The low-rank adaptation (LoRA) algorithm for fine-tuning large models has grown popular in recent years due to its remarkable performance and low computational requirements. LoRA trains two ``adapter" matrices that form a low-rank representation of the model parameters, thereby massively reducing the number of parameters that need to be updated at every step. Although LoRA is simple, its convergence is poorly understood due to the lack of Lipschitz smoothness, a key condition for classic convergence analyses. As a result, current theoretical results only consider asymptotic behavior or assume strong boundedness conditions which artificially enforce Lipschitz smoothness. In this work, we provide for the first time a non-asymptotic convergence analysis of the \textit{original LoRA gradient descent} algorithm, which reflects widespread practice, without such assumptions. Our work relies on three key steps: i) reformulating the problem in terms of the outer product of the stacked adapter matrices, ii) a modified descent lemma for the ``Lipschitz-like" reparametrized function, and iii) controlling the step size. With this approach, we prove that LoRA gradient descent converges to a stationary point at rate $O(\frac{1}{\log T})$, where $T$ is the number of iterations. We conduct numerical experiments to validate our theoretical findings.

Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) dominate the post-training landscape for mathematical reasoning, yet differ fundamentally in their reliance on expert trajectories. To understand the optimal way to harness these trajectories for maximizing performance, we propose the Plasticity-Ceiling Framework. This framework empirically grounds the post-training landscape by decomposing the final performance ceiling into the foundational SFT performance and the subsequent RL plasticity (i.e., the maximum improvement via RL). Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability and premature convergence deficits inherent in synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the Stable or Mild Overfitting Regime of SFT maximizes the final ceiling by securing a robust SFT foundation with substantial RL plasticity; (2) Refuting the ``Less is More'' hypothesis in SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) The Minimum Validation Loss of SFT serves as a reliable indicator for selecting the expert trajectories that maximize the ultimate performance ceiling. Our findings provide actionable guidelines for extracting maximum value from expert trajectories.

Learning fast and robust ball-kicking skills is a critical capability for humanoid soccer robots, yet it remains a challenging problem due to the need for rapid leg swings, postural stability on a single support foot, and robustness under noisy sensory input and external perturbations (e.g., opponents). This paper presents a reinforcement learning (RL)-based system that enables humanoid robots to execute robust continual ball-kicking with adaptability to different ball-goal configurations. The system extends a typical teacher-student training framework -- in which a "teacher" policy is trained with ground truth state information and the "student" learns to mimic it with noisy, imperfect sensing -- by including four training stages: (1) long-distance ball chasing (teacher); (2) directional kicking (teacher); (3) teacher policy distillation (student); and (4) student adaptation and refinement (student). Key design elements -- including tailored reward functions, realistic noise modeling, and online constrained RL for adaptation and refinement -- are critical for closing the sim-to-real gap and sustaining performance under perceptual uncertainty. Extensive evaluations in both simulation and on a real robot demonstrate strong kicking accuracy and goal-scoring success across diverse ball-goal configurations. Ablation studies further highlight the necessity of the constrained RL, noise modeling, and the adaptation stage. This work presents a system for learning robust continual humanoid ball-kicking under imperfect perception, establishing a benchmark task for visuomotor skill learning in humanoid whole-body control.

