arXiv subjects

Somayeh Sojoudi

Publications and source records attributed to Somayeh Sojoudi.

At least 19 recordsLinked to original sources

arXiv2026

SWE-Proof: Can Language Models Resolve Real-World Issues with Machine-Checked Proofs?

Ensuring the correctness of LLM-generated code is a core challenge for modern software engineering. Benchmarks for agentic code generation check correctness with held-out test suites, which are inherently incomplete and increasingly susceptible to memorization. Formal verification avoids both problems, but existing work covers only standalone tasks whose specifications are given as input, not real issues, which touch large repositories and state intent in vague natural language. We present Benchproofer, a pipeline that turns a coding task with a known correct patch into a formally verified one: it writes a specification for the new code, summarizes the existing functions that code calls with axioms, and admits an instance only after mechanical and adversarial gates agree. Applying it to SWE-bench Verified yields SWE-Proof, 500 real issues whose correctness is formally verified rather than tested, and it extends to SWE-bench Pro. Across two frontier models, verification catches what tests miss: a quarter to a half of test-passing patches admit counterexamples, which a structured natural-language specification does not fix, while a correct formal one lifts resolution from 85% to 95% for Opus 4.8. Writing that specification is the hard part: models that must write their own gain nothing over an unaided baseline, and only 62% of their specifications pass our audit. The usual failure is faithfulness, a specification that constrains part of the required behavior and leaves the rest free. Specification quality still tracks the outcome, failing on 89% of unresolved instances against 47% of resolved ones, making faithful specification synthesis a concrete open problem.

cs.LG↗

arXiv2026

Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge

Autoregressive large language models (LLMs) have achieved remarkable success in many complex tasks, yet they can still fail in very simple logical reasoning such as the "reversal curse" -- when trained on forward knowledge data of the form "$A \rightarrow B$" (e.g., Alice's husband is Bob), the model is unable to deduce the reversal knowledge "$B \leftarrow A$" (e.g., Bob's wife is Alice) during test. Extensive prior research suggests that this failure is an inherent, fundamental limit of autoregressive causal LLMs, indicating that these models tend to memorize factual-level knowledge rather than capture higher-level rules. In this paper, we challenge this view by showing that this seemingly fundamental limit can be mitigated by slightly tweaking the training data with a simple regularization data recipe called the Identity Bridge of the form "$A \to A$" (e.g., The name of Alice is Alice). Theoretically, we prove that under this recipe, even a one-layer transformer can break the reversal curse by analyzing the implicit bias of gradient descent. Empirically, we show that a 1B pretrained language model finetuned with the proposed data recipe achieves a 50% success rate on reversal tasks, in stark contrast to a near-zero success rate when trained solely on forward-knowledge data. Our work provides a novel theoretical foundation for the reversal curse and offers a principled, low-cost path to encouraging LLMs to learn higher-level rules from data.

cs.AI↗

arXiv2026

Transformers Provably Learn to Internalize Chain-of-Thought

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning steps at inference is computationally expensive. Implicit Chain-of-Thought (ICoT) has emerged as a promising empirical remedy that trains models to internalize intermediate steps within their hidden states, but its theoretical foundations remain poorly understood. We give the first theoretical analysis of ICoT, proving that an $L$-layer transformer trained under our proposed Log-ICoT curriculum learns $k$-parity with $\mathsf{poly}(n)$ samples and $L = \log_2 k$ training stages. This matches the sample efficiency of explicit CoT while eliminating its inference overhead, and extends prior one-layer parity guarantees to multi-layer architectures. Compared to standard ICoT, which removes thinking tokens one at a time, Log-ICoT removes them in geometric chunks, reducing the number of stages from linear in $k$ to logarithmic. Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.

cs.LG↗

arXiv2026

Multi-Objective Learning for Diffusion Models: A Statistical Theory under Semi-Supervised Learning

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

cs.LG↗

arXiv2026

Do Sparse Autoencoders Identify Reasoning Features in Language Models?

