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Reinforcement Learning · Policy Search

Daniel Russo

A widely used technique for improving policies is success conditioning, in which one collects trajectories, identifies those that achieve a desired outcome, and updates the policy to imitate the actions taken along successful trajectories. This principle appears under many names---rejection sampling with SFT, goal-conditioned RL, Decision Transformers---yet what optimization problem it solves, if any, has remained unclear. We prove that success conditioning exactly solves a trust-region optimization problem, maximizing policy improvement subject to a $\chi^2$ divergence constraint whose radius is determined automatically by the data. This yields an identity: relative policy improvement, the magnitude of policy change, and a quantity we call action-influence---measuring how random variation in action choices affects success rates---are exactly equal at every state. Success conditioning thus emerges as a conservative improvement operator. Exact success conditioning cannot degrade performance or induce dangerous distribution shift, but when it fails, it does so observably, by hardly changing the policy at all. We apply our theory to the common practice of return thresholding, showing this can amplify improvement, but at the cost of potential misalignment with the true objective.

Applications · Computer Vision

Senmao Tian, Xiang Wei, Shunli Zhang

Efficient transfer learning of vision–language models (VLMs) commonly suffers from a Base–New Trade-off (BNT): improving performance on unseen (new) classes often degrades accuracy on known (base) classes. Addressing how to boost recognition of unseen classes without sacrificing known-class performance remains a central challenge. Existing work often simplistically attributes the BNT to overfitting on known classes. We observe an interesting phenomenon: VLMs frequently exhibit asymmetric confusion on certain downstream data, i.e., samples of class A are systematically mispredicted as class B, while the reverse confusion (B → A) rarely occurs. For known classes, this kind of bias can be mitigated by tuning using a cross-entropy loss, but for unseen classes, such pretraining-induced bias persists and harms generalization. Motivated by this, we propose NeRP, a plug-and-play prompting correction strategy that improves discrimination on unseen classes without modifying model parameters. NeRP leverages neutral text prompts and reference images to measure class-wise prior preferences along the pre-trained inter-class geometry, and combines them with the sample likelihood to obtain the model’s surrogate score. If, for a given sample, the prior strongly favors the current prediction while the observed evidence is clearly insufficient, we perform a local flip between easily confusable class pairs, thereby correcting prior-dominated mispredictions. Extensive experiments across multiple backbones and 15 few-shot and cross-domain benchmarks show that NeRP substantially improves accuracy on unseen classes while preserving known-class prediction performance.

Optimization · Convex

Alexander Tyurin

We study first‐order methods for convex optimization problems with functions $f$ satisfying the recently proposed $\ell$-smoothness condition $||\nabla^{2}f(x)|| \le \ell\left(||\nabla f(x)||\right),$ which generalizes the $L$-smoothness and $(L_{0},L_{1})$-smoothness. While accelerated gradient descent (AGD) is known to reach the optimal complexity $\mathcal{O}(\sqrt{L} R / \sqrt{\varepsilon})$ under $L$-smoothness, where $\varepsilon$ is an error tolerance and $R$ is the distance between a starting and an optimal point, existing extensions to $\ell$-smoothness either incur extra dependence on the initial gradient, suffer exponential factors in $L_{1} R$, or require costly auxiliary sub-routines, leaving open whether an AGD‐type $\mathcal{O}(\sqrt{\ell(0)} R / \sqrt{\varepsilon})$ rate is possible for small-$\varepsilon$, even in the $(L_{0},L_{1})$-smoothness case. We resolve this open question. Developing new proof techniques, we achieve $\mathcal{O}(\sqrt{\ell(0)} R / \sqrt{\varepsilon})$ oracle complexity for small-$\varepsilon$ and virtually any $\ell$. For instance, for $(L_{0},L_{1})$-smoothness, our bound $\mathcal{O}(\sqrt{L_0} R / \sqrt{\varepsilon})$ is provably optimal in the small-$\varepsilon$ regime and removes all non-constant multiplicative factors present in prior accelerated algorithms.

General Machine Learning · Methodology

Hanyang Jiang, Yao Xie

Reliable uncertainty quantification at unobserved spatial locations is a key challenge in spatial statistics, particularly for complex and heterogeneous datasets. While traditional methods such as Kriging rely on strong distributional assumptions, conformal prediction (CP) offers a distribution-free alternative. However, although non-i.i.d. CP theory is well established for time-series data, a significant gap remains for spatial data, where the lack of a natural ordering and discrete index complicates theoretical guarantees. Existing CP theory for spatial data often relies on exchangeability. We propose Localized Spatial Conformal Prediction (LSCP), a model-agnostic framework that bridges this gap by coupling local quantile regression with conformal calibration. LSCP conditions on spatial neighborhoods to capture local heterogeneity. We show that LSCP retains finite-sample marginal coverage under spatial exchangeability and attains asymptotic conditional coverage under stationarity and spatial mixing. Across synthetic and real datasets, LSCP consistently achieves near-nominal coverage with tighter and more stable prediction intervals than existing methods that fail to capture these spatial dependencies.

Deep Learning · Foundation Models

Hasan Amin, Yuan Gao, Yaser Souri, Subhojit Som, Ming Yin, Rajiv Khanna, Xia Song

Diffusion language models (DLMs) promise sublinear-time generation via parallel decoding, yet realizing this efficiency remains elusive as high-quality sampling typically requires hundreds of refinement steps. In continuous domains, consistency-based training accelerates diffusion by enforcing invariance along a probability flow ODE. However, discrete diffusion admits no such ODE, rendering direct adaptation ill-defined. We bridge this gap with Multi-Path Discrete Consistency (MPDC), a new principle that replaces the non-existent unique trajectory with a distributional ensemble of exact posterior bridges connecting different noise levels. Building on this idea, we introduce the Consistent Diffusion Language Model (CDLM), a general framework that learns path-independent denoisers by enforcing prediction consistency across these stochastic bridges. We show that CDLM unifies and generalizes discrete diffusion, consistency, and distillation objectives within a single view applicable to diverse corruption processes, including both masked and uniform diffusion. Empirically, CDLM establishes a new state of the art on conditional and unconditional text-generation benchmarks, consistently outperforming strong base DLMs and often even multi-stage distilled baselines, with particularly large gains in the few-step regime. Together, these results position CDLM as a principled and scalable paradigm for efficient, high-fidelity discrete generative modeling.

Applications · Computer Vision

Xuan Yao, Yuze Zhu, JUNYU GAO, Zongmeng Wang, Changsheng Xu

Vision-and-Language Navigation in Continuous Environments (VLN-CE) requires agents to make fine-grained navigation decisions under partial observability. However, most existing methods rely on open-loop execution, lacking mechanisms to detect and correct internal state drift during inference. We propose SC$^{2}$-WM, a self-correcting world model framework that introduces internal feedback for closed-loop decision making in VLN-CE. Our method derives feedback from world-model foresight to perform state-level plan refinement before action execution. To handle challenging scenarios, we further introduce conditional world-aware adaptation, which enables model-level correction by selectively updating the world model at test time when feedback indicates model capacity insufficiency. Experiments on standard VLN-CE benchmarks demonstrate improved navigation robustness and generalization. Code is available in the Supplementary Material.

Theory · Online Learning and Bandits

VIKAS DEEP, Shubhada Agrawal

We revisit the problem of sequentially testing the mean of bounded distributions in a level-$\alpha$ power-one framework. We study a $\mathrm{KL_{inf}}$-based sequential test that is known to attain the information-theoretic lower bound on the expected stopping time with exact constants as $\alpha \to 0$. Going beyond first-order asymptotics, we establish a central limit theorem (CLT) for the stopping time of this test. Our analysis proceeds in two steps. First, we prove a novel CLT for the $\mathrm{KL_{inf}}$ statistic itself, characterizing its fluctuations around its deterministic linear growth. We then leverage this result to show that the stopping time, centered appropriately, and scaled by $\sqrt{\log(1/\alpha)}$, converges in distribution to a Gaussian limit with an explicit variance. This yields a second-order characterization of an asymptotically optimal sequential test for bounded distributions. Finally, we present numerical experiments that corroborate our theoretical findings.

Arwen Bradley

Conditional diffusion models appear capable of compositional generalization, i.e., generating convincing samples for out-of-distribution combinations of conditioners, but the mechanisms underlying this ability remain unclear. To make this concrete, we study length generalization, the ability to generate images with more objects than seen during training. In a controlled CLEVR setting (Johnson et al., 2017), we find that length generalization is achievable in some cases but not others, suggesting that models only sometimes learn the underlying compositional structure. We then investigate locality as a structural mechanism for compositional generalization. Prior works proposed score locality as a mechanism for creativity in unconditional diffusion models (Kamb & Ganguli, 2024; Niedoba et al., 2024), but did not address flexible conditioning or compositional generalization. In this paper, we prove an exact equivalence between a specific compositional structure (*conditional projective composition*) (Bradley et al., 2025) and scores with sparse dependencies on both pixels and conditioners (*local conditional scores*). This theory also extends to compositions of concepts (such as style+content) in feature-space. We validate our theory empirically: CLEVR models that succeed at length generalization exhibit local conditional scores, while those that fail do not. Furthermore, we show that a causal intervention explicitly enforcing local conditional scores enables length generalization in a previously failing model. Finally, we investigate feature-space compositionality in color-conditioned CLEVR, and find preliminary evidence of compositional structure and corresponding local mechanisms in SDXL.

Gen Li, Changxiao Cai, Yuting Wei

Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for accurate sample generation should scale linearly with data dimension, this does not reflect the practical efficiency of widely used algorithms like Denoising Diffusion Probabilistic Models (DDPMs). This paper investigates the effectiveness of diffusion models in sampling complex high-dimensional distributions that can be well-approximated by Gaussian Mixture Models (GMMs). For these distributions, our main result shows that DDPM takes at most $\widetilde{O}(1/\varepsilon)$ iterations to attain an $\varepsilon$-accurate distribution in total variation (TV) distance, independent of both the ambient dimension $d$ and the number of components $K$, up to logarithmic factors. Furthermore, this result remains robust to score estimation errors. These findings highlight the remarkable effectiveness of diffusion models in high-dimensional settings given the universal approximation capability of GMMs, and provide theoretical insights into their practical success.

Pierre-Louis Cauvin, Panayotis Mertikopoulos

We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time model of SMD as a stochastic differential equation (SDE) driven by a centered Lévy noise process with finite $p$-th order moments, $1 < p \leq 2$. This scheme---which we call the Lévy mirror flow (LMF)---arises naturally as the scaling limit of SMD in the presence of heavy-tailed noise. In particular, when $p < 2$---the heavy noise regime---the trajectories of LMF generically exhibit jump discontinuities of arbitrary magnitude which, if frequent enough, lead to infinite variance. Nonetheless, despite this highly singular behavior, we show that LMF attains $\epsilon$-optimality within $\mathcal{O}(\epsilon^{-p/(p-1)})$ time in the convex case, and within $\tilde{\mathcal{O}}(\epsilon^{-1/(p-1)})$ time for (relatively) strongly convex objectives. These guarantees provide a transparent characterization of the impact of frequent long jumps on the convergence of the process, and percolate to a series of matching discrete-time guarantees for several variants of SMD under heavy-tailed noise.

Probabilistic Methods · Monte Carlo and Sampling Methods

Jie Hu, Lingyun Chen, Geeho Kim, Jinyoung Choi, Bohyung Han, Do-Young Eun

History-dependent sampling can reduce long-run Monte Carlo variance by discouraging redundant revisits, but existing schemes typically encode history through empirical measure on finite state spaces, which is infeasible in high-dimensional discrete configuration spaces or ill-posed in continuous domains. We propose *Score-Repellent Monte Carlo* (SRMC) framework that summarizes trajectory history by a fixed, $d$-dimensional running average of score evaluations and converts it into a history-dependent surrogate target via an exponential *score tilt*. The resulting surrogate family is normalization-free in the standard MCMC sense, yielding a generic wrapper: at each iteration, any standard base kernel designed for the target $\pi$ can be run on the current surrogate $\pi_{\theta_n}$ while updating the history online. We analyze the coupled evolution of any estimator and the history recursion using stochastic approximation with controlled Markovian noise, establishing almost sure convergence and a joint central limit theorem. We identify regimes where the asymptotic covariance decreases as the repellence strength $\alpha$ increases, exhibiting a scaling of $O(1/\alpha)$, reproducing near-zero variance effect but now on general state spaces with constant memory. Empirical results across continuous targets and discrete energy-based models demonstrate that SRMC delivers notable improvements in estimator variance and in effectively covering modes in Gaussian mixtures, all while retaining $O(d)$ memory usage and minimal overhead per iteration.

