While recent advancements in Vector Quantization (VQ) models have successfully achieved complete codebook utilization, a critical bottleneck remains largely unexplored: the effective dimensionality of the codebook embedding space. We observe that discrete codebook representations tend to degenerate into low-dimensional subspaces, characterized by significantly lower effective rank than continuous representations during quantization. Through comprehensive spectral analysis, we identify that this dimensional collapse stems from the suppression of low-variance components inherent to the vector quantization process, thereby severely limiting the expressive capacity of VQ models. To mitigate this fundamental issue, we propose a simple yet effective codebook regularization strategy designed to restore low-variance components, effectively bridging the spectral gap between discrete codebook spaces and continuous representations. Extensive experiments demonstrate that this regularization objective is compatible with diverse VQ training paradigms, yielding significant improvements in reconstruction fidelity and downstream performance in autoregressive image generative models.
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Theory · Deep Learning
The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, a concept of *feature* **un***learning*, in which a neural network progressively loses previously learned features over long training, has gained attention as a way to explain overfitting. In this study, we consider the infinite-width limit of a two-layer neural network updated with a large-batch stochastic gradient, then derive differential equations with different time scales, revealing the mechanism and conditions for feature unlearning to occur. Specifically, we utilize the *fast-slow dynamics*: while an alignment of first-layer weights develops rapidly, the second-layer weights develop slowly. The direction of a flow on a critical manifold, determined by the slow dynamics, decides whether feature unlearning occurs. We give numerical validation of the result, and derive theoretical grounding and scaling laws of the feature unlearning. Our results yield the following insights: (i) the strength of the primary nonlinear term in data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning. Technically, our analysis utilizes Tensor Programs and the singular perturbation theory.
Social Aspects · Accountability, Transparency, and Interpretability
Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as *error slices*. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce *CB-SLICE*, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword-concepts most responsible for each slice’s failure-mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.
Probabilistic Methods · Monte Carlo and Sampling Methods
We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie alge- bra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines.
Theory · Reinforcement Learning and Planning
We study reinforcement learning with delayed state observation, where the agent observes the current state after some random number of time steps. We propose an algorithm that combines the augmentation method and the upper confidence bound approach. For tabular Markov decision processes (MDPs), we derive a regret bound of $\tilde{\mathcal{O}}(H \sqrt{D_{\max} SAK})$, where $S$ and $A$ are the cardinalities of the state and action spaces, $H$ is the time horizon, $K$ is the number of episodes, and $D_{\max}$ is the maximum length of the delay. We also provide a matching lower bound up to logarithmic factors, showing the optimality of our approach. Our analytical framework formulates this problem as a special case of a broader class of MDPs, where their transition dynamics decompose into a known component and an unknown but structured component. We establish general results for this abstract setting, which may be of independent interest.
Applications · Computer Vision
Open-Vocabulary Aerial Detection (OVAD) and Remote Sensing Visual Grounding (RSVG) have emerged as two key paradigms for aerial scene understanding. However, each paradigm suffers from inherent limitations when operating in isolation: OVAD is restricted to coarse category-level semantics, while RSVG is structurally limited to single-target localization. These limitations prevent existing methods from simultaneously supporting rich semantic understanding and multi-target detection. To address this, we propose OTA-Det, the first unified framework that bridges both paradigms into a cohesive architecture. Specifically, we introduce a task reformulation strategy that unifies task objectives and supervision mechanisms, enabling joint training across datasets from both paradigms with dense supervision signals. Furthermore, we propose a dense semantic alignment strategy that establishes explicit correspondence at multiple granularities, from holistic expressions to individual attributes, enabling fine-grained semantic understanding. To ensure real-time efficiency, OTA-Det builds upon the RT-DETR architecture, extending it from closed-set detection to open-text detection by introducing several high efficient modules, achieving state-of-the-art performance on six benchmarks spanning both OVAD and RSVG tasks while maintaining real-time inference at 34 FPS.