A cognitive map is an internal model which encodes the abstract relationships among entities in the world, giving humans and animals the flexibility to adapt to new situations, with a strong out-of-distribution (OOD) generalization that current AI systems still do not possess. To bridge this gap, we introduce $\textit{MapFormers}$, new Transformer-based architectures, which can learn cognitive maps from observational data and perform path-integration without supervision. Cognitive maps are learned in the model by disentangling structural relationships in the inputs from their specific content, a property that can be achieved by updating position encodings with input-dependent matrices, built as exponentials of learned combinations of Lie-algebra generators. We developed two variants of $\textit{MapFormers}$ that unify absolute and relative positional encoding to model episodic (EM) and working memory (WM), respectively. We tested $\textit{MapFormers}$ on several formal tasks targeting distinct cognitive capacities, including gating, 2D navigation and nested hierarchies (Dyck Languages). Our results demonstrate that $\textit{MapFormers}$ significantly outperform current AI architectures, achieving near-perfect OOD generalization where standard models fail. Furthermore, we show that $\textit{MapFormers}$ are scalable; evaluations on naturalistic data yield perplexity improvements over baselines, suggesting that these principles extend to large-scale, real-world domains. These results are obtained through efficient parallel computation on commutative maps, though our models can also learn non-commutative cognitive maps via sequential path-integration. Overall, these results suggest that input-dependent matrices provide a critical structural bias, by disentangling abstract relations from content in order to drive robust OOD generalization.

We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, fully analytic horizon-selection rule that guarantees a prescribed approximation tolerance without iterative set computations. The choice of vector norm enters as a design lever: norm shaping -- through diagonal or Lyapunov-based weighting -- tightens both the contraction factor and the resulting certificate, with direct consequences for robust invariant-set approximation and tube-based model predictive control (MPC) constraint tightening. Numerical examples illustrate the accuracy, scalability, and practical impact of the proposed bound.

Most applications of generative AI involve a sequential interaction in which a person inputs a prompt and waits for a response, and where reaction time and adaptivity are not important factors. In contrast, live jamming is a collaborative interaction that requires real-time coordination and adaptation without access to the other player's future moves, while preserving diversity to sustain a creative flow. Reinforcement learning post-training enables effective adaptation through on-policy interaction, yet it often reduces output diversity by exploiting coherence-based rewards. This collapse, known as ``reward hacking'', affects many RL post-training pipelines, but is especially harmful in live jamming, where musical creativity relies on dynamic variation and mutual responsiveness. In this paper, we propose a novel adversarial training method on policy-generated trajectories to mitigate reward hacking in RL post-training for melody-to-chord accompaniment. A co-evolving discriminator separates policy trajectories from the data distribution, while the policy maximizes the discriminator output in addition to coherence rewards to prevent collapse to trivial outputs. We evaluate accompaniment quality and output diversity in simulation with both fixed test melodies and learned melody agents, and we conduct a user study with the model deployed in a real-time interactive system with expert musicians. Quantitative evaluation and user feedback demonstrate improved output diversity, harmonic coherence, adaptation speed and user agency. Our results demonstrate a simple yet effective method to mitigate reward hacking in RL post-training of generative sequence models.

Forecasting how human hands move in egocentric views is critical for applications like augmented reality and human-robot policy transfer. Recently, several hand trajectory prediction (HTP) methods have been developed to generate future possible hand waypoints, which still suffer from insufficient prediction targets, inherent modality gaps, entangled hand-head motion, and limited validation in downstream tasks. To address these limitations, we present a universal hand motion forecasting framework considering multi-modal input, multi-dimensional and multi-target prediction patterns, and multi-task affordances for downstream applications. We harmonize multiple modalities by vision-language fusion, global context incorporation, and task-aware text embedding injection, to forecast hand waypoints in both 2D and 3D spaces. A novel dual-branch diffusion is proposed to concurrently predict human head and hand movements, capturing their motion synergy in egocentric vision. By introducing target indicators, the prediction model can forecast the specific joint waypoints of the wrist or the fingers, besides the widely studied hand center points. In addition, we enable Uni-Hand to additionally predict hand-object interaction states (contact/separation) to facilitate downstream tasks better. As the first work to incorporate downstream task evaluation in the literature, we build novel benchmarks to assess the real-world applicability of hand motion forecasting algorithms. The experimental results on multiple publicly available datasets and our newly proposed benchmarks demonstrate that Uni-Hand achieves the state-of-the-art performance in multi-dimensional and multi-target hand motion forecasting. Extensive validation in multiple downstream tasks also presents its impressive human-robot policy transfer to enable robotic manipulation, and effective feature enhancement for action anticipation/recognition.