We study how reliably sparse autoencoders (SAEs) support claims about reasoning-related internal features in large language models. We first give a stylized analysis showing that sparsity-regularized decoding can preferentially retain stable low-dimensional correlates while suppressing high-dimensional within-behavior variation, motivating the possibility that contrastively selected "reasoning" features may concentrate on cue-like structure when such cues are coupled with reasoning traces. Building on this perspective, we propose a falsification-based evaluation framework that combines causal token injection with LLM-guided counterexample construction. Across 22 configurations spanning multiple model families, layers, and reasoning datasets, we find that many contrastively selected candidates are highly sensitive to token-level interventions, with 45%-90% activating after injecting only a few associated tokens into non-reasoning text. For the remaining context-dependent candidates, LLM-guided falsification produces targeted non-reasoning inputs that trigger activation and meaning-preserving paraphrases of top-activating reasoning traces that suppress it. A small steering study yields minimal changes on the evaluated benchmarks. Overall, our results suggest that, in the settings we study, sparse decompositions can favor low-dimensional correlates that co-occur with reasoning, underscoring the need for falsification when attributing high-level behaviors to individual SAE features. Code is available at https://github.com/GeorgeMLP/reasoning-probing.

cs.LG↗

arXiv2026

ScribbleEdit: Synthetic Data for Image Editing with Scribbles and Text

Recent progress in generative models has significantly advanced image editing capabilities, yet precise and intuitive user control remains difficult. Specifically, users often struggle to communicate both exact spatial layouts and specific semantic details simultaneously. While natural language instructions effectively convey high-level semantics like texture and color, they lack spatial specificity. Conversely, freehand scribbles provide rough spatial boundaries but cannot express detailed visual attributes. Consequently, achieving precise control requires combining both modalities. However, existing models struggle to jointly interpret abstract scribbles alongside text due to a lack of specialized training data. In this work, we introduce ScribbleEdit, a large-scale synthetic dataset designed to bridge this gap by combining natural language instructions with freehand scribble inputs for more accurate, controllable edits. We construct this dataset through a synthetic pipeline that automatically generates source-target image pairs via inpainting, which are then paired with human-drawn scribbles and VLM-generated text instructions. Using ScribbleEdit, we evaluate and finetune both diffusion-based and autoregressive unified multimodal image editing models. Our experiments reveal that while off-the-shelf models struggle with abstract scribble inputs, finetuning on our synthetic dataset significantly improves their ability to generate spatially aligned and semantically consistent edits.

cs.CV↗

arXiv2026

Reinforcement Learning via Value Gradient Flow

We study behavior-regularized reinforcement learning (RL), where regularization toward a reference distribution (the dataset in offline RL or the base model in LLM RL finetuning) is essential to prevent value over-optimization caused by erroneous out-of-distribution extrapolation. Existing methods either rely on reparameterized policy gradient, which are difficult to scale to large generative models, or on reject sampling, which can be overly conservative when attempting to move beyond the behavior support. In this paper, we propose Value Gradient Flow (VGF), a scalable new paradigm for behavior-regularized RL. VGF casts behavior-regularized RL as an optimal transport problem that maps the reference distribution to the value-induced optimal policy distribution. We solve this transport problem via discrete gradient flow, where value gradients guide particles initialized from the reference distribution. Our analysis shows that VGF imposes regularization implicitly by controlling the transport budget. VGF eliminates explicit policy parameterization while remaining expressive and flexible, this enables adaptive test-time scaling by adjusting the transport budget. Extensive experiments demonstrate that VGF significantly outperforms prior methods, achieving state-of-the-art results on offline RL benchmarks (D4RL, OGBench) and LLM RL tasks. Code and runs can be found at https://ryanxhr.github.io/vgf.

cs.LG↗

arXiv2026

Multi-Agent Guided Policy Search for Non-Cooperative Dynamic Games

Multi-agent reinforcement learning (MARL) optimizes strategic interactions in non-cooperative dynamic games, where agents have misaligned objectives. However, data-driven methods such as multi-agent policy gradients (MA-PG) often suffer from instability and limit-cycle behaviors. Prior stabilization techniques typically rely on entropy-based exploration, which slows learning and increases variance. We propose a model-based approach that incorporates approximate priors into the reward function as regularization. In linear quadratic (LQ) games, we prove that such priors stabilize policy gradients and guarantee local exponential convergence to an approximate Nash equilibrium. We then extend this idea to infinite-horizon nonlinear games by introducing Multi-agent Guided Policy Search (MA-GPS), which constructs short-horizon local LQ approximations from trajectories of current policies to guide training. Experiments on nonlinear vehicle platooning and a six-player strategic basketball formation show that MA-GPS achieves faster convergence and more stable learning than existing MARL methods.

