. To bridge this gap, we introduce a physically-grounded bi-directional optimization pipeline that treats the physics simulator as an active supervisor to jointly refine human dynamics and scene geometry. In the forward direction, we employ Scene-targeted Reinforcement Learning to optimize human motion under dual supervision of motion fidelity and contact stability. In the reverse direction, we propose Direct Simulation Reward Optimization, which leverages simulation feedback on gravitational stability and interaction success to refine scene geometry. We further present HSIBench, a new benchmark with diverse objects and interaction scenarios. Extensive experiments demonstrate that HSImul3R produces the first stable, simulation-ready HSI reconstructions and can be directly deployed to real-world humanoid robots.

Existing driving automation (DA) systems on production vehicles rely on human drivers to decide when to engage DA while requiring them to remain continuously attentive and ready to intervene. This design demands substantial situational judgment and imposes significant cognitive load, leading to steep learning curves, suboptimal user experience, and safety risks from both over-reliance and delayed takeover. Predicting when drivers hand over control to DA and when they take it back is therefore critical for designing proactive, context-aware HMI, yet existing datasets rarely capture the multimodal context, including road scene, driver state, vehicle dynamics, and route environment. To fill this gap, we introduce BATON, a large-scale naturalistic dataset capturing real-world DA usage across 127 drivers, and 136.6 hours of driving. The dataset synchronizes front-view video, in-cabin video, decoded CAN bus signals, radar-based lead-vehicle interaction, and GPS-derived route context, forming a closed-loop multimodal record around each control transition. We define three benchmark tasks: driving action understanding, handover prediction, and takeover prediction, and evaluate baselines spanning sequence models, classical classifiers, and zero-shot VLMs. Results show that visual input alone is insufficient for reliable transition prediction: front-view video captures road context but not driver state, while in-cabin video reflects driver readiness but not the external scene. Incorporating CAN and route-context signals substantially improves performance over video-only settings, indicating strong complementarity across modalities. We further find takeover events develop more gradually and benefit from longer prediction horizons, whereas handover events depend more on immediate contextual cues, revealing an asymmetry with direct implications for HMI design in assisted driving systems.

Large Language Models (LLMs) have improved programming efficiency, but their performance degrades significantly as requirements scale; when faced with multi-modal documents containing hundreds of scenarios, LLMs often produce incorrect implementations or omit constraints. We propose Agentic Requirement Compilation (ARC), a technique that moves beyond simple code generation to requirement compilation, enabling the creation of runnable web systems directly from multi-modal DSL documents. ARC generates not only source code but also modular designs for UI, API, and database layers, enriched test suites (unit, modular, and integration), and detailed traceability for software maintenance. Our approach employs a bidirectional test-driven agentic loop: a top-down architecture phase decomposes requirements into verifiable interfaces, followed by a bottom-up implementation phase where agents generate code to satisfy those tests. ARC maintains strict traceability across requirements, design, and code to facilitate intelligent asset reuse. We evaluated ARC by generating six runnable web systems from documents spanning 50-200 multi-modal scenarios. Compared to state-of-the-art baselines, ARC-generated systems pass 50.6% more GUI tests on average. A user study with 21 participants showed that novice users can successfully write DSL documents for complex systems, such as a 10K-line ticket-booking system, in an average of 5.6 hours. These results demonstrate that ARC effectively transforms non-trivial requirement specifications into maintainable, runnable software.

Standard training pipelines for large language models (LLMs) are typically unidirectional, progressing from pre-training to post-training. However, the potential for a bidirectional process--where insights from post-training retroactively improve the pre-trained foundation--remains unexplored. We aim to establish a self-reinforcing flywheel: a cycle in which reinforcement learning (RL)-tuned model strengthens the base model, which in turn enhances subsequent post-training performance, requiring no specially trained teacher or reference model. To realize this, we analyze training dynamics and identify the mid-training (annealing) phase as a critical turning point for model capabilities. This phase typically occurs at the end of pre-training, utilizing high-quality corpora under a rapidly decaying learning rate. Building upon this insight, we introduce ReMiT (Reinforcement Learning-Guided Mid-Training). Specifically, ReMiT leverages the reasoning priors of RL-tuned models to dynamically reweight tokens during the mid-training phase, prioritizing those pivotal for reasoning. Empirically, ReMiT achieves an average improvement of 3\% on 10 pre-training benchmarks, spanning math, code, and general reasoning, and sustains these gains by over 2\% throughout the post-training pipeline. These results validate an iterative feedback loop, enabling continuous and self-reinforcing evolution of LLMs.

We introduce WAM-Flow, a vision-language-action (VLA) model that casts ego-trajectory planning as discrete flow matching over a structured token space. In contrast to autoregressive decoders, WAM-Flow performs fully parallel, bidirectional denoising, enabling coarse-to-fine refinement with a tunable compute-accuracy trade-off. Specifically, the approach combines a metric-aligned numerical tokenizer that preserves scalar geometry via triplet-margin learning, a geometry-aware flow objective and a simulator-guided GRPO alignment that integrates safety, ego progress, and comfort rewards while retaining parallel generation. A multi-stage adaptation converts a pre-trained auto-regressive backbone (Janus-1.5B) from causal decoding to non-causal flow model and strengthens road-scene competence through continued multimodal pretraining. Thanks to the inherent nature of consistency model training and parallel decoding inference, WAM-Flow achieves superior closed-loop performance against autoregressive and diffusion-based VLA baselines, with 1-step inference attaining 89.1 PDMS and 5-step inference reaching 90.3 PDMS on NAVSIM v1 benchmark. These results establish discrete flow matching as a new promising paradigm for end-to-end autonomous driving. The code will be publicly available soon.

The pursuit of data efficiency, where quality outweighs quantity, has emerged as a cornerstone in robotic manipulation, especially given the high costs associated with real-world data collection. We propose that maximizing the informational density of individual demonstrations can dramatically reduce reliance on large-scale datasets while improving task performance. To this end, we introduce Adversarial Data Collection, a Human-in-the-Loop (HiL) framework that redefines robotic data acquisition through real-time, bidirectional human-environment interactions. Unlike conventional pipelines that passively record static demonstrations, ADC adopts a collaborative perturbation paradigm: during a single episode, an adversarial operator dynamically alters object states, environmental conditions, and linguistic commands, while the tele-operator adaptively adjusts actions to overcome these evolving challenges. This process compresses diverse failure-recovery behaviors, compositional task variations, and environmental perturbations into minimal demonstrations. Our experiments demonstrate that ADC-trained models achieve superior compositional generalization to unseen task instructions, enhanced robustness to perceptual perturbations, and emergent error recovery capabilities. Strikingly, models trained with merely 20% of the demonstration volume collected through ADC significantly outperform traditional approaches using full datasets. These advances bridge the gap between data-centric learning paradigms and practical robotic deployment, demonstrating that strategic data acquisition, not merely post-hoc processing, is critical for scalable, real-world robot learning. Additionally, we are curating a large-scale ADC-Robotics dataset comprising real-world manipulation tasks with adversarial perturbations. This benchmark will be open-sourced to facilitate advancements in robotic imitation learning.