The forward Kullback-Leibler (KL) divergence is a ubiquitous objective for fitting a parameterized distribution to samples due to its tractability and equivalence to maximum likelihood estimation (MLE). Its inherent asymmetry, however, may lead to degenerate solutions that generalize poorly. While the symmetric Jeffreys divergence offers a more balanced alternative, its optimization is challenging due to the presence of a reverse KL term. Generative adversarial networks (GANs) bypass this intractability using a min-max formulation at the cost of introducing new instability issues. This work proposes a non-adversarial approach to minimize the Jeffreys divergence. To do so, it uses a proxy model to tractably approximate the reverse KL divergence of the main model. The main and proxy models are jointly fitted to the data using a constrained optimization formulation to obtain a practical algorithm that adapts the models' priorities throughout training. We evaluate our framework on various tasks, including density estimation and simulation-based inference, and demonstrate that this approach is more stable and more accurate than MLE and GANs, particularly in low-data regimes.

Graph contrastive learning (GCL) learns node and graph representations by contrasting multiple views of the same graph. Existing methods typically rely on fixed, handcrafted views-usually a local and a global perspective, which limits their ability to capture multi-scale structural patterns. We present an augmentation-free, multi-view GCL framework grounded in fractional-order continuous dynamics. By varying the fractional derivative order $α\in (0,1]$, our encoders produce a continuous spectrum of views: small $α$ yields localized features, while large $α$ induces broader, global aggregation. We treat $α$ as a learnable parameter so the model can adapt diffusion scales to the data and automatically discover informative views. This principled approach generates diverse, complementary representations without manual augmentations. Extensive experiments on standard benchmarks demonstrate that our method produces more robust and expressive embeddings and outperforms state-of-the-art GCL baselines.

Large Language Models (LLMs) often struggle with the precise logic and schema alignment required for complex Text-to-SQL tasks. While current methods rely heavily on static prompting, they lack the ability to dynamically adapt and self-correct through environmental interaction. To bridge this gap, we propose MARS-SQL, a trainable multi-agent framework for Text-to-SQL. Rather than introducing a new standalone SQL primitive, MARS-SQL makes an agentic workflow trainable by decomposing the problem into three specialized roles: schema grounding, query generation, and solution validation. Central to our approach is a generation agent trained via a multi-turn RL policy within a ReAct-style loop. The agent learns to iteratively reason, execute intermediate SQL actions on a live database, and refine its strategy based on execution feedback. To improve robustness, we further introduce a validation mechanism that treats solution selection as a generative modeling task, identifying the optimal interaction trajectory through next-token prediction probabilities. Empirical evaluations demonstrate the effectiveness of coupling interactive learning with trajectory ranking. MARS-SQL achieves state-of-the-art performance, recording an execution accuracy of 77.84% on the BIRD development dataset and 89.75% on the Spider test dataset, while also transferring strongly to out-of-domain benchmarks. Code is available at https://github.com/YangHaolin0526/MARS-SQL.

Although 3D Gaussian Splatting (3D-GS) achieves efficient rendering for novel view synthesis, extending it to dynamic scenes still results in substantial memory overhead from replicating Gaussians across frames. To address this challenge, we propose 4D Neural Voxel Splatting (4D-NVS), which combines voxel-based representations with neural Gaussian splatting for efficient dynamic scene modeling. Instead of generating separate Gaussian sets per timestamp, our method employs a compact set of neural voxels with learned deformation fields to model temporal dynamics. The design greatly reduces memory consumption and accelerates training while preserving high image quality. We further introduce a novel view refinement stage that selectively improves challenging viewpoints through targeted optimization, maintaining global efficiency while enhancing rendering quality for difficult viewing angles. Experiments demonstrate that our method outperforms state-of-the-art approaches with significant memory reduction and faster training, enabling real-time rendering with superior visual fidelity.

