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版本更新 · v3arXiv:2504.13336

On the minimax optimality of Flow Matching through the connection to kernel density estimation

Lea Kunkel, Mathias Trabs

原文摘要

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different perspective by connecting Flow Matching to kernel density estimation. We first verify that the kernel density estimator matches the optimal rate of convergence in Wasserstein distance up to logarithmic factors, improving existing bounds for the Gaussian kernel. Based on this result, we prove that for sufficiently large networks, Flow Matching achieves the optimal rate up to logarithmic factors. If the target distribution lies on a lower-dimensional manifold, we show that the kernel density estimator profits from the smaller intrinsic dimension on a small tube around the manifold. The faster rate also applies to Flow Matching, providing a theoretical foundation for its empirical success in high-dimensional settings.

stat.ML · cs.LG · math.ST

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.40056

Reinforcement Learning Under Runtime Confounding: Policy Learning and Off-Policy Evaluation

Raphael Kim, Michele Santacatterina, Ramin Zabih, Keith Barnatchez

原文摘要

Reinforcement learning (RL) is increasingly used to train robust, adaptable systems across healthcare, e-commerce, and robotics. In these settings, legal, ethical, or logistical concerns may preclude certain key variables that drive decisions from being collected during deployment time. This gives rise to a setting known as runtime confounding: the logged data hold full observability, but deployment time lacks knowledge of certain variables, known as runtime confounders. Unlike single timepoint and non-adaptive settings, runtime confounding under reinforcement learning has the potential to propagate over time, as earlier decisions affect future states, observations, and action assignments, leading to biased learning. We address these problems with three contributions: we (1) develop policy learning algorithms under runtime-confounding, (2) develop semi-parametric efficient off-policy estimation procedures, and (3) provide diagnostics for understanding the price of runtime confounding.

stat.ML · cs.LG · stat.ME

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.21607

Market Incentives for AI Safety Investment

Nikita Tsoy

原文摘要

Despite their practical significance, modern AI systems pose significant societal risks, including toxicity, malicious use, and misinformation. Their mitigation depends not only on technical feasibility but also on the incentives of firms that develop and deploy these systems. We show how profit maximization shapes safety investment in an AI supply chain with an upstream LLM provider and several competing downstream firms. In our game-theoretic model, we derive the market-driven level of safety investment and compare it with the levels that maximize industry profit and market welfare. We find that downstream competition generally induces downstream firms to invest more in safety than the industry-profit-optimal level. By contrast, the upstream provider may underinvest relative to these benchmarks because it is not fully compensated for the surplus from safety investments. Finally, we analyze how different regulatory interventions affect the participants' incentives and profits, and the resulting levels of model safety.

cs.LG · cs.GT · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39827

Deep Reinforcement Learning for Blind Passive Beamforming in RIS-Assisted MIMO Systems

Oumaïma Bounhar, Thomas Chêne, Ghaya Rekaya-Ben Othman, Oussama Damen

原文摘要

Reconfigurable Intelligent Surfaces (RIS) are a promising solution for improving millimeter-wave (mmWave) communications by controlling signal propagation. Yet, selecting the optimal RIS configuration remains challenging due to the high-dimensional search space and signaling overhead. We propose a Deep Reinforcement Learning (DRL) framework for blind passive beamforming, where a Deep Q-Learning (DQL) agent learns an adaptive policy to select near-optimal RIS configurations while sounding only few codewords, without channel state information. Results show that our approach outperforms Q-Learning (QL) and conventional baselines in convergence, performance, and overhead reduction.

cs.IT · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.36078

Learning on-the-fly quasi-stationarity diagnostics from low-dimensional surrogates

Noé Blassel

原文摘要

Accelerated dynamics methods, such as parallel replica dynamics, require estimates of the decorrelation time, after which a process trapped in one of its metastable states is distributed according to the quasi-stationary distribution (QSD). In a method proposed by Binder, Lelièvre and Simpson, decorrelation times are defined by coupling a particle approximation of the non-linear conditioned probability flow of the process with MCMC-inspired diagnostics. We explore an alternative to MCMC diagnostics, based on coarse-graining of non-linear probability flows and simulation-based inference. We first develop a coarse-graining framework for killed Markov jump processes conditioned on survival, proving uniform-in-time, non-asymptotic estimates approximating the non-linear probability flow of the true process by the non-linear flow of a surrogate process, defined with a collective variable. The framework does not assume reversibility of the true process, and also gives bounds which scale explicitly in an adiabatic regime. Motivated by these results, we then construct a quasi-stationarity diagnostic using simulation-based inference: a recurrent neural network (RNN), trained on particle approximations of non-linear effective flows, estimates posterior probabilities of decorrelation. The learned diagnostic is then transferred to collective-variable traces of high-dimensional particle approximations. We investigate the behavior and robustness of this diagnostic on a set of numerical experiments, comparing it to the MCMC diagnostic of Binder et al.\ on both synthetic examples and a molecular system, in and out of its training prior distribution. When its prior assumptions hold, the RNN diagnostic outperforms the MCMC diagnostic in ROC analysis, is less conservative, fails less often, and has an interpretable decision threshold.

stat.ML · cs.LG · math.PR

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2411.04852

Conformalized Credal Regions for Classification with Ambiguous Ground Truth

Michele Caprio, David Stutz, Shuo Li, Arnaud Doucet

原文摘要

An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39709

Bayes-Consistent Losses for Adaptive Inference in Classification

Shirley Xiaoqi Liu, Florence Regol, Antonios Valkanas, Patrick Rebeschini, Mark Coates

原文摘要

Adaptive inference systems balance accuracy and inference cost by routing inputs to models with varying capabilities. Although jointly training models and routers is empirically more sample-efficient than training them separately, principled losses for joint training remain underexplored. We address this gap in a classification setting by proposing cost-sensitive hinge losses for jointly training classifiers with single-stage or cascade routers. Single-stage routers directly select a model per input, whereas cascade routers sequentially decide at each stage whether to predict with the current model or defer to the next stage, which uses a more accurate but more costly model. For both settings, we prove linear calibration bounds establishing Bayes consistency: minimizing the hinge risk recovers the Bayes-optimal risk under the target cost-sensitive zero-one loss. Moreover, since routers can require more labeled data to train than classifiers, we propose a novel post-training prediction-powered inference (PPI) procedure that uses unlabeled data to refine a trained single-stage router. Experiments on synthetic and real datasets demonstrate that the proposed hinge losses are effective for joint training and that PPI can correct routing errors when labeled data is scarce.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39674

Formalizing the Intrinsic Dimension of Objective Landscapes by a Generalized Notion of Co-dimension

Ernesto Araya, Gitta Kutyniok, Weilin Li, Johannes Maly, Manjot Singh

原文摘要

In this work, we formalize the concept of intrinsic dimension of objective landscapes introduced in Li et al. (2018), which measures the structural complexity of learning problems by training along randomly generated subspaces. We define the intrinsic dimension of a set $Θ\subset\mathbb{R}^p$ as the minimal dimension $d_{\mathrm{int}}(Θ)$ such that a random plane of dimension $d_{\mathrm{int}}(Θ)$ in $\mathbb{R}^p$ intersects $Θ$ with probability one. We show that it is a generalized notion of co-dimension that depends on the global geometry of $Θ$. We study mathematical properties of the intrinsic dimension and develop techniques to estimate the intrinsic dimension of sets $Θ$ that arise in learning problems. More specifically, we derive upper and/or lower bounds where $Θ$ is the set of optimal parameters in student-teacher settings with shallow and deep ReLU networks, including finite and infinite sample cases, and with and without regularization. We discuss how our theory leads to novel types of generalization bounds, thereby showing that the intrinsic dimension is a measure of learning complexity. Our results connect techniques from seemingly different areas of machine learning research such as classification of symmetries of ReLU networks and stochastic geometry.

stat.ML · cs.LG · math.MG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2510.09177

Distributionally robust approximation property of neural networks

Mihriban Ceylan, David J. Prömel

原文摘要

The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional $L^p$-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks.