Deep Learning · Everything Else
Model fusion aims to combine the knowledge of multiple models by creating one representative model that captures the strengths of all of its parents. However, this process is non-trivial due to differences in internal representations, which can stem from permutation invariance, random initialization, or differently distributed training data. We present a novel, neuron-centric family of model fusion algorithms designed to integrate multiple trained neural networks into a single network effectively regardless of training data distribution. Our algorithms group intermediate neurons of parent models to create target representations that the fused model approximates with its corresponding sub-network. Unlike prior approaches, our approach incorporates neuron attribution scores into the fusion process. Furthermore, our algorithms can generalize to arbitrary layer types. Experimental results on various benchmark datasets demonstrate that our algorithms consistently outperform previous fusion techniques, particularly in zero-shot and non-IID fusion scenarios. We make our code publicly available.
Reinforcement Learning · Multi-agent
The Policy-Space Response Oracles (PSRO) framework scales equilibrium computation to large zero-sum games by iteratively expanding a restricted strategy set using deep reinforcement learning (DRL). A central challenge is to construct, under limited computational budgets, a small strategy population whose induced game well approximates the full game. Existing PSRO variants typically expand the population using best responses to meta-strategies computed from restricted-game payoffs, which can lead to inefficient expansions that provide limited global improvement. We propose to guide population expansion by directly evaluating the post-expansion population quality. Specifically, we adopt Population Exploitability (PE) to measure how well a restricted strategy set represents the full game, and introduce a two-phase exploration--selection framework that explicitly minimizes PE during expansion. We instantiate this framework as Global PSRO, a practical DRL-based algorithm that efficiently generates candidate responses and estimates PE via parameter-sharing conditional neural networks. Experiments across multiple two-player zero-sum games show that Global PSRO achieves lower exploitability and approximates Nash equilibria with significantly fewer policy iterations than prior PSRO methods.
Deep Learning · Everything Else
While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through complex, computationally intensive designs. We introduce the Platonic Transformer to resolve this trade-off. By defining attention relative to reference frames from the Platonic solid symmetry groups, our method induces a principled weight-sharing scheme. This enables combined equivariance to continuous translations and Platonic symmetries, while preserving the exact architecture and computational cost of a standard Transformer. Furthermore, we show that this attention is formally equivalent to a dynamic group convolution, which reveals that the model learns adaptive geometric filters and enables a *highly scalable, linear-time convolutional variant*. Across diverse benchmarks in computer vision (CIFAR-10), 3D point clouds (ScanObjectNN), and molecular dynamics, property prediction and generation (OMol25, ProteinMD, QM9), the Platonic Transformer achieves competitive performance by leveraging these geometric constraints at no additional cost.
Theory · Online Learning and Bandits
This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime. We quantify MDP complexity using a first-order quantity and several new data-dependent measures for the adversarial regime, including a second-order quantity and a path-length measure, as well as variance-based measures for the stochastic regime. To adapt to these measures, we develop algorithms based on global optimization and policy optimization, both built on optimistic follow-the-regularized-leader with log-barrier regularization. For global optimization, our algorithms achieve first-order, second-order, and path-length regret bounds in the adversarial regime, and in the stochastic regime, they achieve a variance-aware gap-independent bound and a variance-aware gap-dependent bound that is polylogarithmic in the number of episodes. For policy optimization, our algorithms achieve the same data- and variance-dependent adaptivity, up to a factor of the episode horizon, by exploiting a new optimistic $Q$-function estimator. Finally, we establish regret lower bounds in terms of data-dependent complexity measures for the adversarial regime and a variance measure for the stochastic regime, implying that the regret upper bounds achieved by the global-optimization approach are nearly optimal.
Deep Learning · Large Language Models
As large language models are increasingly deployed in high-stakes settings, there is a growing need for tools that audit not only model outputs but also the internal computations that produce them. Circuit analysis is a central approach in mechanistic interpretability, but it is typically target-conditioned, explaining a single prompt paired with a chosen completion. This target-conditioned setup obscures mechanistic heterogeneity and hinders scalable discovery. We introduce distribution-level unsupervised feature discovery, which discovers interpretable clusters across a prompt’s continuation distribution and provides a knob to trade off semantic granularity against mechanistic specificity, without manual target selection. Our method samples continuations, represents each with (i) a semantic embedding and (ii) a mechanistic signature derived from sparse feature attributions, and clusters them via a rate–distortion objective that trades off semantic coherence and mechanistic consistency. We also show that our method has cluster-level causality, which validates the discovery of cluster-level mechanistic representation. Overall, our approach complements circuit analysis and behavioral evaluation by providing a scalable, unsupervised audit of the mechanisms underlying a model’s continuation distribution.