In Socratic debugging, instructors guide students towards identifying and fixing a bug on their own, instead of providing the bug fix directly. Most novice programmer bugs are caused by programming misconceptions, namely false beliefs about a programming concept. In this context, Socratic debugging can be formulated as a guided Reasoning Trajectory (RT) leading to a statement about the program behavior that contradicts the bug-causing misconception. Upon reaching this contradiction, the ensuing cognitive dissonance is expected to lead the student to identify the false belief on their own, followed by an enduring belief update. In this paper, we introduce the task of reasoning trajectory generation, together with a dataset of debugging problems annotated with RTs that are manually created or LLM-generated. We then describe LLM-based solutions for generating RTs and Socratic conversations that are anchored on them. A large-scale LLM-as-judge evaluation shows that large language and reasoning models can generate up to 91% correct reasoning trajectories and 98.7% valid conversation turns.

Tensegrity robots combine rigid rods and elastic cables, offering high resilience and deployability but at the same time posing major challenges for locomotion control due to their underactuated and highly coupled dynamics. This paper introduces a morphology-aware reinforcement learning framework that integrates a graph neural network (GNN) into the Soft Actor-Critic (SAC) algorithm. By representing the robot's physical topology as a graph, the proposed GNN-based policy captures coupling among components, enabling faster and more stable learning than conventional multilayer perceptron (MLP) policies. The method is validated on a physical 3-bar tensegrity robot across three locomotion primitives, including straight-line tracking and bidirectional turning. It shows superior sample efficiency, robustness to noise and stiffness variations, and improved trajectory accuracy. Additionally, the learned policies transfer directly from simulation to hardware without fine-tuning, achieving stable real-world locomotion. These results demonstrate the advantages of incorporating structural priors into reinforcement learning for tensegrity robot control.

Large Language Models (LLMs) typically come with a fixed architecture, despite growing evidence that not all layers contribute equally to every downstream task. We introduce TALE (Task-Aware Layer Elimination), an inference-time method that improves task performance by selectively removing layers that are irrelevant or detrimental for a given task. TALE optimizes task-specific performance, yielding a task-optimized architecture without retraining. Across 9 tasks and 5 model families, under both zero-shot and few-shot settings, TALE consistently matches or surpasses baseline performance while simultaneously reducing computational costs. TALE also synergizes with fine-tuning, leading to further performance improvements. Computing TALE for a new task requires modest resources, making it a practical and deployable solution for task-specialized LLM inference.

Large Language Models (LLMs) are trained to support an increasing number of languages, yet their predefined tokenizers remain a bottleneck for adapting models to lower-resource or distinct-script languages. Existing tokenizer transfer methods typically rely on semantic heuristics to initialize new embeddings, ignoring higher-layer model dynamics and limiting transfer quality. We propose Model-Aware Tokenizer Transfer (MATT), a method that incorporates model internals into the tokenizer transfer process. MATT introduces an Attention Influence Modeling (AIM) objective that distills inter-token communication patterns from a source model into a target model with a new tokenizer, providing an efficient warm-up before standard language modeling. Unlike approaches that focus solely on embedding similarity, MATT leverages attention behavior to guide embedding initialization and adaptation. Experiments across diverse linguistic settings show that MATT recovers a large fraction of the original model's performance within a few GPU hours, outperforming heuristic baselines. These results demonstrate that incorporating model-level signals offers a practical and effective path toward robust tokenizer transfer in multilingual LLMs.

Context compression reduces Transformer inference costs by replacing lengthy inputs with shorter pre-computed representations. It carries significant benefits for retrieval-augmented generation (RAG) and has attracted growing research attention. However, progress remains difficult to measure due to inconsistent evaluations and baselines. We design a standard, easy-to-reproduce evaluation suite for context compression, BenchPress, along with simple, high-performance baselines for English reading comprehension. BenchPress supports benchmarking across model scales, datasets, compression ratios, and short ($<$1K tokens) to mid-range ($<$8K tokens) contexts. While the suite is applicable to any compression paradigm, our baselines target soft context compression. We establish two simple baselines that strongly outperform the widely used causal compression-token approach: mean pooling and a bidirectional compression-token variant. Our results show the benefit of bidirectional attention when computing compressed representations, and that simple pooling is an expressive compression operator.