Cutscenes are carefully choreographed cinematic sequences embedded in video games and interactive media, serving as the primary vehicle for narrative delivery, character development, and emotional engagement. Producing cutscenes is inherently complex: it demands seamless coordination across screenwriting, cinematography, character animation, voice acting, and technical direction, often requiring days to weeks of collaborative effort from multidisciplinary teams to produce minutes of polished content. In this work, we present Cutscene Agent, an LLM agent framework for automated end-to-end cutscene generation. The framework makes three contributions: (1)~a Cutscene Toolkit built on the Model Context Protocol (MCP) that establishes bidirectional integration between LLM agents and the game engine -- agents not only invoke engine operations but continuously observe real-time scene state, enabling closed-loop generation of editable engine-native cinematic assets; (2)~a multi-agent system where a director agent orchestrates specialist subagents for animation, cinematography, and sound design, augmented by a visual reasoning feedback loop for perception-driven refinement; and (3)~CutsceneBench, a hierarchical evaluation benchmark for cutscene generation. Unlike typical tool-use benchmarks that evaluate short, isolated function calls, cutscene generation requires long-horizon, multi-step orchestration of dozens of interdependent tool invocations with strict ordering constraints -- a capability dimension that existing benchmarks do not cover. We evaluate a range of LLMs on CutsceneBench and analyze their performance across this challenging task.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

We present a simple and effective pretraining strategy -- bidirectional training (BiT) for neural machine translation. Specifically, we bidirectionally update the model parameters at the early stage and then tune the model normally. To achieve bidirectional updating, we simply reconstruct the training samples from "srcrightarrowtgt" to "src+tgtrightarrowtgt+src" without any complicated model modifications. Notably, our approach does not increase any parameters or training steps, requiring the parallel data merely. Experimental results show that BiT pushes the SOTA neural machine translation performance across 15 translation tasks on 8 language pairs (data sizes range from 160K to 38M) significantly higher. Encouragingly, our proposed model can complement existing data manipulation strategies, i.e. back translation, data distillation, and data diversification. Extensive analyses show that our approach functions as a novel bilingual code-switcher, obtaining better bilingual alignment.

Modeling users' dynamic and evolving preferences from their historical behaviors is challenging and crucial for recommendation systems. Previous methods employ sequential neural networks (e.g., Recurrent Neural Network) to encode users' historical interactions from left to right into hidden representations for making recommendations. Although these methods achieve satisfactory results, they often assume a rigidly ordered sequence which is not always practical. We argue that such left-to-right unidirectional architectures restrict the power of the historical sequence representations. For this purpose, we introduce a Bidirectional Encoder Representations from Transformers for sequential Recommendation (BERT4Rec). However, jointly conditioning on both left and right context in deep bidirectional model would make the training become trivial since each item can indirectly "see the target item". To address this problem, we train the bidirectional model using the Cloze task, predicting the masked items in the sequence by jointly conditioning on their left and right context. Comparing with predicting the next item at each position in a sequence, the Cloze task can produce more samples to train a more powerful bidirectional model. Extensive experiments on four benchmark datasets show that our model outperforms various state-of-the-art sequential models consistently.

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. The learning process of BL tries to reproduce the neuroplasticity stated in Hebbian theory using only backward propagation of errors. In this paper, two novel learning techniques are introduced which use BL for improving robustness to white noise static and adversarial examples. The first method is bidirectional propagation of errors, which the error propagation occurs in backward and forward directions. Motivated by the fact that its generative model receives as input a constant vector per class, we introduce as a second method the hybrid adversarial networks (HAN). Its generative model receives a random vector as input and its training is based on generative adversarial networks (GAN). To assess the performance of BL, we perform experiments using several architectures with fully and convolutional layers, with and without bias. Experimental results show that both methods improve robustness to white noise static and adversarial examples, and even increase accuracy, but have different behavior depending on the architecture and task, being more beneficial to use the one or the other. Nevertheless, HAN using a convolutional architecture with batch normalization presents outstanding robustness, reaching state-of-the-art accuracy on adversarial examples of hand-written digits.

Bidirectional transformers are the foundation of many sequence modeling tasks across natural, biological, and chemical language domains, but they are permutation-invariant without explicit positional embeddings. In contrast, unidirectional attention inherently encodes positional information through its triangular mask, enabling models to operate without positional embeddings altogether. Here, we introduce Dual Triangle Attention, a novel bidirectional attention mechanism that separates the query-key subspace of each attention head into two complementary triangular masks: one that attends to past-and-self positions and one that attends to future-and-self positions. This design provides bidirectional context while maintaining the causal mask's implicit positional inductive bias in both directions. Using PyTorch's flex_attention, Dual Triangle Attention is implemented as a single compiled kernel call with no additional parameters beyond standard multi-head attention. We evaluated Dual Triangle Attention across three settings: (1) a synthetic argmax position probe, (2) masked language modeling (MLM) on natural language, and (3) MLM on protein sequences. In the argmax task, both Dual Triangle Attention and causal attention learn positional information without explicit positional embeddings, whereas standard bidirectional attention cannot. In the MLM experiments, Dual Triangle Attention with Rotary Positional Embeddings (RoPE) achieved the best context extension performance and strong performance across the board. These findings suggest that Dual Triangle Attention is a viable attention mechanism for bidirectional transformers, with or without positional embeddings.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Offline model-based optimization aims to maximize a black-box objective function with a static dataset of designs and their scores. In this paper, we focus on biological sequence design to maximize some sequence score. A recent approach employs bidirectional learning, combining a forward mapping for exploitation and a backward mapping for constraint, and it relies on the neural tangent kernel (NTK) of an infinitely wide network to build a proxy model. Though effective, the NTK cannot learn features because of its parametrization, and its use prevents the incorporation of powerful pre-trained Language Models (LMs) that can capture the rich biophysical information in millions of biological sequences. We adopt an alternative proxy model, adding a linear head to a pre-trained LM, and propose a linearization scheme. This yields a closed-form loss and also takes into account the biophysical information in the pre-trained LM. In addition, the forward mapping and the backward mapping play different roles and thus deserve different weights during sequence optimization. To achieve this, we train an auxiliary model and leverage its weak supervision signal via a bi-level optimization framework to effectively learn how to balance the two mappings. Further, by extending the framework, we develop the first learning rate adaptation module Adaptive-eta, which is compatible with all gradient-based algorithms for offline model-based optimization. Experimental results on DNA/protein sequence design tasks verify the effectiveness of our algorithm. Our code is available~https://anonymous.4open.science/r/BIB-ICLR2023-Submission/README.md{here.}

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

Current AI alignment through RLHF follows a single directional paradigm that AI conforms to human preferences while treating human cognition as fixed. We propose a shift to co-alignment through Bidirectional Cognitive Alignment (BiCA), where humans and AI mutually adapt. BiCA uses learnable protocols, representation mapping, and KL-budget constraints for controlled co-evolution. In collaborative navigation, BiCA achieved 85.5% success versus 70.3% baseline, with 230% better mutual adaptation and 332% better protocol convergence. Emergent protocols outperformed handcrafted ones by 84%, while bidirectional adaptation unexpectedly improved safety (+23% out-of-distribution robustness). The 46% synergy improvement demonstrates optimal collaboration exists at the intersection, not union, of human and AI capabilities, validating the shift from single-directional to co-alignment paradigms.

Efficient state space models (SSMs), such as linear recurrent neural networks and linear attention variants, offer computational advantages over Transformers but struggle with tasks requiring long-range in-context retrieval-like text copying, associative recall, and question answering over long contexts. Previous efforts to address these challenges have focused on architectural modifications, often reintroducing computational inefficiencies. In this paper, we propose a novel training procedure, Birdie, that significantly enhances the in-context retrieval capabilities of SSMs without altering their architecture. Our approach combines bidirectional input processing with dynamic mixtures of specialized pre-training objectives, optimized via reinforcement learning. We introduce a new bidirectional SSM architecture that seamlessly transitions from bidirectional context processing to causal generation. Experimental evaluations demonstrate that Birdie markedly improves performance on retrieval-intensive tasks such as multi-number phone book lookup, long paragraph question-answering, and infilling. This narrows the performance gap with Transformers, while retaining computational efficiency. Our findings highlight the importance of training procedures in leveraging the fixed-state capacity of SSMs, offering a new direction to advance their capabilities. All code and pre-trained models are available at https://www.github.com/samblouir/birdie, with support for JAX and PyTorch.

Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage bidirectional context, enabling richer dependency modeling. However, they often assume token independence during prediction, which undermines the modeling of sequential dependencies. Additionally, the corruption of sequences through masking or absorption can introduce unnatural distortions, complicating the learning process. To address these issues, we propose Bidirectional Autoregressive Diffusion (BAD), a novel approach that unifies the strengths of autoregressive and mask-based generative models. BAD utilizes a permutation-based corruption technique that preserves the natural sequence structure while enforcing causal dependencies through randomized ordering, enabling the effective capture of both sequential and bidirectional relationships. Comprehensive experiments show that BAD outperforms autoregressive and mask-based models in text-to-motion generation, suggesting a novel pre-training strategy for sequence modeling. The codebase for BAD is available on https://github.com/RohollahHS/BAD.

Large language models such as GPT-3 (Brown et al., 2020) can perform arbitrary tasks without undergoing fine-tuning after being prompted with only a few labeled examples. An arbitrary task can be reformulated as a natural language prompt, and a language model can be asked to generate the completion, indirectly performing the task in a paradigm known as prompt-based learning. To date, emergent prompt-based learning capabilities have mainly been demonstrated for unidirectional language models. However, bidirectional language models pre-trained on denoising objectives such as masked language modeling produce stronger learned representations for transfer learning. This motivates the possibility of prompting bidirectional models, but their pre-training objectives have made them largely incompatible with the existing prompting paradigm. We present SAP (Sequential Autoregressive Prompting), a technique that enables the prompting of bidirectional models. Utilizing the machine translation task as a case study, we prompt the bidirectional mT5 model (Xue et al., 2021) with SAP and demonstrate its few-shot and zero-shot translations outperform the few-shot translations of unidirectional models like GPT-3 and XGLM (Lin et al., 2021), despite mT5's approximately 50% fewer parameters. We further show SAP is effective on question answering and summarization. For the first time, our results demonstrate prompt-based learning is an emergent property of a broader class of language models, rather than only unidirectional models.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

We introduce Bitune, a method that improves instruction-tuning of pretrained decoder-only large language models, leading to consistent gains on downstream tasks. Bitune applies both causal and bidirectional attention to the prompt, to obtain a better representation of the query or instruction. We realize this by introducing two sets of parameters, for which we apply parameter-efficient finetuning techniques. These causal and bidirectional features are then combined into a weighted average with trainable coefficients, which is subsequently used to generate new tokens. We demonstrate significant improvements in zero-shot performance on commonsense reasoning, arithmetic, and language understanding tasks, while extensive ablation studies validate the role of each component and demonstrate the method's agnosticism to different PEFT techniques.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

Recent studies have highlighted a phenomenon in large language models (LLMs) known as "the reversal curse," in which the order of knowledge entities in the training data biases the models' comprehension. For example, if a model is trained on sentences where entity A consistently appears before entity B, it can respond to queries about A by providing B as the answer. However, it may encounter confusion when presented with questions concerning B. We contend that the reversal curse is partially a result of specific model training objectives, particularly evident in the prevalent use of the next-token prediction within most causal language models. For the next-token prediction, models solely focus on a token's preceding context, resulting in a restricted comprehension of the input. In contrast, we illustrate that the GLM, trained using the autoregressive blank infilling objective where tokens to be predicted have access to the entire context, exhibits better resilience against the reversal curse. We propose a novel training method, BIdirectional Casual language modeling Optimization (BICO), designed to mitigate the reversal curse when fine-tuning pretrained causal language models on new data. BICO modifies the causal attention mechanism to function bidirectionally and employs a mask denoising optimization. In the task designed to assess the reversal curse, our approach improves Llama's accuracy from the original 0% to around 70%. We hope that more attention can be focused on exploring and addressing these inherent weaknesses of the current LLMs, in order to achieve a higher level of intelligence.

Linear Transformers and State Space Models have emerged as efficient alternatives to softmax Transformers for causal sequence modeling, enabling parallel training via matrix multiplication and efficient RNN-style inference. However, despite their success in causal tasks, no unified framework exists for applying Linear Transformers to bidirectional sequence modeling. We introduce LION, the first framework to systematically extend Linear Transformers to the bidirectional setting. LION generalizes three core representations commonly used in the causal case - full Linear Attention , bidirectional RNN, and chunkwise parallel form - to the bidirectional setting. These forms are theoretically equivalent and enable models to exploit the strengths of each during training and inference. We prove that a broad class of Linear Transformers can be extended using LION and validate our framework via three core examples based on the choice of decay type: LION-LIT, the bidirectional extension of arXiv:2006.16236; LION-D, based on arXiv:2307.08621; and LION-S, a variant using selective decay arXiv:2103.02143, arXiv:2312.0075. Across standard bidirectional tasks, LION enables models to match or exceed the performance of softmax Transformers, while offering significantly faster training and more efficient inference than existing State Space Models.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

While originally designed for unidirectional generative modeling, decoder-only large language models (LLMs) are increasingly being adapted for bidirectional modeling. However, unidirectional and bidirectional models are typically trained separately with distinct objectives (generation and representation learning). This separation overlooks the opportunity for developing a more versatile language model and for these objectives to complement each other. In this work, we propose MAGNET, a method for adapting decoder-only LLMs to generate robust representations and infill missing text spans. MAGNET employs three self-supervised training objectives and introduces an attention mechanism that combines bidirectional and causal attention, enabling unified training across all objectives. Our results demonstrate that LLMs adapted with MAGNET (1) surpass strong text encoders on token-level and sentence-level representation learning tasks, (2) generate contextually appropriate text infills by leveraging past and future contexts, (3) perform open-ended text generation without excessive repetition of words or phrases, and (4) preserve the knowledge and reasoning capability gained by the LLM during pretraining.