General Machine Learning · Methodology
We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure. Specifically, CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation operators. Consequently, the proposed regularization improves the robustness to local geometric variations. We further prove that the resulting CDOT discrepancy is a valid pseudometric on the space of attributed compact metric-measure spaces. In addition, we characterize the relationship between CDOT and Gromov--Wasserstien (GW) through a new notion of dispersion gap, formally elucidating the geometric source of non-convexity in GW compared to the convexity of CDOT. In the finite-sample regime, we derive a non-asymptotic risk bound decomposed into optimization and statistical errors, establishing risk consistency under a globally convergent Frank--Wolfe algorithm. Experiments on synthetic point clouds, brain connectomes, and graph classification benchmarks demonstrate better performance over existing methods, with stable and reliable behavior in practice.
General Machine Learning · Evaluation
Evaluating long-context language models on natural language conflates architectural capacity to capture dependencies with semantic knowledge and vocabulary statistics. When models fail at long contexts, we cannot determine whether failures stem from fundamental architectural limitations or insufficient domain knowledge, preventing clean diagnosis of efficient architectures before expensive training on real data. We introduce **L-CUBE** (Long-Context Utilization Benchmark), a synthetic benchmark that isolates dependency-capturing capacity from semantic knowledge through hierarchical Gaussian sequences with controllable bipartite mutual information scaling. The generator provides exact ground-truth conditionals that scale efficiently to arbitrarily long sequences, enabling unconfounded evaluation via conditional KL divergence rather than perplexity alone. We define *long-context utilization* to measure the amount of available predictive information that models extract as context grows. Experiments across transformers, state space models, and efficient alternatives validate L²M capacity theory predictions and uncover new phenomena. L-CUBE enables practitioners to test whether a particular design will maintain long-context capability at target sequence lengths before committing to real-data training.
Social Aspects · Alignment
Pre-trained Large Language Models (LLMs) are increasingly used for zero-shot annotation and LLM-as-a-judge tasks, yet their reliability hinges on how pre-trained priors interact with user-provided instructions. We investigate three dimensions of this interaction: (1) how an LLM’s familiarity with data and task definitions affects performance, (2) the extent to which additional information in prompts can correct zero-shot errors (“decision stickiness”), and (3) model susceptibility to misaligned task definitions. Through experiments on toxicity detection across diverse datasets (spanning social media, gaming, news, and forums) using both dense and mixture-of-experts models, we find that nearly two-thirds of zero-shot errors are resistant to correction, with an overall rescue rate (fraction of initial errors corrected by prompting) of only 36.4%. High-confidence errors prove especially resistant to correction. When given misaligned definitions, LLMs follow them while maintaining confidence levels unchanged from the aligned condition. Crucially, we introduce Definition-Specific Familiarity (DSF), a metric measuring alignment between a model’s internal concept and the task definition. After controlling for dataset-level confounds, DSF shows positive association with model performance (partial r = +0.34), while text memorization as measured by ROUGE-L shows no positive association (partial r = −0.19). Overall, these findings suggest clear limits on prompt-based correction in annotation tasks and underscore the importance of definition alignment over text-level memorization.
Deep Learning · Large Language Models
Parallel diffusion decoding can accelerate diffusion language model inference by unmasking multiple tokens per step, but aggressive parallelism often harms quality. Revocable decoding mitigates this by rechecking earlier tokens, yet we observe that existing verification schemes frequently trigger flip-flop oscillations, where tokens are remasked and later restored unchanged. This behaviour slows inference in two ways: remasking verified positions weakens the conditioning context for parallel drafting, and repeated remask cycles consume the revision budget with little net progress. We propose COVER (Cache Override Verification for Efficient Revision), which performs leave-one-out verification and stable drafting within a single forward pass. COVER constructs two attention views via KV cache override: selected seeds are masked for verification, while their cached key value states are injected for all other queries to preserve contextual information, with a closed form diagonal correction preventing self leakage at the seed positions. COVER further prioritises seeds using a stability aware score that balances uncertainty, downstream influence, and cache drift, and it adapts the number of verified seeds per step. Across benchmarks, COVER markedly reduces unnecessary revisions and yields faster decoding while preserving output quality.