eess.SY↗

arXiv2026

Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers

Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This mathematical structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.

cs.CL↗

arXiv2025

DRAGON: Distributional Rewards Optimize Diffusion Generative Models

We present Distributional RewArds for Generative OptimizatioN (DRAGON), a versatile framework for fine-tuning media generation models towards a desired outcome. Compared with traditional reinforcement learning with human feedback (RLHF) or pairwise preference approaches such as direct preference optimization (DPO), DRAGON is more flexible. It can optimize reward functions that evaluate either individual examples or distributions of them, making it compatible with a broad spectrum of instance-wise, instance-to-distribution, and distribution-to-distribution rewards. Leveraging this versatility, we construct novel reward functions by selecting an encoder and a set of reference examples to create an exemplar distribution. When cross-modal encoders such as CLAP are used, the reference may be of a different modality (text versus audio). Then, DRAGON gathers online and on-policy generations, scores them with the reward function to construct a positive demonstration set and a negative set, and leverages the contrast between the two finite sets to approximate distributional reward optimization. For evaluation, we fine-tune an audio-domain text-to-music diffusion model with 20 reward functions, including a custom music aesthetics model, CLAP score, Vendi diversity, and Frechet audio distance (FAD). We further compare instance-wise (per-song) and full-dataset FAD settings while ablating multiple FAD encoders and reference sets. Over all 20 target rewards, DRAGON achieves an 81.45% average win rate. Moreover, reward functions based on exemplar sets enhance generations and are comparable to model-based rewards. With an appropriate exemplar set, DRAGON achieves a 60.95% human-voted music quality win rate without training on human preference annotations. DRAGON is a new approach to designing and optimizing reward functions for improving human-perceived quality. Demos at https://ml-dragon.github.io/web

cs.SD↗

arXiv2025

Intent Demonstration in General-Sum Dynamic Games via Iterative Linear-Quadratic Approximations

Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within general-sum dynamic games. We model this problem and propose an algorithm that balances intent demonstration with task performance. To handle nonlinear dynamic games with continuous state-action spaces, our method leverages iterative linear-quadratic game approximations and provides efficient intent-teaching guarantees: the uncertain agent's belief can be driven rapidly to the ground truth, while the demonstrating agent avoids expending effort on unnecessary belief alignment when it does not improve task performance. Theoretical analysis and hardware experiments confirm that our approach enables the demonstrating agent to reconcile task execution with belief alignment and strategically manage the information asymmetry among agents, even as its intent evolves during deployment.

eess.SY↗

arXiv2025

OVERT: A Benchmark for Over-Refusal Evaluation on Text-to-Image Models

Text-to-Image (T2I) models have achieved remarkable success in generating visual content from text inputs. Although multiple safety alignment strategies have been proposed to prevent harmful outputs, they often lead to overly cautious behavior -- rejecting even benign prompts -- a phenomenon known as $\textit{over-refusal}$ that reduces the practical utility of T2I models. Despite over-refusal having been observed in practice, there is no large-scale benchmark that systematically evaluates this phenomenon for T2I models. In this paper, we present an automatic workflow to construct synthetic evaluation data, resulting in OVERT ($\textbf{OVE}$r-$\textbf{R}$efusal evaluation on $\textbf{T}$ext-to-image models), the first large-scale benchmark for assessing over-refusal behaviors in T2I models. OVERT includes 4,600 seemingly harmful but benign prompts across nine safety-related categories, along with 1,785 genuinely harmful prompts (OVERT-unsafe) to evaluate the safety-utility trade-off. Using OVERT, we evaluate several leading T2I models and find that over-refusal is a widespread issue across various categories (Figure 1), underscoring the need for further research to enhance the safety alignment of T2I models without compromising their functionality. As a preliminary attempt to reduce over-refusal, we explore prompt rewriting; however, we find it often compromises faithfulness to the meaning of the original prompts. Finally, we demonstrate the flexibility of our generation framework in accommodating diverse safety requirements by generating customized evaluation data adapting to user-defined policies.