As LLMs have become capable of processing more complex types of inputs, researchers have recently studied how to efficiently and affordably process possibly arbitrarily long sequences. One effective approach is to use a FIFO memory to store keys and values of an attention sublayer from past chunks to allow subsequent queries to attend. However, this approach requires a large memory and/or takes into the consideration the specific LM architecture. Moreover, due to the causal nature between the key-values in prior context and the queries at present, this approach cannot be extended to bidirectional attention such as in an encoder-decoder or PrefixLM decoder-only architecture. In this paper, we propose to use eviction policies, such as LRA and LFA, to reduce the memory size and adapt to various architectures, and we also propose the Attendre layer, a wait-to-attend mechanism by retrieving the key-value memory (K/V memory) with evicted queries in the query memory (Q memory). As a first step, we evaluate this method in the context length extension setup using the TriviaQA reading comprehension task, and show the effectiveness of the approach.

Autoregressive language models are trained exclusively left-to-right. We explore the complementary factorization, training right-to-left at scale, and ask what reasoning patterns emerge when a model conditions on future context to predict the past. We train LEDOM, an open-source purely reverse autoregressive language model (2B/7B parameters, 435B tokens), and find it develops capabilities distinct from forward models, including abductive inference, question synthesis, and natural resolution of the reversal curse. We then explore one application of the reverse model: combining forward likelihood P(y mid x) with reverse posterior P(x mid y) through noisy channel duality. We propose Reverse Reward, which reranks forward outputs using reverse posterior estimates, and prove that bidirectional scoring penalizes hallucinated reasoning chains whose backward reconstruction degrades. Reverse Reward yields gains of up to 6.6\% on AIME 2024 and 15\% on AMC 2023 across multiple strong baselines. We release all models, code, and data here.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

BatGPT is a large-scale language model designed and trained jointly by Wuhan University and Shanghai Jiao Tong University. It is capable of generating highly natural and fluent text in response to various types of input, including text prompts, images, and audio. In the modeling level, we employ a bidirectional autoregressive architecture that allows the model to efficiently capture the complex dependencies of natural language, making it highly effective in tasks such as language generation, dialog systems, and question answering. Moreover, the bidirectional autoregressive modeling not only operates from left to right but also from right to left, effectively reducing fixed memory effects and alleviating model hallucinations. In the training aspect, we propose a novel parameter expansion method for leveraging the pre-training of smaller models and employ reinforcement learning from both AI and human feedback, aimed at improving the model's alignment performance. Overall, these approaches significantly improve the effectiveness of BatGPT, and the model can be utilized for a wide range of natural language applications.

Gross, Mansour, and Tucker introduced the partial-duality polynomial of a ribbon graph [Distributions, European J. Combin. 86, 1--20, 2020], the generating function enumerating partial duals by the Euler genus. Chmutov and Vignes-Tourneret wondered if this polynomial and its conjectured properties would hold for general delta-matroids, which are combinatorial abstractions of ribbon graphs. Yan and Jin contributed to this inquiry by identifying a subset of delta-matroids-specifically, even normal binary ones-whose twist polynomials are characterized by a singular term. Building upon this foundation, the current paper expands the scope of the investigation to encompass even non-binary delta-matroids, revealing that none of them have width-changing twists.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Mechanism-targeted synthetic data is increasingly proposed as a way to steer pretraining toward desirable capabilities, but it remains unclear how such interventions should be evaluated. We study this question for in-context learning (ICL) under matched compute (iso-FLOPs) using Bi-Induct, a lightweight data rewrite that interleaves short directional copy snippets into a natural pretraining stream: forward-copy (induction), backward-copy (anti-induction, as a directional control), or a balanced mix. Across 0.13B-1B decoder-only models, we evaluate (i) few-shot performance on standard LM benchmarks and function-style ICL probes, (ii) head-level copy telemetry, and (iii) held-out perplexity as a guardrail. Bi-Induct reliably increases induction-head activity, but this does not translate into consistent improvements in few-shot generalization: on standard LM benchmarks, Bi-Induct is largely performance-neutral relative to natural-only training, while on function-style probes the 1B natural-only model performs best. Despite explicit backward-copy cues, anti-induction scores remain near zero across scales, revealing a strong forward/backward asymmetry. Targeted ablations show a sharper distinction: removing the top 2% induction heads per layer harms ICL more than matched random ablations, with the largest relative drop occurring in the natural-only models. This indicates that natural-only training produces more centralized, load-bearing induction circuitry, whereas Bi-Induct tends to create more distributed and redundant induction activity. Our main conclusion is that eliciting a mechanism is not the same as making it load-bearing. For data-centric foundation model design, this suggests that synthetic data interventions should be evaluated not only by signature amplification, but by whether they create causally necessary computation while preserving natural-data modeling quality.

Using token representation from bidirectional language models (LMs) such as BERT is still a widely used approach for token-classification tasks. Even though there exist much larger unidirectional LMs such as Llama-2, they are rarely used to replace the token representation of bidirectional LMs. In this work, we hypothesize that their lack of bidirectionality is keeping them behind. To that end, we propose to newly train a small backward LM and concatenate its representations to those of existing LM for downstream tasks. Through experiments in named entity recognition, we demonstrate that introducing backward model improves the benchmark performance more than 10 points. Furthermore, we show that the proposed method is especially effective for rare domains and in few-shot learning settings.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

We introduce the Diffusion Chain of Lateral Thought (DCoLT), a reasoning framework for diffusion language models. DCoLT treats each intermediate step in the reverse diffusion process as a latent "thinking" action and optimizes the entire reasoning trajectory to maximize the reward on the correctness of the final answer with outcome-based Reinforcement Learning (RL). Unlike traditional Chain-of-Thought (CoT) methods that follow a causal, linear thinking process, DCoLT allows bidirectional, non-linear reasoning with no strict rule on grammatical correctness amid its intermediate steps of thought. We implement DCoLT on two representative Diffusion Language Models (DLMs). First, we choose SEDD as a representative continuous-time discrete diffusion model, where its concrete score derives a probabilistic policy to maximize the RL reward over the entire sequence of intermediate diffusion steps. We further consider the discrete-time masked diffusion language model -- LLaDA, and find that the order to predict and unmask tokens plays an essential role to optimize its RL action resulting from the ranking-based Unmasking Policy Module (UPM) defined by the Plackett-Luce model. Experiments on both math and code generation tasks show that using only public data and 16 H800 GPUs, DCoLT-reinforced DLMs outperform other DLMs trained by SFT or RL or even both. Notably, DCoLT-reinforced LLaDA boosts its reasoning accuracy by +9.8%, +5.7%, +11.4%, +19.5% on GSM8K, MATH, MBPP, and HumanEval.