stat.ML · cs.LG · math.FA · math.PR

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2608.19491

Activation-Keyed Momentum: An Anisotropic Momentum Update via the Delta Rule

Euijin Hong, Guannan Qu

原文摘要

Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate. However, the inputs a deep network sees during training can be highly anisotropic, with a few directions queried frequently while most are seen rarely. Preconditioning methods address this anisotropy by wrapping extra processing around this buffer and leave the momentum update itself unchanged. We propose Activation-Keyed Momentum (AK-Momentum), which builds direction-awareness into the momentum update rule. The gradient of a linear layer splits into an input activation that acts as a $\textit{key}$ and an output-side error that acts as a $\textit{value}$. Keying on that activation, AK-Momentum updates the momentum buffer by the canonical delta rule, so each direction is forgotten at a rate set by how often it appears. We prove that it is a valid momentum, that it applies the input-side curvature correction without matrix inversion, and that it clears stale directions faster than EMA under both a fixed and a drifting optimum. It is a drop-in replacement for the momentum buffer of any optimizer, its coefficient transfers across widths under $μ$P, and its extra compute stays between $22.2\%$ and $25.0\%$ of a gated-MLP block's linear cost with no persistent memory. In FineWeb-Edu pretraining, AdamW with AK-Momentum (AK-AdamW) reaches AdamW's validation loss in up to $46.64 \pm 4.52\%$ fewer steps at 67M and $22.14 \pm 0.81\%$ at 370M over three seeds, and the gain persists at 1B on a Chinchilla-optimal budget. A Muon baseline tuned under the same protocol sits above AK-AdamW at both language-model scales, and the gain holds for SGD, ResNet-18, and ViT-Tiny on CIFAR-10. Training-time diagnostics confirm the predicted mechanism, better gradient tracking and healthier input directions. Code is available at https://github.com/euijinh/AK-Momentum.

cs.LG · cs.CL · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2512.03062

FermiGrad-SVD: An LLM Compression Pipeline with Global Rank Selection and Gauge Fixing

Roman Rausch, David Jansen, Sukhbinder Singh, Román Orús

原文摘要

Low-rank factorization of weight matrices is a promising approach to compress large language models (LLMs), but its practical effectiveness depends on allocating ranks across layers and efficiently representing the resulting factors. We introduce three complementary methods for improving SVD-based LLM compression. First, FermiGrad formulates global layer-wise rank allocation as a differentiable optimization problem by replacing discrete singular-value truncation with continuous Fermi gates. Because FermiGrad optimizes only rank parameters over precomputed low-rank factors, it avoids repeated activation decompositions and backpropagation through SVD operations. Second, the Targeted Compressor extends FermiGrad with a task-specific objective that directs limited model capacity toward a selected domain. At 60% parameter density for Llama-3.1-8B-Instruct, SciQ-targeted compression achieves 60% MMLU accuracy, exceeding the reported quantized Dobi-SVD result by 10 percentage points, while deliberately trading performance on unrelated tasks for domain specialization. Third, PivGa provides a lossless secondary compression of low-rank factors by exploiting the gauge freedom in their parametrization. The proposed framework is modular, computationally efficient, and applicable at scale, as demonstrated by compressing Llama-3.3-70B-Instruct to 50% parameter density.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39614

Emergence of the transformer architecture as the score of entropic laws of random measures

Giacomo Greco

原文摘要

We show that the transformer architecture emerges as the score of last-token laws in a natural statistical model of language, where sentences are empirical measures of tokens, a language is a law on $P(S^d)$, and our prior belief is that sentences carry no structure at all. By the maximum-entropy principle, we select the law closest to this prior in relative entropy among those reproducing an observed sentence-level statistic. We discuss the relevance of the statistic in the posterior interaction between tokens and we build a statistic, able to capture that interaction, with Luce's choice axiom truncated at the lowest relational order. This procedure gives the softmax choice rule, with the attention cross-moment as its mean parameter. The query--key matrix is then the Lagrange multiplier of a maximum-entropy problem inside each sentence, and the value matrix the multiplier of the constraint over the language, so that the two are untied. Under the optimal entropic law we then show that a transformer head appears in the score of the last-token law. For ordered sentences, causal masking follows from the masked reference choice rule, and with a next-token cross-moment the score equals one causally masked attention head. We also discuss multi-head attention, weight-tied unembedding, and a heuristic reading of residual blocks as projected Langevin steps.

cs.AI · math.PR · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39558

TabCUQ: Context-Uncertainty Quantification for Tabular Foundation Models

Yuebei Shi, Molei Liu, Zijian Guo

原文摘要

Tabular foundation models use in-context learning to estimate conditional expected outcomes and average treatment effects for specific groups of individuals. Using these estimates to guide scientific decisions requires reliable uncertainty quantification. The challenge is to account simultaneously for two sources of uncertainty: limited-context bias and context variation arising from the small labeled sample supplied at inference. Predictive spread does not directly quantify both sources of uncertainty, and we observe that the ordinary bootstrap may substantially overestimate context variation, whereas subsampling may underestimate it. We introduce TabCUQ, a perturbation-based framework that injects noise into observed outcomes and applies the foundation model to the perturbed contexts. TabCUQ estimates context variation using wild-bootstrap dispersion and accounts for limited-context bias using the maximum deviation between perturbed and original estimates. For a kernel-regression analogue whose estimation error admits an exact decomposition into these two components, we show that our framework provides asymptotically valid pointwise coverage. In simulations, TabCUQ substantially improves coverage, with average interval widths typically about twice those of an oracle bias-aware benchmark. Across seven real-world tasks, it also improves coverage of reference functions learned from much larger samples.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2602.19513