Many real-world optimization problems are guided by complex, subjective preferences that are difficult to express as explicit closed-form objectives. In response, we introduce Language-in-the-Loop Optimization (LILO), a Bayesian optimization (BO) framework that employs a large language model (LLM) to translate free-form natural language feedback and prior knowledge from a decision maker into structured preference signals, going beyond the restrictive scalar or pairwise feedback formats typically assumed in preferential BO. The LLM-derived preferences are integrated by a Gaussian process proxy model, enabling principled acquisition-driven exploration with calibrated uncertainty. By placing the LLM in a supporting role rather than as the optimizer itself, LILO preserves the sample efficiency and stability of BO while providing a flexible and expressive feedback interface. Across synthetic and real-world benchmarks, LILO consistently outperforms both conventional preference-based BO methods and LLM-only optimizers, with particularly strong gains in feedback-limited regimes.

Real-time Spoken Language Models (SLMs) struggle to leverage Chain-of-Thought (CoT) reasoning due to the prohibitive latency of generating the entire thought process sequentially. Enabling SLMs to think while speaking, similar to humans, is attracting increasing attention. We present, for the first time, Mind-Paced Speaking (MPS), a brain-inspired framework that enables high-fidelity, real-time reasoning. Similar to how humans utilize distinct brain regions for thinking and responding, we propose a novel dual-brain approach, employing a "Formulation Brain" for high-level reasoning to pace and guide a separate "Articulation Brain" for fluent speech generation. This division of labor eliminates mode-switching, preserving the integrity of the reasoning process. Experiments show that MPS significantly outperforms existing think-while-speaking methods and achieves reasoning performance comparable to models that pre-compute the full CoT before speaking, while drastically reducing latency. Under a zero-latency configuration, the proposed method achieves an accuracy of 92.8% on the mathematical reasoning task Spoken-MQA and attains a score of 82.5 on the speech conversation task URO-Bench. MPS is the methodology underlying our released Step-Audio R1.1 system, effectively bridging the gap between high-quality reasoning and real-time interaction.

Researchers have pursued neurosymbolic artificial intelligence (AI) applications for nearly three decades. A marriage of the neural and symbolic components can lead to rapid advancements in AI. Yet, the field has not realized this promise since most neurosymbolic AI frameworks fail to scale. In addition, the implicit representations and approximate reasoning of purely neural approaches limit interpretability and trust. Knowledge graphs (KGs), a gold-standard representation of explicit semantic knowledge, can address the symbolic side of the problem. However, automatically deriving reliable KGs from text corpora remains an open problem. We address these challenges by introducing GraphMERT, a tiny graphical encoder-only model that distills high-quality KGs from unstructured text corpora and its own internal representations. GraphMERT and its equivalent KG form a modular neurosymbolic stack: neural learning of abstractions; symbolic KGs for verifiable reasoning. GraphMERT + KG is the first efficient and scalable neurosymbolic model to achieve state-of-the-art benchmark accuracy along with superior symbolic representations relative to baselines. Concretely, we target reliable domain-specific KGs that are both (1) factual (with provenance) and (2) valid (ontology-consistent relations with domain-appropriate semantics). When a large language model (LLM), e.g., Qwen3-32B, generates domain-specific KGs, it falls short on reliability due to prompt sensitivity, shallow domain expertise, and hallucinated relations. On text obtained from PubMed papers on diabetes, our 80M-parameter GraphMERT yields a KG with a 69.8% FActScore; a 32B-parameter baseline LLM yields a KG that achieves only 40.2% FActScore. The GraphMERT KG also attains a higher ValidityScore of 68.8%, versus 43.0% for the LLM baseline.