"Forward-only" algorithms, which train neural networks while avoiding a backward pass, have recently gained attention as a way of solving the biologically unrealistic aspects of backpropagation. Here, we first address compelling challenges related to the "forward-only" rules, which include reducing the performance gap with backpropagation and providing an analytical understanding of their dynamics. To this end, we show that the forward-only algorithm with top-down feedback is well-approximated by an "adaptive-feedback-alignment" algorithm, and we analytically track its performance during learning in a prototype high-dimensional setting. Then, we compare different versions of forward-only algorithms, focusing on the Forward-Forward and PEPITA frameworks, and we show that they share the same learning principles. Overall, our work unveils the connections between three key neuro-inspired learning rules, providing a link between "forward-only" algorithms, i.e., Forward-Forward and PEPITA, and an approximation of backpropagation, i.e., Feedback Alignment.

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter sigma > 0. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be O(sigma)-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as O(sigma)-approximation of the original BO, we propose first-order algorithms that find an epsilon-stationary solution by optimizing the penalty formulation with sigma = O(epsilon). When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an epsilon-stationary point of the penalty function, using in total O(epsilon^{-3}) and O(epsilon^{-7}) accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with O(1) samples per iteration, and achieves the improved oracle-complexity of O(epsilon^{-3}) and O(epsilon^{-5}), respectively.

Bilevel optimization enjoys a wide range of applications in hyper-parameter optimization, meta-learning and reinforcement learning. However, bilevel optimization problems are difficult to solve. Recent progress on scalable bilevel algorithms mainly focuses on bilevel optimization problems where the lower-level objective is either strongly convex or unconstrained. In this work, we tackle the bilevel problem through the lens of the penalty method. We show that under certain conditions, the penalty reformulation recovers the solutions of the original bilevel problem. Further, we propose the penalty-based bilevel gradient descent (PBGD) algorithm and establish its finite-time convergence for the constrained bilevel problem without lower-level strong convexity. Experiments showcase the efficiency of the proposed PBGD algorithm.

Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop-repeatedly sampling and rewarding dominant modes-that further erodes exploration. We introduce Exploration-Enhanced Policy Optimization (EEPO), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This sample-then-forget mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base.

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.

We introduce a new function-preserving transformation for efficient neural architecture search. This network transformation allows reusing previously trained networks and existing successful architectures that improves sample efficiency. We aim to address the limitation of current network transformation operations that can only perform layer-level architecture modifications, such as adding (pruning) filters or inserting (removing) a layer, which fails to change the topology of connection paths. Our proposed path-level transformation operations enable the meta-controller to modify the path topology of the given network while keeping the merits of reusing weights, and thus allow efficiently designing effective structures with complex path topologies like Inception models. We further propose a bidirectional tree-structured reinforcement learning meta-controller to explore a simple yet highly expressive tree-structured architecture space that can be viewed as a generalization of multi-branch architectures. We experimented on the image classification datasets with limited computational resources (about 200 GPU-hours), where we observed improved parameter efficiency and better test results (97.70% test accuracy on CIFAR-10 with 14.3M parameters and 74.6% top-1 accuracy on ImageNet in the mobile setting), demonstrating the effectiveness and transferability of our designed architectures.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

Steering Large Language Models (LLMs) through activation interventions has emerged as a lightweight alternative to fine-tuning for alignment and personalization. Recent work on Bi-directional Preference Optimization (BiPO) shows that dense steering vectors can be learned directly from preference data in a Direct Preference Optimization (DPO) fashion, enabling control over truthfulness, hallucinations, and safety behaviors. However, dense steering vectors often entangle multiple latent factors due to neuron multi-semanticity, limiting their effectiveness and stability in fine-grained settings such as cultural alignment, where closely related values and behaviors (e.g., among Middle Eastern cultures) must be distinguished. In this paper, we propose Yet another Policy Optimization (YaPO), a reference-free method that learns sparse steering vectors in the latent space of a Sparse Autoencoder (SAE). By optimizing sparse codes, YaPO produces disentangled, interpretable, and efficient steering directions. Empirically, we show that YaPO converges faster, achieves stronger performance, and exhibits improved training stability compared to dense steering baselines. Beyond cultural alignment, YaPO generalizes to a range of alignment-related behaviors, including hallucination, wealth-seeking, jailbreak, and power-seeking. Importantly, YaPO preserves general knowledge, with no measurable degradation on MMLU. Overall, our results show that YaPO provides a general recipe for efficient, stable, and fine-grained alignment of LLMs, with broad applications to controllability and domain adaptation. The associated code and data are publicly availablehttps://github.com/MBZUAI-Paris/YaPO.

Transforming causal generative language models into bidirectional encoders offers a powerful alternative to BERT-style architectures. However, current approaches remain limited: they lack consensus on optimal training objectives, suffer from catastrophic forgetting at scale, and fail to flexibly integrate the vast ecosystem of specialized generative models. In this work, through systematic ablations on the Gemma3 and Qwen3 families, we identify the key factors driving successful adaptation, highlighting the critical role of an often-omitted prior masking phase. To scale this process without original pre-training data, we introduce a dual strategy combining linear weight merging with a lightweight multi-domain data mixture that mitigates catastrophic forgetting. Finally, we augment our encoders by merging them with specialized causal models, seamlessly transferring modality- and domain-specific capabilities. This open-source recipe, designed for any causal decoder LLM, yields BidirLM, a family of five encoders that outperform alternatives on text, vision, and audio representation benchmarks.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2.1 and 26 under various settings.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of distributed alignment search (DAS), the standard for causal variable localization, to propose a new steering method: Concept DAS (CDAS). While we adopt the core mechanism of DAS, distributed interchange intervention (DII), we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering. Our code is available at https://github.com/colored-dye/concept_das.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These challenges involve ensuring computational efficiency and providing theoretical guarantees. While recent advances in scalable BLO algorithms have primarily relied on lower-level convexity simplification, our work specifically tackles large-scale BLO problems involving nonconvexity in both the upper and lower levels. We simultaneously address computational and theoretical challenges by introducing an innovative single-loop gradient-based algorithm, utilizing the Moreau envelope-based reformulation, and providing non-asymptotic convergence analysis for general nonconvex BLO problems. Notably, our algorithm relies solely on first-order gradient information, enhancing its practicality and efficiency, especially for large-scale BLO learning tasks. We validate our approach's effectiveness through experiments on various synthetic problems, two typical hyper-parameter learning tasks, and a real-world neural architecture search application, collectively demonstrating its superior performance.

Large language model (LLM)-based embedding models, benefiting from large scale pre-training and post-training, have begun to surpass BERT and T5-based models on general-purpose text embedding tasks such as document retrieval. However, a fundamental limitation of LLM embeddings lies in the unidirectional attention used during autoregressive pre-training, which misaligns with the bidirectional nature of text embedding tasks. To this end, We propose adopting diffusion language models for text embeddings, motivated by their inherent bidirectional architecture and recent success in matching or surpassing LLMs especially on reasoning tasks. We present the first systematic study of the diffusion language embedding model, which outperforms the LLM-based embedding model by 20% on long-document retrieval, 8% on reasoning-intensive retrieval, 2% on instruction-following retrieval, and achieve competitive performance on traditional text embedding benchmarks. Our analysis verifies that bidirectional attention is crucial for encoding global context in long and complex text.

We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are related to competitive bidding by persons for objects and the attendant market equilibrium, which underlie auction processes. However, the starting point of our algorithms is different, namely weighted and unweighted path construction in directed graphs, rather than assignment of persons to objects. The new algorithms have several potential advantages over existing methods: they are empirically faster in some important contexts, such as max-flow, they are well-suited for on-line replanning, and they can be adapted to distributed asynchronous operation. Moreover, they allow arbitrary initial prices, without complementary slackness restrictions, and thus are better-suited to take advantage of reinforcement learning methods that use off-line training with data, as well as on-line training during real-time operation. The new algorithms may also find use in reinforcement learning contexts involving approximation, such as multistep lookahead and tree search schemes, and/or rollout algorithms.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

The left-corner transformation (Rosenkrantz and Lewis, 1970) is used to remove left recursion from context-free grammars, which is an important step towards making the grammar parsable top-down with simple techniques. This paper generalizes prior left-corner transformations to support semiring-weighted production rules and to provide finer-grained control over which left corners may be moved. Our generalized left-corner transformation (GLCT) arose from unifying the left-corner transformation and speculation transformation (Eisner and Blatz, 2007), originally for logic programming. Our new transformation and speculation define equivalent weighted languages. Yet, their derivation trees are structurally different in an important way: GLCT replaces left recursion with right recursion, and speculation does not. We also provide several technical results regarding the formal relationships between the outputs of GLCT, speculation, and the original grammar. Lastly, we empirically investigate the efficiency of GLCT for left-recursion elimination from grammars of nine languages.

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, we first design a counter-example to illustrate the invalidation of such LLS condition. Then by formulating BLPs from the view point of optimistic bi-level and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for generic bi-level optimization. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules. Additionally, as an interesting byproduct, we also improve these conventional first-order bi-level schemes (under the LLS simplification). Particularly, we establish their convergences with weaker assumptions. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

Researchers have been studying approaches to steer the behavior of Large Language Models (LLMs) and build personalized LLMs tailored for various applications. While fine-tuning seems to be a direct solution, it requires substantial computational resources and may significantly affect the utility of the original LLM. Recent endeavors have introduced more lightweight strategies, focusing on extracting "steering vectors" to guide the model's output toward desired behaviors by adjusting activations within specific layers of the LLM's transformer architecture. However, such steering vectors are directly extracted from the activations of human preference data and thus often lead to suboptimal results and occasional failures, especially in alignment-related scenarios. This work proposes an innovative approach that could produce more effective steering vectors through bi-directional preference optimization. Our method is designed to allow steering vectors to directly influence the generation probability of contrastive human preference data pairs, thereby offering a more precise representation of the target behavior. By carefully adjusting the direction and magnitude of the steering vector, we enabled personalized control over the desired behavior across a spectrum of intensities. Extensive experimentation across various open-ended generation tasks, particularly focusing on steering AI personas, has validated the efficacy of our approach. Moreover, we comprehensively investigate critical alignment-concerning scenarios, such as managing truthfulness, mitigating hallucination, and addressing jailbreaking attacks. Remarkably, our method can still demonstrate outstanding steering effectiveness across these scenarios. Furthermore, we showcase the transferability of our steering vectors across different models/LoRAs and highlight the synergistic benefits of applying multiple vectors simultaneously.

Large Language Models (LLMs) require high quality preference datasets to align with human preferences. However, conventional methods for constructing such datasets face significant challenges: reliance on pre-collected instructions often leads to distribution mismatches with target models, while the need for sampling multiple stochastic responses introduces substantial computational overhead. In this work, we explore a paradigm shift by leveraging inherent regulation of LLMs' representation space for efficient and tailored preference dataset construction, named Icon^{2}. Specifically, it first extracts layer-wise direction vectors to encode sophisticated human preferences and then uses these vectors to filter self-synthesized instructions based on their inherent consistency. During decoding, bidirectional inherent control is applied to steer token representations, enabling the precise generation of response pairs with clear alignment distinctions. Experimental results demonstrate significant improvements in both alignment and efficiency. Llama3-8B and Qwen2-7B achieve an average win rate improvement of 13.89% on AlpacaEval 2.0 and 13.45% on Arena-Hard, while reducing computational costs by up to 48.1%.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

We introduce SteeringControl, a benchmark for evaluating representation steering methods across core alignment objectives--bias, harmful generation, and hallucination--and their effects on secondary behaviors such as sycophancy and commonsense morality. While prior alignment work often highlights truthfulness or reasoning ability to demonstrate the side effects of representation steering, we find there are many unexplored tradeoffs not yet understood in a systematic way. We collect a dataset of safety-relevant primary and secondary behaviors to evaluate steering effectiveness and behavioral entanglement centered around five popular steering methods. To enable this, we craft a modular steering framework based on unique components that serve as the building blocks of many existing methods. Our results on Qwen-2.5-7B and Llama-3.1-8B find that strong steering performance is dependent on the specific combination of steering method, model, and targeted behavior, and that severe concept entanglement can result from poor combinations of these three as well. We release our code here: https://github.com/wang-research-lab/SteeringControl.git.

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower- Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

Code large language models (LLMs) have become indispensable tools for building efficient and automated coding pipelines. Existing models are typically post-trained using reinforcement learning (RL) from general-purpose LLMs using "human instruction-final answer" pairs, where the instructions are usually from manual annotations. However, collecting high-quality coding instructions is both labor-intensive and difficult to scale. On the other hand, code snippets are abundantly available from various sources. This imbalance presents a major bottleneck in instruction-based post-training. We propose CodeBoost, a post-training framework that enhances code LLMs purely from code snippets, without relying on human-annotated instructions. CodeBoost introduces the following key components: (1) maximum-clique curation, which selects a representative and diverse training corpus from code; (2) bi-directional prediction, which enables the model to learn from both forward and backward prediction objectives; (3) error-aware prediction, which incorporates learning signals from both correct and incorrect outputs; (4) heterogeneous augmentation, which diversifies the training distribution to enrich code semantics; and (5) heterogeneous rewarding, which guides model learning through multiple reward types including format correctness and execution feedback from both successes and failures. Extensive experiments across several code LLMs and benchmarks verify that CodeBoost consistently improves performance, demonstrating its effectiveness as a scalable and effective training pipeline.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

Among adversarial attacks against sequential recommender systems, model extraction attacks represent a method to attack sequential recommendation models without prior knowledge. Existing research has primarily concentrated on the adversary's execution of black-box attacks through data-free model extraction. However, a significant gap remains in the literature concerning the development of surrogate models by adversaries with access to few-shot raw data (10\% even less). That is, the challenge of how to construct a surrogate model with high functional similarity within the context of few-shot data scenarios remains an issue that requires resolution.This study addresses this gap by introducing a novel few-shot model extraction framework against sequential recommenders, which is designed to construct a superior surrogate model with the utilization of few-shot data. The proposed few-shot model extraction framework is comprised of two components: an autoregressive augmentation generation strategy and a bidirectional repair loss-facilitated model distillation procedure. Specifically, to generate synthetic data that closely approximate the distribution of raw data, autoregressive augmentation generation strategy integrates a probabilistic interaction sampler to extract inherent dependencies and a synthesis determinant signal module to characterize user behavioral patterns. Subsequently, bidirectional repair loss, which target the discrepancies between the recommendation lists, is designed as auxiliary loss to rectify erroneous predictions from surrogate models, transferring knowledge from the victim model to the surrogate model effectively. Experiments on three datasets show that the proposed few-shot model extraction framework yields superior surrogate models.