cs.LG↗

arXiv2025

Cross-attention Secretly Performs Orthogonal Alignment in Recommendation Models

Cross-domain sequential recommendation (CDSR) aims to align heterogeneous user behavior sequences collected from different domains. While cross-attention is widely used to enhance alignment and improve recommendation performance, its underlying mechanism is not fully understood. Most researchers interpret cross-attention as residual alignment, where the output is generated by removing redundant and preserving non-redundant information from the query input by referencing another domain data which is input key and value. Beyond the prevailing view, we introduce Orthogonal Alignment, a phenomenon in which cross-attention discovers novel information that is not present in the query input, and further argue that those two contrasting alignment mechanisms can co-exist in recommendation models We find that when the query input and output of cross-attention are orthogonal, model performance improves over 300 experiments. Notably, Orthogonal Alignment emerges naturally, without any explicit orthogonality constraints. Our key insight is that Orthogonal Alignment emerges naturally because it improves scaling law. We show that baselines additionally incorporating cross-attention module outperform parameter-matched baselines, achieving a superior accuracy-per-model parameter. We hope these findings offer new directions for parameter-efficient scaling in multi-modal research.

cs.LG↗

arXiv2025

Coordinating Distributed Energy Resources with Nodal Pricing in Distribution Networks: a Game-Theoretic Approach

We propose a real-time nodal pricing mechanism for cost minimization and voltage control in a distribution network with autonomous distributed energy resources and analyze the resulting market using stochastic game theory. Unlike existing methods, the proposed pricing scheme does not require device-aware centralized coordination or communication between prosumers. By developing new sufficient conditions under which a stochastic game is a Markov potential game, we show that the problem of computing an equilibrium for the proposed model is equivalent to solving a single-agent Markov Decision Process. These new conditions are general and may apply to other applications. We compute the equilibrium for an IEEE test system to empirically demonstrate the effectiveness of the pricing policy.

eess.SY↗

arXiv2025

Reinforcement Learning for Flow-Matching Policies

Flow-matching policies have emerged as a powerful paradigm for generalist robotics. These models are trained to imitate an action chunk, conditioned on sensor observations and textual instructions. Often, training demonstrations are generated by a suboptimal policy, such as a human operator. This work explores training flow-matching policies via reinforcement learning to surpass the original demonstration policy performance. We particularly note minimum-time control as a key application and present a simple scheme for variable-horizon flow-matching planning. We then introduce two families of approaches: a simple Reward-Weighted Flow Matching (RWFM) scheme and a Group Relative Policy Optimization (GRPO) approach with a learned reward surrogate. Our policies are trained on an illustrative suite of simulated unicycle dynamics tasks, and we show that both approaches dramatically improve upon the suboptimal demonstrator performance, with the GRPO approach in particular generally incurring between $50\%$ and $85\%$ less cost than a naive Imitation Learning Flow Matching (ILFM) approach.

cs.LG↗

arXiv2025

Spooky Action at a Distance: Normalization Layers Enable Side-Channel Spatial Communication

This work shows that normalization layers can facilitate a surprising degree of communication across the spatial dimensions of an input tensor. We study a toy localization task with a convolutional architecture and show that normalization layers enable an iterative message passing procedure, allowing information aggregation from well outside the local receptive field. Our results suggest that normalization layers should be employed with caution in applications such as diffusion-based trajectory generation, where maintaining a spatially limited receptive field is crucial.

cs.LG↗

arXiv2025

Efficient Global Optimization of Two-Layer ReLU Networks: Quadratic-Time Algorithms and Adversarial Training

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

cs.LG↗

arXiv2025

Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification

In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP) certification methods, we take a branch-and-bound approach to propose partitioning the input uncertainty set and solving the relaxations on each part separately. We show that this approach reduces relaxation error, and that the error is eliminated entirely upon performing an LP relaxation with a partition intelligently designed to exploit the nature of the ReLU activations. To scale this approach to large networks, we consider using a coarser partition whereby the number of parts in the partition is reduced. We prove that computing such a coarse partition that directly minimizes the LP relaxation error is NP-hard. By instead minimizing the worst-case LP relaxation error, we develop a closed-form branching scheme in the single-hidden layer case. We extend the analysis to the SDP, where the feasible set geometry is exploited to design a branching scheme that minimizes the worst-case SDP relaxation error. Experiments on MNIST, CIFAR-10, and Wisconsin breast cancer diagnosis classifiers demonstrate significant increases in the percentages of test samples certified. By independently increasing the input size and the number of layers, we empirically illustrate under which regimes the branched LP and branched SDP are best applied. Finally, we extend our LP branching method into a multi-layer branching heuristic, which attains comparable performance to prior state-of-the-art heuristics on large-scale, deep neural network certification benchmarks.

cs.LG↗