Recent theoretical results show transformers cannot express sequential reasoning problems over long input lengths, intuitively because their computational depth is bounded. However, prior work treats the depth as a constant, leaving it unclear to what degree bounded depth may suffice for solving problems over short inputs, or how increasing the transformer's depth affects its expressive power. We address these questions by analyzing the expressive power of transformers whose depth can grow minimally with context length $n$. We show even highly uniform transformers with depth $\Theta(\log n)$ can express two important problems: recognizing regular languages, which captures state tracking abilities, and graph connectivity, which underlies multi-step reasoning. Notably, both of these problems cannot be expressed by fixed-depth transformers under standard complexity conjectures, demonstrating the expressivity benefit of growing depth. Moreover, our theory quantitatively predicts how depth must grow with input length to express these problems, showing that depth scaling is more efficient than scaling width or chain-of-thought steps. Empirically, we find our theoretical depth requirements for regular language recognition match the practical depth requirements of transformers remarkably well. Thus, our results clarify precisely how depth affects transformers' reasoning capabilities, providing potential practical insights for designing models that are better at sequential reasoning.

Researchers and practitioners in natural language processing and computational linguistics frequently observe and analyze the real language usage in large-scale corpora. For that purpose, they often employ off-the-shelf pattern-matching tools, such as grep, and keyword-in-context concordancers, which is widely used in corpus linguistics for gathering examples. Nonetheless, these existing techniques rely on surface-level string matching, and thus they suffer from the major limitation of not being able to handle orthographic variations and paraphrasing -- notable and common phenomena in any natural language. In addition, existing continuous approaches such as dense vector search tend to be overly coarse, often retrieving texts that are unrelated but share similar topics. Given these challenges, we propose a novel algorithm that achieves \emph{soft} (or semantic) yet efficient pattern matching by relaxing a surface-level matching with word embeddings. Our algorithm is highly scalable with respect to the size of the corpus text utilizing inverted indexes. We have prepared an efficient implementation, and we provide an accessible web tool. Our experiments demonstrate that the proposed method (i) can execute searches on billion-scale corpora in less than a second, which is comparable in speed to surface-level string matching and dense vector search; (ii) can extract harmful instances that semantically match queries from a large set of English and Japanese Wikipedia articles; and (iii) can be effectively applied to corpus-linguistic analyses of Latin, a language with highly diverse inflections.

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant challenges in generalizing to large-scale problems due to high computational complexity and inefficient capture of structural patterns. To address this issue, we propose a novel learning-based search space reduction method that adaptively selects a small set of promising candidate nodes at each step of the constructive NCO process. Unlike traditional methods that rely on fixed heuristics, our selection model dynamically prioritizes nodes based on learned patterns, significantly reducing the search space while maintaining solution quality. Experimental results demonstrate that our method, trained solely on 100-node instances from uniform distribution, generalizes remarkably well to large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) instances with up to 1 million nodes from the uniform distribution and over 80K nodes from other distributions.

Learning-based controllers are often purposefully kept out of real-world applications due to concerns about their safety and reliability. We explore how state-of-the-art world models in Model-Based Reinforcement Learning can be utilized beyond the training phase to ensure a deployed policy only operates within regions of the state-space it is sufficiently familiar with. This is achieved by continuously monitoring discrepancies between a world model's predictions and observed system behavior during inference. It allows for triggering appropriate measures, such as an emergency stop, once an error threshold is surpassed. This does not require any task-specific knowledge and is thus universally applicable. Simulated experiments on established robot control tasks show the effectiveness of this method, recognizing changes in local robot geometry and global gravitational magnitude. Real-world experiments using an agile quadcopter further demonstrate the benefits of this approach by detecting unexpected forces acting on the vehicle. These results indicate how even in new and adverse conditions, safe and reliable operation of otherwise unpredictable learning-based controllers can be achieved.

Enhancing the mathematical reasoning capabilities of Large Language Models (LLMs) is of great scientific and practical significance. Researchers typically employ process-supervised reward models (PRMs) to guide the reasoning process, effectively improving the models' reasoning abilities. However, existing methods for constructing process supervision training data, such as manual annotation and per-step Monte Carlo estimation, are often costly or suffer from poor quality. To address these challenges, this paper introduces a framework called EpicPRM, which annotates each intermediate reasoning step based on its quantified contribution and uses an adaptive binary search algorithm to enhance both annotation precision and efficiency. Using this approach, we efficiently construct a high-quality process supervision training dataset named Epic50k, consisting of 50k annotated intermediate steps. Compared to other publicly available datasets, the PRM trained on Epic50k demonstrates significantly superior performance. Getting Epic50k at https://github.com/xiaolizh1/EpicPRM.