Theory · Reinforcement Learning and Planning
We introduce OPO-CMDP, the first policy optimization algorithm for stochastic Contextual Markov Decision Process (CMDPs) under general offline function approximation. Our approach achieves a high probability regret bound of $\widetilde{O}(H^4\sqrt{T|S||A|\log(|\mathcal{F}||\mathcal{P}|)}),$ where $S$ and $A$ denote the state and action spaces, $H$ the horizon length, $T$ the number of episodes, and $\mathcal{F}, \mathcal{P}$ the finite function classes used to approximate the losses and dynamics, respectively. This is the first regret bound with optimal dependence on $|S|$ and $|A|$, directly improving the current state-of-the-art (Qian, Hu, and Simchi-Levi, 2024). These results demonstrate that optimistic policy optimization provides a natural, computationally superior and theoretically near-optimal path for solving CMDPs.
Theory · Online Learning and Bandits
We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\top \theta$ where $\theta$ is sampled i.i.d. We show a regret upper bound of $\widetilde{O} (\sqrt{d T \log(K/\delta) \sigma^2_{\max}})$ for a horizon $T$, general action set of size $K$ of dimension $d$, and where $\sigma^2_{\max}$ is the maximal variance of the reward for any action. We further provide a lower bound of $\widetilde{\Omega} (d \sqrt{T \sigma_{\max}^2})$ which is tight (up to logarithmic factors) whenever $\log K \approx d$. For more specific action sets, $\ell_p$ unit balls with $p \leq 2$ and dual norm $q$, we show that the minimax regret is $\widetilde{\Theta} (\sqrt{dT \sigma_q^2})$, where $\sigma_q^2$ is a variance-dependent quantity that is always at most $4$. This is in contrast to the minimax regret attainable for such sets in the classic additive noise model where the regret is of order $d \sqrt{T}$. Surprisingly, we show that this optimal (up to logarithmic factors) regret bound is attainable using a very simple explore-exploit algorithm.
Reinforcement Learning · Everything Else
We study *reward-free* and *reward-agnostic* exploration in episodic finite-horizon Markov decision processes (MDPs), where an agent explores an unknown environment without observing external rewards. Reward-free exploration aims to enable $\epsilon$-optimal policies for *any* reward revealed after exploration, while reward-agnostic exploration targets $\epsilon$-optimality for rewards drawn from a small finite class. In the *reward-agnostic setting*, Li, Yan, Chen, and Fan (2024) achieve minimax sample complexity, but only for restrictively small accuracy parameter $\epsilon$. We propose a new algorithm that significantly relaxes the requirement on $\epsilon$. Our approach is novel and of technical interest by itself. Our algorithm employs an online learning procedure with carefully designed rewards to construct an exploration policy, which is used to gather data sufficient for accurate dynamics estimation and subsequent computation of an $\epsilon$-optimal policy once the reward is revealed. Finally, we establish a tight lower bound for *reward-free exploration*, closing the gap between known upper and lower bounds.
Applications · Chemistry, Physics, and Earth Sciences
Diffusion models typically operate in fixed-dimensional metric spaces, whereas geometric molecular data vary in dimensionality because molecules differ in size (number of atoms). A common adaptation in diffusion models for geometric molecular generation is to use architectures that handle variable-sized inputs, such as graph neural networks and transformers. **However, these approaches ignore that molecular size also sets the spatial scale of atomic coordinates, which induces inconsistent generative trajectories across sizes.** In 3D molecular diffusion, generation can be seen as forming a coarse structure first and then refining atomic positions. Larger molecules form coarse structures earlier than smaller ones because their spatial scales are larger relative to the noise. This makes the generative process inconsistent across sizes, with trajectories driven by molecular size rather than by a unified generative pattern. We are the first to identify and analyze this size-induced inconsistency by decomposing denoising dynamics, showing how spatial scale shapes formation of both 3D structure and atom types. Based on this, we propose Scaling the Prior (StP), which rescales the prior distribution by molecular size to normalize learning and generation across sizes, harmonize denoising trajectories, and enable consistently high-quality molecules.
Optimization · Discrete and Combinatorial Optimization
The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^2$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose **Neural QAOA$^2$**, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach significantly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales.