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Probabilistic Methods · Gaussian Processes

Wenyuan Zhao, Rui Tuo, Chao Tian

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse inducing kernel approximations based on a dyadic ordered template basis, incurring only ${O}(\log M)$ complexity dependence on the number of inducing points. Our approach constructs compact and expressive kernel representations from sparsely activated bases, enabling efficient tensorized GPU computation and seamless integration with modern large-scale models. SIKA-GP can be naturally embedded into Bayesian neural networks (BNNs) with sparse activations, yielding significant speedups in both training and inference without sacrificing predictive performance. The method naturally extends to deep feature learning, addressing the scalability challenges introduced by deep architectures and high-dimensional feature representations. Empirical results on vision and transformer-based language benchmarks demonstrate that our approach consistently delivers fast and accurate GP models, providing a principled path toward scalable kernel learning.

Deep Learning · Graph Neural Networks

Chendi Qian, Christopher Morris, Stefanie Jegelka, Christian Sohler

There has been a growing interest in using neural networks, especially message-passing neural networks (MPNNs), to solve hard combinatorial optimization problems heuristically. However, existing learning-based approaches for hard combinatorial optimization tasks often rely on supervised training data, reinforcement learning, or gradient estimators, leading to significant computational overhead, unstable training, or a lack of provable performance guarantees. In contrast, classical approximation algorithms offer such performance guarantees under worst-case inputs but are non-differentiable and unable to adaptively exploit structural regularities in natural input distributions. We address this dichotomy with the fundamental example of Uniform Facility Location (UniFL), a variant of the combinatorial facility location problem with applications in clustering, data summarization, logistics and supply chain design. We develop a fully differentiable MPNN model that embeds approximation-algorithmic principles while avoiding the need for solver supervision or discrete relaxations. Our approach admits provable approximation and size generalization guarantees to much larger instances than seen during training. Empirically, we show that our approach outperforms standard non-learned approximation algorithms in terms of solution quality, closing the gap with computationally intensive integer linear programming approaches. Overall, this work provides a step toward bridging learning-based methods and approximation algorithms for discrete optimization.

Jiaqi Jin, Siwei Wang, Taichun Zhou, Dong Zhibin, Siqi Wang, Miaomiao Li, Xinwang Liu, En Zhu

In incomplete multi-view clustering, unbalanced missingness is prevalent, where different views exhibit significantly varying missing rates, causing severe observation bias. This imbalance poses two core challenges: models develop serious learning biases by over-relying on low-missing-rate views while neglecting high-missing-rate ones, and cross-view data recovery becomes extremely difficult due to sparse training samples in highly missing views, leading traditional generation methods into a "data starvation" dilemma. Existing methods either naively assume low-missing-rate views as high-quality or lack effective debiasing mechanisms, showing limited performance under imbalance. To address this, we propose the Causal-Invariant Meta-Learning Network (CIMLN). It employs a meta-learning paradigm to transfer knowledge across views, using complete samples as support sets to guide generation for highly missing views. Meanwhile, it incorporates a causal inference framework with counterfactual reasoning and adversarial intervention strategies to eliminate spurious dependencies on observation patterns, learning causally invariant clustering structures. These modules synergistically optimize to ensure generated representations possess both feature fidelity and clustering discriminability. Extensive experiments on benchmarks demonstrate the effectiveness of CIMLN.

Applications · Health / Medicine

Yifan Lin, Kevin Lin

High-dimensional genomics studies are frequently confounded by unmeasured biological processes that obscure disease-specific signals. While existing workflows can estimate these latent confounders, they fail to quantify how robust a discovery is to varying levels of hypothetical confounding. We introduce sensGAN, a deep-learning adversarial framework that systematically explores the confounding spectrum by learning "worst-case" latent variables that nullify the most gene associations under novel predictive-gain constraints. By identifying the minimum confounding strength required to explain away an observed effect, our method shifts the paradigm toward a formal, quantitative sensitivity analysis. In diverse simulations, sensGAN accurately recovers latent structures and outperforms existing methods in identifying confounder-sensitive genes. Applied to human Alzheimer's disease microglia, our framework prioritizes robust disease pathways while successfully isolating signals driven by unmeasured co-occurring neurodegenerative pathologies.