Zhao Mandi, Yifan Hou, Dieter Fox, Yashraj Narang, Ajay Mandlekar, shuran song

We study the problem of functional retargeting: learning dexterous manipulation policies to track object states from human hand-object demonstrations. We focus on long-horizon, bimanual tasks with articulated objects, which are challenging due to large action space, spatiotemporal discontinuities, and the embodiment gap between human and robot hands. We propose DexMachina, a novel curriculum-based algorithm: the key idea is to use virtual object controllers with decaying strength: an object is first driven automatically towards its target states, such that the policy can gradually learn to take over under motion and contact guidance. We release a simulation benchmark with a diverse set of tasks and dexterous hands, and show that DexMachina significantly outperforms baseline methods. Our algorithm and benchmark enable a functional comparison for hardware designs, and we present key findings informed by quantitative and qualitative results. With the recent surge in dexterous hand development, we hope this work will provide a useful platform for identifying desirable hardware capabilities and lower the barrier for contributing to future research. Videos and more at \url{dexmachina-submission.github.io}

Deep Learning · Theory

Amit Daniely

We consider supervised learning with $n$ labels and show that layerwise SGD on residual networks can efficiently learn a class of hierarchical models. This model class assumes the existence of an (unknown) label hierarchy $L_1 \subseteq L_2 \subseteq \dots \subseteq L_r = [n]$, where labels in $L_1$ are simple functions of the input, while for $i > 1$, labels in $L_i$ are simple functions of simpler labels. Our class surpasses models that were previously shown to be learnable by deep learning algorithms, in the sense that it reaches the depth limit of efficient learnability. That is, there are models in this class that require polynomial depth to express, whereas previous models can be computed by log-depth circuits. Furthermore, we suggest that learnability of such hierarchical models might eventually form a basis for understanding deep learning. Beyond their natural fit for domains where deep learning excels, we argue that the mere existence of human ``teachers" supports the hypothesis that hierarchical structures are inherently available. By providing granular labels, teachers effectively reveal ``hints'' or ``snippets'' of the internal algorithms used by the brain. We formalize this intuition, showing that in a simplified model where a teacher is partially aware of their internal logic, a hierarchical structure emerges that facilitates efficient learnability.

Probabilistic Methods · Monte Carlo and Sampling Methods

Qianqian Qu, Jun Liu

We propose a training-free conditional sampling method for flow matching models based on importance sampling. Because a naïve application of importance sampling suffers from weight degeneracy in high-dimensional settings, we modify and incorporate a resampling technique in sequential Monte Carlo (SMC) during intermediate stages of the generation process. To encourage generated samples to diverge along distinct trajectories, we derive a stochastic flow with adjustable noise strength to replace the deterministic flow at the intermediate stage. Our framework requires no additional training, while providing theoretical guarantees of asymptotic accuracy. Experimentally, our method significantly outperforms existing approaches on conditional sampling tasks for MNIST and CIFAR-10. We further demonstrate the applicability of our approach in higher-dimensional, multimodal settings through text-to-image generation experiments on CelebA-HQ.

Theory · Learning Theory

Yan Zhou

Foundation models provide strong but biased priors for downstream tasks with limited labeled data. We formalize black-box assisted nonparametric regression where $\|f^*-f_0\|_{L_2(P_X)}\le\delta$ for unknown $\delta$. We characterize the minimax risk, revealing a phase transition at $\delta_c(n)\asymp n^{-\beta/(2\beta+d)}$ with optimal rate $\min\{\delta^2, n^{-2\beta/(2\beta+d)}\}$. Our Safe Black-Box Residual Estimator integrates zero-initialization (a strong inductive bias) with a holdout selection mechanism. This approach achieves the minimax rate while avoiding negative transfer. Experiments on synthetic data, CIFAR-100 (CLIP), and AG News (Qwen3-8B) validate the theory, improving sample efficiency (e.g., CIFAR-100 at $n=2000$: from 59.4\% zero-shot to 66.7\%).