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH assumes that concepts can be orthogonalized for lossless control, this idealized mapping fails in real representations and cannot account for the observed unpredictability of steering. By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH). In CRH, a central axis captures the main difference between concept absence and presence and drives concept generation. A surrounding normal plane controls steering sensitivity by determining how easily the axis can activate the target concept. Within this plane, only specific sensitive sectors strongly facilitate concept activation, while other sectors can suppress or delay it. While the surrounding normal plane can be reliably identified from difference vectors, the sensitive sector cannot, introducing intrinsic uncertainty at the sector level. This uncertainty provides a principled explanation for why steering outcomes often fluctuate even when using well-aligned directions. Our experiments verify the existence of the cylindrical structure and demonstrate that CRH provides a valid and practical way to interpret model steering behavior in real settings: https://github.com/mbzuai-nlp/CRH.

We present a novel unified bilevel optimization-based framework, PARL, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named A-PARL to solve PARL problem, establishing sample complexity bounds of order O(1/T). Our empirical results substantiate that the proposed PARL can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Backpropagation (BP), a foundational algorithm for training artificial neural networks, predominates in contemporary deep learning. Although highly successful, it is often considered biologically implausible. A significant limitation arises from the need for precise symmetry between connections in the backward and forward pathways to backpropagate gradient signals accurately, which is not observed in biological brains. Researchers have proposed several algorithms to alleviate this symmetry constraint, such as feedback alignment and direct feedback alignment. However, their divergence from backpropagation dynamics presents challenges, particularly in deeper networks and convolutional layers. Here we introduce the Product Feedback Alignment (PFA) algorithm. Our findings demonstrate that PFA closely approximates BP and achieves comparable performance in deep convolutional networks while avoiding explicit weight symmetry. Our results offer a novel solution to the longstanding weight symmetry problem, leading to more biologically plausible learning in deep convolutional networks compared to earlier methods.

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lorentz transformations in hyperbolic geometry, we propose Hyperbolic Rotary Positional Encoding (HoPE), which leverages hyperbolic functions to implement Lorentz rotations on token representations. Theoretical analysis demonstrates that RoPE is a special case of our generalized formulation. HoPE fundamentally resolves RoPE's slation issues by enforcing monotonic decay of attention weights with increasing token distances. Extensive experimental results, including perplexity evaluations under several extended sequence benchmarks, show that HoPE consistently exceeds existing positional encoding methods. These findings underscore HoPE's enhanced capacity for representing and generalizing long-range dependencies. Data and code will be available.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

Generative adversarial networks (GANs) have shown promise for various problems including anomaly detection. When anomaly detection is performed using GAN models that learn only the features of normal data samples, data that are not similar to normal data are detected as abnormal samples. The present approach is developed by employing a dual-encoder in a bidirectional GAN architecture that is trained simultaneously with a generator and a discriminator network. Through the learning mechanism, the proposed method aims to reduce the problem of bad cycle consistency, in which a bidirectional GAN might not be able to reproduce samples with a large difference between normal and abnormal samples. We assume that bad cycle consistency occurs when the method does not preserve enough information of the sample data. We show that our proposed method performs well in capturing the distribution of normal samples, thereby improving anomaly detection on GAN-based models. Experiments are reported in which our method is applied to publicly available datasets, including application to a brain magnetic resonance imaging anomaly detection system.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

The use of deep pre-trained bidirectional transformers has led to remarkable progress in a number of applications (Devlin et al., 2018). For tasks that make pairwise comparisons between sequences, matching a given input with a corresponding label, two approaches are common: Cross-encoders performing full self-attention over the pair and Bi-encoders encoding the pair separately. The former often performs better, but is too slow for practical use. In this work, we develop a new transformer architecture, the Poly-encoder, that learns global rather than token level self-attention features. We perform a detailed comparison of all three approaches, including what pre-training and fine-tuning strategies work best. We show our models achieve state-of-the-art results on three existing tasks; that Poly-encoders are faster than Cross-encoders and more accurate than Bi-encoders; and that the best results are obtained by pre-training on large datasets similar to the downstream tasks.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental question arises: can we develop new paradigms beyond orthogonalization, pushing the efficiency frontier further? We present Adaptively Rotated Optimization (ARO, a new matrix optimization framework that treats gradient rotation as a first class design principle. ARO accelerates LLM training by performing normed steepest descent in a rotated coordinate system, where the rotation is determined by a novel norm-informed policy. This perspective yields update rules that go beyond existing orthogonalization and whitening optimizers, improving sample efficiency in practice. To make comparisons reliable, we propose a rigorously controlled benchmarking protocol that reduces confounding and bias. Under this protocol, ARO consistently outperforms AdamW (by 1.3 sim1.35times) and orthogonalization methods (by 1.1sim1.15times) in LLM pretraining at up to 8B activated parameters, and up to 8times overtrain budget, without evidence of diminishing returns. Finally, we discuss how ARO can be reformulated as a symmetry-aware optimizer grounded in rotational symmetries of residual streams, motivating advanced designs that enable computationally efficient exploitation of cross-layer/cross module couplings.

With the advance of diffusion models, today's video generation has achieved impressive quality. But generating temporal consistent long videos is still challenging. A majority of video diffusion models (VDMs) generate long videos in an autoregressive manner, i.e., generating subsequent clips conditioned on last frames of previous clip. However, existing approaches all involve bidirectional computations, which restricts the receptive context of each autoregression step, and results in the model lacking long-term dependencies. Inspired from the huge success of large language models (LLMs) and following GPT (generative pre-trained transformer), we bring causal (i.e., unidirectional) generation into VDMs, and use past frames as prompt to generate future frames. For Causal Generation, we introduce causal temporal attention into VDM, which forces each generated frame to depend on its previous frames. For Frame as Prompt, we inject the conditional frames by concatenating them with noisy frames (frames to be generated) along the temporal axis. Consequently, we present Video Diffusion GPT (ViD-GPT). Based on the two key designs, in each autoregression step, it is able to acquire long-term context from prompting frames concatenated by all previously generated frames. Additionally, we bring the kv-cache mechanism to VDMs, which eliminates the redundant computation from overlapped frames, significantly boosting the inference speed. Extensive experiments demonstrate that our ViD-GPT achieves state-of-the-art performance both quantitatively and qualitatively on long video generation. Code will be available at https://github.com/Dawn-LX/Causal-VideoGen.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