Deep Learning · Generative Models and Autoencoders

Zhiqi Li, Yuchen Sun, Duowen Chen, Jinjin He, Bo Zhu

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory consistency constraint, which is difficult to supervise and optimize over long time scales, with a principled linear surrogate that enables direct data supervision for long-horizon flow-map compositions. We derive this approximation from the semigroup formulation of flow-based models and show that, under mild regularity assumptions, it faithfully approximates the original consistency objective while being substantially easier to optimize. This formulation leads to a unified, JVP-free training framework that supports both $u$-prediction and $x_1$-prediction variants, avoiding explicit Jacobian computations and significantly reducing memory and computational overhead. Experiments on image synthesis, particle-based geometry generation, and functional generation demonstrate improved optimization stability and sample quality under fixed sampling budgets, together with approximately $50\%$ reductions in training time and memory consumption compared to existing one-step methods for image generation.

Theory · Learning Theory

Sophia Pi, Mingcheng Lu, Jerry Yao-Chieh Hu, Maojiang Su, Weimin Wu, Han Liu

We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first- and higher-order flow matching and ties model complexity to the intrinsic manifold dimension. Building on these, we establish tighter sample-complexity bounds for velocity approximation, velocity estimation, and distribution estimation. These bounds meet near-minimax rates for flow-matching transformers of any order. Our results show how flow-matching transformers escape the curse of dimensionality by utilizing intrinsic data structure.

Social Aspects · Accountability, Transparency, and Interpretability

Yining Jiao, Shankar Bhamidi, Carlton ZDANSKI, Julia Kimbell, Andrew Prince, Cameron Worden, Samuel Kirse, Christopher Rutter, Benjamin Shields, William Dunn 等

Understanding how anatomical shapes evolve in response to developmental covariates—and quantifying their spatially varying uncertainties—is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce \texttt{PRISM}, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. \texttt{PRISM} models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate \texttt{PRISM}'s strong performance across diverse tasks—from modeling shape evolution to anomaly detection—within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

Probabilistic Methods · Everything Else

Sammy Sharief, Justine Zeghal, Gabriel Missael Barco, Pablo Lemos, Yashar Hezaveh, Laurence Perreault-Levasseur

We present Mira, a method for estimating the expected probability that samples from a candidate conditional distribution match the true, unknown conditional distribution, for which only data-label pairs are available. We derive theoretical bounds obtained when the candidate distribution matches the true one and when the conditional distributions are independent. This framework thus enables model comparison by quantifying the alignment between the conditional distribution of a candidate model and the data-label pairs of the true model. Consequently, Mira enables Bayesian model comparison through direct posterior validation, bypassing the challenging evidence computation. We demonstrate its effectiveness across several toy problems and Bayesian inference tasks.

Reinforcement Learning · Everything Else

Xincheng Shi, Changxiao Ma, Yuzhuo Ma, Yongfei Zhang, Rongye Shi

Person re-identification (ReID) models are sensitive to long-tail nuisances (e.g., rare viewpoints, occlusions, complex backgrounds), yet current generative augmentation is largely open-loop: prompts/conditions are sampled heuristically without verifying whether the synthesized samples improve ReID discriminability. We introduce ReasonAug, a closed-loop framework that learns an image-conditioned instruction policy for a frozen generator, turning augmentation into a sequential decision problem over instruction tokens. A Semantic Reasoning Agent (SRA) performs hierarchical planning from global semantics to identity-critical local cues, producing structured edit instructions whose utility is verified by downstream ReID feedback. To make closed-loop optimization reliable, we propose Metric-Aligned Gated Reward (MAGR), which converts metric-learning objectives into a dense reward while gating task shaping by identity preservation to prevent reward hacking, and Structure-Aware Entropy (SAE), which allocates exploration per token to lock identity-critical cues while diversifying nuisance factors. Experiments on Market-1501 and MSMT17 demonstrate state-of-the-art performance, confirming that closing the augmentation loop and learning what to generate yield more discriminative training data than open-loop alternatives.