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence direction. Fundamental momentum methods, such as Nesterov Accelerated Gradient and the Heavy Ball method, as well as more recent optimizers such as AdamW and Lion, all rely on the momentum coefficient that is customarily set to $β= 0.9$ and kept constant during model training, a strategy widely used by practitioners, yet suboptimal. In this paper, we introduce an \textit{adaptive memory} mechanism that replaces constant momentum with a dynamic momentum coefficient that is adjusted online during optimization. We derive our method by approximating the objective function using two planes: one derived from the gradient at the current iterate and the other obtained from the accumulated memory of the past gradients. To the best of our knowledge, such a proximal framework was never used for momentum-based optimization. Our proposed approach is novel, extremely simple to use, and does not rely on extra assumptions or hyperparameter tuning. We implement adaptive memory variants of both SGD and AdamW across a wide range of learning tasks, from simple convex problems to large-scale deep learning scenarios, demonstrating that our approach can outperform standard SGD and Adam with hand-tuned momentum coefficients. Finally, our work opens doors for new ways of inducing adaptivity in optimization.

Continuous learning of novel classes is crucial for edge devices to preserve data privacy and maintain reliable performance in dynamic environments. However, the scenario becomes particularly challenging when data samples are insufficient, requiring on-device few-shot class-incremental learning (FSCIL). Although existing work has explored parameter-efficient FSCIL frameworks based on artificial neural networks (ANNs), their deployment is still fundamentally constrained by limited device resources. Spiking neural networks (SNNs) process spatiotemporal information efficiently, offering lower energy consumption, greater biological plausibility, and compatibility with neuromorphic hardware than ANNs. In this work, we propose an SNN-based method containing Sparsity-Aware neuronal dynamics and Fast Adaptive structure (SAFA-SNN) for on-device FSCIL. By threshold regulation, most neurons exhibit stable spikes and others exhibit adaptive spikes. As a result, synaptic traces that encode base-class knowledge are naturally preserved, thereby alleviating catastrophic forgetting. To cope with spike non-differentiability in backpropagation, we employ a gradient-free technique, i.e., zeroth-order optimization. Moreover, class prototypes can limit overfitting on few-shot data but introduce bias. We enhance prototype discriminability by orthogonal subspace projection. Extensive experiments conducted on two standard benchmark datasets (CIFAR-100 and Mini-ImageNet) and three neuromorphic datasets (CIFAR10-DVS, DVS128 Gesture, and N-Caltech101) demonstrate that SAFA-SNN outperforms baselines, specifically achieving at least 4.01% improvement at the last incremental session on Mini-ImageNet and 20% lower energy cost on CIFAR-100 over baselines with practical implementation.

Graph Contrastive Learning (GCL) has shown strong promise for unsupervised graph representation learning, yet its effectiveness on heterophilic graphs, where connected nodes often belong to different classes, remains limited. Most existing methods rely on complex augmentation schemes, intricate encoders, or negative sampling, which raises the question of whether such complexity is truly necessary in this challenging setting. In this work, we revisit the foundations of supervised and unsupervised learning on graphs and uncover a simple yet effective principle for GCL: mitigating node feature noise by aggregating it with structural features derived from the graph topology. This observation suggests that the original node features and the graph structure naturally provide two complementary views for contrastive learning. Building on this insight, we propose an embarrassingly simple GCL model that uses a GCN encoder to capture structural features and an MLP encoder to isolate node feature noise. Our design requires neither data augmentation nor negative sampling, yet achieves state-of-the-art results on heterophilic benchmarks with minimal computational and memory overhead, while also offering advantages in homophilic graphs in terms of complexity, scalability, and robustness. We provide theoretical justification for our approach and validate its effectiveness through extensive experiments, including robustness evaluations against both black-box and white-box adversarial attacks.

Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty quantification, and are thus limited in practical applicability. Recent permutation-invariant extensions, such as the Variable-Input Deep Operator Network, relax these sensor constraints but still rely on sufficiently dense observations and cannot capture uncertainties arising from incomplete measurements or from operators with inherent randomness. To address these challenges, we propose UQ-SONet, a permutation-invariant operator learning framework with built-in uncertainty quantification. Our model integrates a set transformer embedding to handle sparse and variable sensor locations, and employs a conditional variational autoencoder to approximate the conditional distribution of the solution operator. By minimizing the negative ELBO, UQ-SONet provides principled uncertainty estimation while maintaining predictive accuracy. Numerical experiments on deterministic and stochastic PDEs, including the Navier-Stokes equation, demonstrate the robustness and effectiveness of the proposed framework.

Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through mechanistic independence, which characterizes latent factors by how they act on observed variables rather than by their latent distribution. This perspective is invariant to changes of the latent density, even when such changes induce statistical dependencies among factors. Within this framework, we propose several related independence criteria -- ranging from support-based and sparsity-based to higher-order conditions -- and show that each yields identifiability of latent subspaces, even under nonlinear, non-invertible mixing. We further establish a hierarchy among these criteria and provide a graph-theoretic characterization of latent subspaces as connected components. Together, these results clarify the conditions under which disentangled representations can be identified without relying on statistical assumptions.

Large reasoning models improve accuracy by producing long reasoning traces, but this inflates latency and cost, motivating inference-time efficiency. We propose Retrieval-of-Thought (RoT), which reuses prior reasoning as composable ``thought" steps to guide new problems. RoT organizes steps into a thought graph with sequential and semantic edges to enable fast retrieval and flexible recombination. At inference, RoT retrieves query-relevant nodes and applies reward-guided traversal to assemble a problem-specific template that guides generation. This dynamic template reuse reduces redundant exploration and, therefore, reduces output tokens while preserving accuracy. We evaluate RoT on reasoning benchmarks with multiple models, measuring accuracy, token usage, latency, and memory overhead. Findings show small prompt growth but substantial efficiency gains, with RoT reducing output tokens by up to 40%, inference latency by 82%, and cost by 59% while maintaining accuracy. RoT establishes a scalable paradigm for efficient LRM reasoning via dynamic template construction through retrieval.

High-resolution neural datasets enable foundation models for the next generation of brain-computer interfaces and neurological treatments. The community requires rigorous benchmarks to discriminate between competing modeling approaches, yet no standardized evaluation frameworks exist for intracranial EEG (iEEG) recordings. To address this gap, we present Neuroprobe: a suite of decoding tasks for studying multi-modal language processing in the brain. Unlike scalp EEG, intracranial EEG requires invasive surgery to implant electrodes that record neural activity directly from the brain with minimal signal distortion. Neuroprobe is built on the BrainTreebank dataset, which consists of over 40 hours of iEEG recordings from 10 human subjects performing a naturalistic movie viewing task. Neuroprobe serves two critical functions. First, it is a source from which neuroscience insights can be drawn. The high temporal and spatial resolution of the labeled iEEG allows researchers to systematically determine when and where computations for each aspect of language processing occur in the brain by measuring the decodability of each feature across time and all electrode locations. Using Neuroprobe, we visualize how information flows from key language and audio processing sites in the superior temporal gyrus to sites in the prefrontal cortex. We also demonstrate the time evolution of processing from simple auditory features (e.g., pitch and volume) to more complex language features (e.g., part of speech) in a purely data-driven manner. Second, as the field moves toward neural foundation models trained on large-scale datasets, Neuroprobe provides a rigorous framework for comparing competing architectures and training protocols. We make the code for Neuroprobe openly available, aiming to enable rapid progress in the field of iEEG foundation models. Public leaderboard: https://neuroprobe.dev/