Theory · Game Theory

Rubi Hudson

An AI agent will learn a desired goal more effectively if it does not resist the training process, but many partially learned goals incentivize an AI to avoid further goal updates. We would like goals to be corrigible, meaning they allow requested changes, so that we can confidently correct errors and shut down the AI if necessary. Despite this being a crucial safety property, the existing literature does not specify goals that are both corrigible and competitive with alternatives. We introduce a transformation that constructs a corrigible version of nearly any goal, without sacrificing performance. This is done by eliciting predictions of reward conditional on costlessly preventing updates, and having that target be pursued myopically. These goals are then shown to lead to optimal performance among the class of corrigible goals, incentivize allowing mid-action overrides, disincentivize deliberate self-modification, and induce corrigible behavior in gridworld settings.

General Machine Learning · Scalable Algorithms

Khai Nguyen

Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability. In this work, we further enhance computational scalability by proposing the first method for estimating SW from sample streams, called streaming sliced Wasserstein (Stream-SW). To define Stream-SW, we first introduce a streaming estimator of the one-dimensional Wasserstein distance (1DW). Since the 1DW has a closed-form expression, given by the absolute difference between the quantile functions of the compared distributions, we leverage quantile approximation techniques for sample streams to define a streaming 1DW estimator. By applying the streaming 1DW to all projections, we obtain Stream-SW. The key advantage of Stream-SW is its low memory complexity while providing theoretical guarantees on the approximation error. We demonstrate that Stream-SW achieves a more accurate approximation of SW than random subsampling, with lower memory consumption, when comparing Gaussian distributions and mixtures of Gaussians from streaming samples. Additionally, we conduct experiments on point cloud classification, point cloud gradient flows, and streaming change point detection to further highlight the favorable performance of the proposed Stream-SW.

Deep Learning · Theory

Zixuan Wang, Xingyu Dang, Jason Lee, Kaifeng Lyu

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data toward a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn serves as a stepping stone to efficiently learn rare long-tailed skills. Our results offer an alternative perspective on what constitutes an effective data distribution for training models.

Applications · Computer Vision

QuanWei Gao, Shuqi Zhao, Ruyu Wang, Shuyin Zhang, Cong Liu, Zirui Luo

Multimodal fusion object detection faces a substantial modality gap at the same backbone stage. This makes predefined stage-aligned fusion insufficient for cross-stage interactions. We propose MFH-NAS, a hybrid neural architecture search framework that automatically discovers fusion architectures to better leverage cross-modal complementarity. MFH-NAS searches both local fusion primitives and stage-level fusion connectivity. It targets fusion operator design and fusion stage selection. It couples differentiable search with evolutionary search. Differentiable search learns architecture parameters for local fusion primitives. Evolutionary search explores global fusion topologies, including stage selection and cross-stage connection patterns. The joint search balances exploitation and exploration and mitigates premature convergence. It yields fusion structures that strengthen cross-stage interactions.We evaluate MFH-NAS on three public benchmarks, LLVIP, RGBT-Tiny, and M3FD. MFH-NAS consistently outperforms handcrafted fusion-stage designs and prior stage-searching NAS baselines, improving mAP@0.5 from 85.3% to 88.2% over strong fixed-stage fusion methods and delivering gains across all benchmarks.

Stefan Szeider

We consider the computational problem of compacting Tsetlin Machine (TM) classifiers by reducing the number of propositional clauses while preserving predictive accuracy. TMs trained with limited clause capacity often perform poorly because stochastic optimization cannot reliably find the few precise clauses needed in a vast configuration space. High-quality compact subsets also exist for larger TMs. The main challenge is to extract them. Heuristic pruning does not work for TMs because clauses interact through Boolean logic. A clause is unimportant in isolation, but it becomes critical when others are removed. We formalize compression as the Minimum Discriminating Clause Set (MDCS) problem: find the smallest subset of clauses that preserves the trained model's separation of training samples. We prove that MDCS is NP-hard. We solve MDCS via weighted partial Maximum Satisfiability (MaxSAT). A partition-and-merge strategy allows us to scale to 100K samples. MaxSAT compression significantly outperforms direct training on all but one of 13 datasets at matched capacity, with improvements up to 26 percentage points and a median of 6 percentage points.