Reinforcement Learning · Policy Search

Doyeon Lee, Eunyi Lyou, Hyunsoo Cho, Soo Kyung Kim, Joonseok Lee, Jaemoo Choi

GRPO-style reinforcement learning (RL)-based LLM fine-tuning algorithms have recently gained popularity. Relying on heuristic trust-region approximations, however, they can lead to brittle optimization behavior, as global importance-ratio clipping and group-wise normalization fail to regulate samples whose importance ratios fall outside the clipping range. We propose Query-Adaptive Trust-Region policy Optimization (QUATRO), which directly enforces trust-region constraints through a principled optimization. This yields a clear and interpretable objective that enables explicit control over policy updates and stable, entropy-controlled optimization, with a stabilizer terms arising intrinsically from the exact trust-region formulation. Empirically verified on diverse mathematical reasoning benchmarks, QUATRO shows stable training under increased policy staleness and aggressive learning rates, maintaining well-controlled entropy throughout training.

General Machine Learning · Transfer, Multitask and Meta-learning

Zhiming Zhang, Rong Yin, Xiaoshuai Hao, Hansong Zhang, Hao Peng, Yong Liu, Can Ma, Dan Meng

Merging multiple low-rank adapters (LoRA) provides a practical route to scaling multi-task learning and deployment more efficiently than full-model weight merging, while avoiding reliance on task-specific training data. However, most existing approaches either treat LoRA updates as dense weight deltas or depend on expensive subspace factorizations, making the merge step a primary latency bottleneck. To address this issue, this paper establishes a theoretically positive relationship between merging quality and the effective rank of the matrices being merged. Motivated by this insight, we propose **CircuMerge**, a sketch-based framework for low-rank model merging built on shared circulant transforms. Especially, this approach treats each adapter as a pair of low-rank matrices and applies a shared circulant transform to align all tasks in a common coordinate system. This alignment enables more efficient sampling, allowing us to generate compact sketches that effectively summarize the interactions between tasks. These compact sketches enable applying the merging rules directly to them and reconstructing a standard low-rank adapter, preserving the essential information while significantly reducing computational overhead. Across a broad multi-task LoRA benchmarks covering both vision and language settings, extensive empirical results demonstrate that CircuMerge reduces the overall merging time by at least 44\% compared to the state-of-the-art approaches, with accuracy matching or exceeding the optimal level.

Deep Learning · Large Language Models

Lizhuo Luo, Shenggui Li, Yonggang Wen, Tianwei Zhang

Diffusion large language models (dLLMs) have emerged as a promising alternative for text generation, distinguished by their native support for parallel decoding. In practice, block inference is crucial for avoiding order misalignment in global bidirectional decoding and improving output quality. However, the widely-used fixed, predefined block (naive) schedule is agnostic to semantic difficulty, making it a suboptimal strategy for both quality and efficiency: it can force premature commitments to uncertain positions while delaying easy positions near block boundaries. In this work, we analyze the limitations of naive block scheduling and disclose the importance of dynamically adapting the schedule to semantic difficulty for reliable and efficient inference. Motivated by this, we propose **Dynamic Sliding Block (DSB)**, a training-free block scheduling method that uses a sliding block with a dynamic size to overcome the rigidity of the naive block. To further improve efficiency, we introduce **DSB Cache**, a training-free KV-cache mechanism tailored to DSB. Extensive experiments across multiple models and benchmarks demonstrate that DSB, together with DSB Cache, consistently improves both generation quality and inference efficiency for dLLMs.