The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap remains between its practical performance and theoretical understanding. Existing analyses show that the Muon variants achieve only a suboptimal ergodic convergence rate of $\mathcal{O}(T^{-1/4})$ in stochastic non-convex settings, where $T$ denotes the number of iterations. To study the theoretical limits of Muon, we analyze two momentum-based variance-reduced variants: the one-batch Muon-MVR1 and the two-batch Muon-MVR2. We provide the first rigorous proof that, under \textbf{horizon-free} learning-rate schedules, variance reduction enables Muon-MVR2 to attain the optimal anytime convergence rate $\widetilde{\mathcal{O}}(T^{-1/3})$, matching the lower bound for this problem class. Under the Polyak--Łojasiewicz (PL) condition, we establish anytime guarantees for Muon-MVR1 and Muon-MVR2: they attain best-iterate rates of $\widetilde{\mathcal{O}}(T^{-1/4})$ and $\widetilde{\mathcal{O}}(T^{-1/3})$ for the expected square-root suboptimality, and, given an additional uniform gradient bound along the iterates, achieve last-iterate rates of $\mathcal{O}(T^{-1/4})$ and $\mathcal{O}(T^{-1/3})$ for the objective gap, respectively. Experiments on CIFAR-10 and C4 support the practical effectiveness of the proposed variance-reduced Muon variants. Code is available at \href{https://github.com/MaeChd/MUON-MVR}{Muon-MVR} Codebase.

Understanding group-level social interactions in public spaces is crucial for urban planning, informing the design of socially vibrant and inclusive environments. Detecting such interactions from images involves interpreting subtle visual cues such as relations, proximity, and co-movement - semantically complex signals that go beyond traditional object detection. To address this challenge, we introduce a social group region detection task, which requires inferring and spatially grounding visual regions defined by abstract interpersonal relations. We propose MINGLE (Modeling INterpersonal Group-Level Engagement), a modular three-stage pipeline that integrates: (1) off-the-shelf human detection and depth estimation, (2) VLM-based reasoning to classify pairwise social affiliation, and (3) a lightweight spatial aggregation algorithm to localize socially connected groups. To support this task and encourage future research, we present a new dataset of 100K urban street-view images annotated with bounding boxes and labels for both individuals and socially interacting groups. The annotations combine human-created labels and outputs from the MINGLE pipeline, ensuring semantic richness and broad coverage of real-world scenarios.

As Large Language Models (LLMs) are increasingly adopted as automated judges in benchmarking and reward modeling, ensuring their reliability, efficiency, and robustness has become critical. In this work, we present a systematic comparison of "thinking" and "non-thinking" LLMs in the LLM-as-a-judge paradigm using open-source Qwen 3 models of relatively small sizes (0.6B, 1.7B, and 4B parameters). We evaluate both accuracy and computational efficiency (FLOPs) on RewardBench tasks, and further examine augmentation strategies for non-thinking models, including in-context learning, rubric-guided judging, reference-based evaluation, and n-best aggregation. Our results show that despite these enhancements, non-thinking models generally fall short of their thinking counterparts. Our results show that thinking models achieve approximately 10% points higher accuracy with little overhead (under 2x), in contrast to augmentation strategies like few-shot learning, which deliver modest gains at a higher cost (>8x). Bias and robustness analyses further demonstrate that thinking models maintain significantly greater consistency under a variety of bias conditions such as positional, bandwagon, identity, diversity, and random biases (6% higher on average). We further extend our experiments to the multilingual setting and our results confirm that explicit reasoning extends its benefits beyond English. Overall, our work results in several important findings that provide systematic evidence that explicit reasoning offers clear advantages in the LLM-as-a-judge paradigm not only in accuracy and efficiency but also in robustness.

We prove under practical assumptions that Rotary Positional Embedding (RoPE) introduces an intrinsic distance-dependent bias in attention scores that limits RoPE's ability to model long-context. RoPE extension methods may alleviate this issue, but they typically require post-hoc adjustments after pretraining, such as rescaling or hyperparameters retuning. This paper introduces Token-Aware Phase Attention (TAPA), a new positional encoding method that incorporates a learnable phase function into the attention mechanism. TAPA preserves token interactions over long range, extends to longer contexts with direct and light continual pretraining, extrapolates to unseen lengths, and attains substantially lower perplexity and stronger retrieval performance in the long-context regime than RoPE-style baselines.