Recent great advances in video generation models have demonstrated their potential to produce high-quality videos, bringing challenges to effective evaluation. Unlike human evaluation, existing automated evaluation metrics lack high-level semantic understanding and reasoning capabilities for video, thus making them infeasible and unexplainable. To fill this gap, we curate GRADEO-Instruct, a multi-dimensional T2V evaluation instruction tuning dataset, including 3.3k videos from over 10 existing video generation models and multi-step reasoning assessments converted by 16k human annotations. We then introduce GRADEO, one of the first specifically designed video evaluation models, which grades AI-generated videos for explainable scores and assessments through multi-step reasoning. Experiments show that our method aligns better with human evaluations than existing methods. Furthermore, our benchmarking reveals that current video generation models struggle to produce content that aligns with human reasoning and complex real-world scenarios. The models, datasets, and codes will be released soon.

Recent advancements in multimodal reasoning have largely overlooked the audio modality. We introduce Audio-Reasoner, a large-scale audio language model for deep reasoning in audio tasks. We meticulously curated a large-scale and diverse multi-task audio dataset with simple annotations. Then, we leverage closed-source models to conduct secondary labeling, QA generation, along with structured COT process. These datasets together form a high-quality reasoning dataset with 1.2 million reasoning-rich samples, which we name CoTA. Following inference scaling principles, we train Audio-Reasoner on CoTA, enabling it to achieve great logical capabilities in audio reasoning. Experiments show state-of-the-art performance across key benchmarks, including MMAU-mini (+25.42%), AIR-Bench chat/foundation(+14.57%/+10.13%), and MELD (+8.01%). Our findings stress the core of structured CoT training in advancing audio reasoning.

Existing Multimodal Large Language Models (MLLMs) are predominantly trained and tested on consistent visual-textual inputs, leaving open the question of whether they can handle inconsistencies in real-world, layout-rich content. To bridge this gap, we propose the Multimodal Inconsistency Reasoning (MMIR) benchmark to assess MLLMs' ability to detect and reason about semantic mismatches in artifacts such as webpages, presentation slides, and posters. MMIR comprises 534 challenging samples, each containing synthetically injected errors across five reasoning-heavy categories: Factual Contradiction, Identity Misattribution, Contextual Mismatch, Quantitative Discrepancy, and Temporal/Spatial Incoherence. We evaluate six state-of-the-art MLLMs, showing that models with dedicated multimodal reasoning capabilities, such as o1, substantially outperform their counterparts while open-source models remain particularly vulnerable to inconsistency errors. Detailed error analyses further show that models excel in detecting pairwise inconsistencies but struggle with inconsistencies confined to single elements in complex layouts. Probing experiments reveal that single-modality prompting, including Chain-of-Thought (CoT) and Set-of-Mark (SoM) methods, yields marginal gains, revealing a key bottleneck in cross-modal reasoning. Our findings highlight the need for advanced multimodal reasoning and point to future research on multimodal inconsistency.

Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like Chain-of-Thought, debating, and self-refinement have been applied to auto-regressive LLMs, achieving significant successes in tasks such as mathematical reasoning, commonsense reasoning, and multi-hop question answering. Despite these successes, the theoretical basis for how multi-round reasoning enhances problem-solving abilities remains underexplored. In this work, we investigate the approximation, learnability, and generalization properties of multi-round auto-regressive models. We show that Transformers with finite context windows are universal approximators for steps of Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning. We extend PAC learning to sequence generation and demonstrate that multi-round generation is learnable even when the sequence length exceeds the model's context window. Finally, we examine how generalization error propagates across rounds, and show how the aforementioned approaches can help constrain this error, ensuring outputs stay within an expectation boundary. This work sheds light on the systemic theoretical foundations of multi-round sequence learning and reasoning, emphasizing its role in inference complexity.

Exploration is a cornerstone of reinforcement learning (RL). Intrinsic motivation attempts to decouple exploration from external, task-based rewards. However, established approaches to intrinsic motivation that follow general principles such as information gain, often only uncover low-level interactions. In contrast, children's play suggests that they engage in meaningful high-level behavior by imitating or interacting with their caregivers. Recent work has focused on using foundation models to inject these semantic biases into exploration. However, these methods often rely on unrealistic assumptions, such as language-embedded environments or access to high-level actions. We propose SEmaNtically Sensible ExploratIon (SENSEI), a framework to equip model-based RL agents with an intrinsic motivation for semantically meaningful behavior. SENSEI distills a reward signal of interestingness from Vision Language Model (VLM) annotations, enabling an agent to predict these rewards through a world model. Using model-based RL, SENSEI trains an exploration policy that jointly maximizes semantic rewards and uncertainty. We show that in both robotic and video game-like simulations SENSEI discovers a variety of meaningful behaviors from image observations and low-level actions. SENSEI provides a general tool for learning from foundation model feedback, a crucial research direction, as VLMs become more powerful.