Deep Learning · Large Language Models

Luca Moschella, Laura Manduchi, Ozan Sener

The growing size of Large Language Models (LLMs) makes efficient inference challenging, primarily due to the memory demands of the autoregressive Key-Value (KV) cache. Existing eviction or compression methods reduce cost but rely on heuristics, such as recency or past attention scores, which serve only as indirect proxies for a token’s future utility and introduce computational overhead. We reframe KV cache eviction as a reinforcement learning (RL) problem: learning to rank tokens by their predicted usefulness for future decoding. To this end, we introduce KV Policy (KVP), a framework of lightweight per-head RL agents trained on pre-computed generation traces using only key and value vectors. Each agent learns a specialized eviction policy guided by a holistic reward, derived from future utility, that evaluates the quality of the ranking across all cache budgets, requiring no modifications to the underlying LLM or additional inference. Evaluated across two different model families on the long-context benchmark RULER and the multi-turn dialogue benchmark OASST2-4k, KVP significantly outperforms baselines. Furthermore, zero-shot tests on standard downstream tasks (e.g., LongBench, BOOLQ, ARC) indicate that KVP generalizes well beyond its training distribution and to longer sequence lengths. These results demonstrate that learning to predict future token utility is a powerful and scalable paradigm for adaptive KV cache management.

Deep Learning · Algorithms

Hans Gundlach, Hrvoje Kukina, Jayson Lynch, Neil Thompson

Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion based on a first-of-its-kind survey of quantum algorithms and how they match potential deep learning applications. This survey reveals three important areas where quantum computing could potentially accelerate deep learning, each of which faces a challenging roadblock to realizing its potential. First, quantum algorithms for matrix multiplication and other algorithms central to deep learning offer small theoretical improvements in the number of operations needed, but this advantage is overwhelmed on practical problem sizes by how slowly quantum computers do each operation. Second, some promising quantum algorithms depend on practical Quantum Random Access Memory (QRAM), which is underdeveloped. Finally, there are quantum algorithms that offer large theoretical advantages, but which are only applicable to special cases, limiting their practical benefits. In each of these areas, we support our arguments using quantitative forecasts of quantum advantage that build on the work by Choi et al. (2023) as well as new research on limitations and quantum hardware trends. Our analysis outlines the current scope of quantum deep learning and points to research directions that could lead to greater practical advances in the field.

Masahiro Kato

We propose \emph{ScoreMatchingRiesz}, a family of Riesz representer estimators based on score matching. The Riesz representer is a key nuisance component in debiased machine learning, enabling $\sqrt{n}$-consistent and asymptotically efficient estimation of causal and structural targets via Neyman-orthogonal scores. We formulate Riesz representer estimation as a score estimation problem. This perspective stabilizes representer estimation by allowing us to leverage denoising score matching and telescoping density ratio estimation. We also introduce the policy path, a parameter that captures how policy effects evolve under continuous treatments. We show that the policy path can be estimated via score matching by smoothly connecting average marginal effect (AME) and average policy effect (APE) estimation, which improves the interpretability of policy effects.

Applications · Computer Vision

Jiaxu Leng, Jiankang Zheng, Mengjingcheng Mo, Zhanjie Wu, Haosheng Chen, Ji Gan, Xinbo Gao

Video anomaly detection (VAD) with multimodal large language models has shown strong potential, yet most existing methods still depend on large-scale annotations or expert-designed priors, limiting their ability to acquire anomaly knowledge with as little human intervention as possible. To address this, we propose Linguistic Relative Policy Optimization (LRPO), which distills group-relative semantic advantages from multiple reasoning trajectories into a linguistically expressed anomaly experience prior, and adapts the model by injecting this prior into the context to steer its output distribution without any parameter updates. LRPO builds two complementary experience representations: general experience captures transferable anomaly preferences across scenarios, while scenario experience models context-dependent anomaly rules for targeted refinement. To further improve the learned experience, we introduce an anomaly alignment reward that guides trajectory optimization to match human risk preferences and reinforce temporally grounded reasoning. Extensive experiments on XD-Violence, UCF-Crime, and UBNormal demonstrate that LRPO significantly outperforms existing state-of-the-art methods under tuning-free settings.