Current large language models have dangerous capabilities, which are likely to become more problematic in the future. Activation steering techniques can be used to reduce risks from these capabilities. In this paper, we investigate the efficacy of activation steering for broad skills and multiple behaviours. First, by comparing the effects of reducing performance on general coding ability and Python-specific ability, we find that steering broader skills is competitive to steering narrower skills. Second, we steer models to become more or less myopic and wealth-seeking, among other behaviours. In our experiments, combining steering vectors for multiple different behaviours into one steering vector is largely unsuccessful. On the other hand, injecting individual steering vectors at different places in a model simultaneously is promising.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain neural networks such as recurrent neural networks (RNNs) and long-short-term memory networks (LSTMs) exhibit potential unbounded smoothness, rendering conventional bilevel optimization algorithms unsuitable. In this paper, we design a new bilevel optimization algorithm, namely BO-REP, to address this challenge. This algorithm updates the upper-level variable using normalized momentum and incorporates two novel techniques for updating the lower-level variable: initialization refinement and periodic updates. Specifically, once the upper-level variable is initialized, a subroutine is invoked to obtain a refined estimate of the corresponding optimal lower-level variable, and the lower-level variable is updated only after every specific period instead of each iteration. When the upper-level problem is nonconvex and unbounded smooth, and the lower-level problem is strongly convex, we prove that our algorithm requires mathcal{O}(1/epsilon^4) iterations to find an epsilon-stationary point in the stochastic setting, where each iteration involves calling a stochastic gradient or Hessian-vector product oracle. Notably, this result matches the state-of-the-art complexity results under the bounded smoothness setting and without mean-squared smoothness of the stochastic gradient, up to logarithmic factors. Our proof relies on novel technical lemmas for the periodically updated lower-level variable, which are of independent interest. Our experiments on hyper-representation learning, hyperparameter optimization, and data hyper-cleaning for text classification tasks demonstrate the effectiveness of our proposed algorithm.

Modern deployments require LLMs to enforce safety policies at scale, yet many controls rely on inference-time interventions that add recurring compute cost and serving complexity. Activation steering is widely used, but it requires runtime hooks and scales cost with the number of generations; conditional variants improve selectivity by gating when steering is applied but still retain an inference-time control path. We ask whether selective refusal can be moved entirely offline: can a mechanistic understanding of category-specific refusal be distilled into a circuit-restricted weight update that deploys as a standard checkpoint? We propose C-Δθ: Circuit Restricted Weight Arithmetic, which (i) localizes refusal-causal computation as a sparse circuit using EAP-IG and (ii) computes a constrained weight update ΔθC supported only on that circuit (typically <5% of parameters). Applying ΔθC yields a drop-in edited checkpoint with no inference-time hooks, shifting cost from per-request intervention to a one-time offline update. We evaluate category-targeted selectivity and capability retention on refusal and utility benchmarks.

This paper presents methods for dramatically improving the performance of sampling-based kinodynamic planners. The key component is the first-known complete, exact steering method that produces a time-optimal trajectory between any states for a vector of synchronized double integrators. This method is applied in three ways: 1) to generate RRT edges that quickly solve the two-point boundary-value problems, 2) to produce a (quasi)metric for more accurate Voronoi bias in RRTs, and 3) to iteratively time-optimize a given collision-free trajectory. Experiments are performed for state spaces with up to 2000 dimensions, resulting in improved computed trajectories and orders of magnitude computation time improvements over using ordinary metrics and constant controls.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Despite significant progress in alignment, large language models (LLMs) remain vulnerable to adversarial attacks that elicit harmful behaviors. Activation steering techniques offer a promising inference-time intervention approach, but existing methods suffer from critical limitations: activation addition requires careful coefficient tuning and is sensitive to layer-specific norm variations, while directional ablation provides only binary control. Recent work on Angular Steering introduces continuous control via rotation in a 2D subspace, but its practical implementation violates norm preservation, causing distribution shift and generation collapse, particularly in models below 7B parameters. We propose Selective Steering, which addresses these limitations through two key innovations: (1) a mathematically rigorous norm-preserving rotation formulation that maintains activation distribution integrity, and (2) discriminative layer selection that applies steering only where feature representations exhibit opposite-signed class alignment. Experiments across nine models demonstrate that Selective Steering achieves 5.5x higher attack success rates than prior methods while maintaining zero perplexity violations and approximately 100\% capability retention on standard benchmarks. Our approach provides a principled, efficient framework for controllable and stable LLM behavior modification. Code: https://github.com/knoveleng/steering

Recent advances in real-world applications of reinforcement learning (RL) have relied on the ability to accurately simulate systems at scale. However, domains such as fluid dynamical systems exhibit complex dynamic phenomena that are hard to simulate at high integration rates, limiting the direct application of modern deep RL algorithms to often expensive or safety critical hardware. In this work, we introduce "Box o Flows", a novel benchtop experimental control system for systematically evaluating RL algorithms in dynamic real-world scenarios. We describe the key components of the Box o Flows, and through a series of experiments demonstrate how state-of-the-art model-free RL algorithms can synthesize a variety of complex behaviors via simple reward specifications. Furthermore, we explore the role of offline RL in data-efficient hypothesis testing by reusing past experiences. We believe that the insights gained from this preliminary study and the availability of systems like the Box o Flows support the way forward for developing systematic RL algorithms that can be generally applied to complex, dynamical systems. Supplementary material and videos of experiments are available at https://sites.google.com/view/box-o-flows/home.

We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed à la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamiołkowski correspondence and develop a Cholesky algorithm for bi-partite systems. This enables a canonical construction of adjoint actions which recover the behaviour of the original CP-maps. Our results hold under separability assumptions and the requirement that the maps are completely bounded and preserve the subideal of finite rank operators.

Large language models (LLMs) commonly employ autoregressive generation during inference, leading to high memory bandwidth demand and consequently extended latency. To mitigate this inefficiency, we present Bi-directional Tuning for lossless Acceleration (BiTA), an innovative method expediting LLMs via streamlined semi-autoregressive generation and draft verification. Inspired by the concept of prompt tuning, we enhance LLMs with a parameter-efficient design called bi-directional tuning for the capability in semi-autoregressive generation. Employing efficient tree-based decoding, the models perform draft candidate generation and verification in parallel, ensuring outputs identical to their autoregressive counterparts under greedy sampling. BiTA serves as a lightweight plug-in module, seamlessly boosting the inference efficiency of existing LLMs without requiring additional assistance models or incurring significant extra memory costs. Applying the proposed BiTA, LLaMA-2-70B-Chat achieves a 2.7times speedup on the MT-Bench benchmark. Extensive experiments confirm our method surpasses state-of-the-art acceleration techniques.

We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague semantics based on a lambda calculus where the primitives act on string diagrams rather than logical formulae. As a special case, we show how to translate from the Lambek calculus into Peirce's system beta for first-order logic. This allows us to give a purely diagrammatic treatment of higher-order and non-linear processes in natural language semantics: adverbs, prepositions, negation and quantifiers. The theoretical definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.