Social Aspects · Alignment

Nora Petrova, John Burden

Evaluating alignment in language models requires testing how they behave under realistic pressure, not just what they claim they would do. While alignment failures increasingly cause real-world harm, comprehensive evaluation frameworks with realistic multi-turn scenarios remain lacking. We introduce an alignment benchmark spanning 904 scenarios across six categories---Honesty, Safety, Non-Manipulation, Robustness, Corrigibility, and Scheming---validated as realistic by human raters. Our scenarios place models under conflicting instructions, simulated tool access, and multi-turn escalation to reveal behavioral tendencies that single-turn evaluations miss. Evaluating 24 frontier models using LLM judges validated against human annotations, we find that even top-performing models exhibit gaps in specific categories, while the majority of models show consistent weaknesses across the board. Factor analysis reveals that alignment behaves as a unified construct (analogous to the g-factor in cognitive research) with models scoring high on one category tending to score high on others. We publicly release the benchmark and an interactive leaderboard to support ongoing evaluation, with plans to expand scenarios in areas where we observe persistent weaknesses and to add new models as they are released.

Theory · Learning Theory

Andrew Ilyas, Joonhyuk Ko, Jingwu Tang, Steven Wu, Jiahao Zhang

Conformal prediction converts any black-box predictor into one with finite-sample, distribution-free coverage guarantees, outputting prediction sets $T(x)$ that contain the true label with probability at least $1-\alpha$. To construct these prediction sets, conformal prediction relies on a randomly sampled ``calibration set'' of labeled examples. In many applications, however, this labeled calibration set is costly to collect, creating a tradeoff between upfront labeling cost and downstream utility of the conformal predictor. In this work, we study *conformal prediction with costly label queries*, where unlabeled examples arrive i.i.d. and labels can be queried one at a time. After $m$ queries, we form a conformal predictor; the upfront cost of this predictor is the calibration set size $m$, and its efficiency is the expected prediction set size $\mathbb{E}|T_m(X)|$. We design an online stopping rule $\hat{m}$ that automatically balances the upfront cost against conformal efficiency *while preserving the original conformal guarantee*. Theoretically, we show that under mild regularity assumptions, the expected total cost of our stopping rule matches the best fixed calibration size in hindsight. Experimentally, we find that our stopping rule reduces cost compared to standard choices of $m$ from the literature by 41.4% $\pm$ 2.3%. Finally, as a concrete application we demonstrate a reduction from CP to the probably approximately correct labeling problem of Candès et al. (2025), under which our stopping rule minimizes the total labeling cost.

Theory · Deep Learning

Michelle Ching, Ioana Popescu, Nico Smith, Tianyi Ma, William Underwood, Richard Samworth

We study in-context learning for nonparametric regression with $\alpha$-Hölder smooth regression functions, for some $\alpha>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained transformer with $\Theta(\log n)$ parameters and $\Omega\bigl(n^{2\alpha/(2\alpha+d)}\log^3 n\bigr)$ pretraining sequences can achieve the minimax-optimal rate of convergence $O\bigl(n^{-2\alpha/(2\alpha+d)}\bigr)$ in mean squared error. Our result requires substantially fewer transformer parameters and pretraining sequences than previous results in the literature. This is achieved by showing that transformers are able to approximate local polynomial estimators efficiently by implementing a kernel-weighted polynomial basis and then running gradient descent.

Applications · Social Sciences

Haofei Yu, Yining Zhao, Guanyu Lin, Jiaxuan You

Understanding and predicting how social beliefs evolve in response to events—from policy changes to scientific breakthroughs—remains a fundamental challenge in social science. Given LLMs’ commonsense knowledge and social intelligence, we ask: *Can LLMs model the dynamics of social beliefs following social events?* In this work, we introduce the concept of the Social World Model (SWM), a general framework designed to capture how social beliefs evolve in response to major events. SWM learns state-transition functions for social beliefs by mining temporal patterns in social data and optimizing evidence lower bound, without the need for explicit human annotations that link events to belief shifts or expensive census data. To evaluate SWM, we introduce a benchmark, SWM-Bench, derived from real-world prediction market data from both Kalshi and Polymarket. SWM-Bench includes over 10k datapoints for social belief prediction tasks spanning diverse domains such as politics, sports, cryptocurrency, and elections. Our experimental results show that SWM significantly outperforms time-series foundation models, achieving RMSE reductions of 8.4% and 11.2% on Polymarket and Kalshi respectively, while offering interpretable insights into the underlying mechanisms of social belief dynamics.