Real-time Win Probability and Latent Player Ability via STATS X in Team Sports

Yasutaka Shimizu, Atsushi Yamanobe

原文摘要

This study proposes a statistically grounded framework for real-time win probability evaluation and player assessment in score-based team sports, based on minute-by-minute cumulative box-score data. We introduce a continuous dominance indicator (T-score) that maps final scores to real values consistent with win/lose outcomes, and formulate it as a time-evolving stochastic representation (T-process) driven by standardized cumulative statistics. This structure captures temporal game dynamics and enables sequential, analytically tractable updates of in-game win probability. Through this stochastic formulation, competitive advantage is decomposed into interpretable statistical components. Furthermore, we define a latent contribution index, STATS X, which quantifies a player's involvement in favorable dominance intervals identified by the T-process. This allows us to separate a team's baseline strength from game-specific performance fluctuations and provides a coherent, structural evaluation framework for both teams and players. While we do not implement AI methods in this paper, our framework is positioned as a foundational step toward hybrid integration with AI. By providing a structured time-series representation of dominance with an explicit probabilistic interpretation, the framework enables flexible learning mechanisms and incorporation of high-dimensional data, while preserving statistical coherence and interpretability. This work provides a basis for advancing AI-driven sports analytics.

stat.AP · stat.ML

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2411.19193

The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization

Pekka Malo, Lauri Viitasaari, Antti Suominen, Eeva Vilkkumaa, Olli Tahvonen

原文摘要

In many control problems, actions consume a resource budget, such as a wear allowance, and the probability of exhausting it within a given horizon must stay below a tolerance. A simple, widely used approach is to augment the state with the remaining budget, subtract an interior barrier from the utility and penalize exhaustion, so that policy-gradient methods can be applied unchanged. We clip the combined one-step reward from below at a level m to keep the returns of exploratory policies finite. The clip level is a price of failure risk, since the clipped value decomposes exactly into the utility before failure, the cost of the interior margin and m times a geometric failure risk. Consequently, an approximately optimal policy maximizes utility net of margin cost among policies with no greater risk. Its risk exceeds that of any comparison policy by at most order 1/m and can be certified from its value or from validation data. Our main result proves exponential convergence of the population policy-gradient flow for every parameter regularizer that is convex along generalized geodesics and sufficiently strong relative to the price. This extends the mean-field analysis from relative entropy to weight decay and to finite networks. Relative entropy adds parameter noise and a pull toward a prior, whereas weight decay provides only the pull. Action regularization bounds changes in failure risk by the relative entropy to a reference policy. The bounds are evaluated on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task.

cs.LG · cs.AI · math.OC · math.PR · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39549

Non-Asymptotic Confidence Regions for Separable Nonlinear Models

Szabolcs Szentpéteri, Péter Kovács, Balázs Csanád Csáji

原文摘要

This paper studies robust uncertainty quantification for separable nonlinear least squares (SNLLS) problems. We propose two identification methods, (i) Residual-Perturbed Gradient (RPG) and (ii) Global-Fit-Gap (GFG), to construct joint distribution-free confidence regions for both the linear and nonlinear parameters. By exploiting assumed group invariance of the noise (such as symmetry or exchangeability), we apply random perturbations (such as sign-changes or permutations) to build the regions based on resampling and ranking. We prove that both methods guarantee non-asymptotically exact coverage (type I error). Finally, we illustrate the constructions through two numerical experiments: (i) identifying generalized finite impulse response (GFIR) systems using Laguerre polynomials with an adjustable decay rate and (ii) fitting Gaussian radial basis function (RBF) models with variable knots and widths.

eess.SY · math.ST · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39540

The Cost of Working Memory in Streaming Mean Estimation

Zeyu Wu, Zihao Wang, Minghua Deng

原文摘要

A streaming estimator must compute from the evidence that fits in memory. We determine when storing an accurate mean is easier than computing it. For Gaussian mean estimation over the Euclidean unit ball in $\mathbb{R}^d$, we establish the minimax rate under squared error with $K$ persistent states, a known horizon, and a public time index: $\min\{1, K^{-2/d}+\frac{d}{n} (1+\frac{\log(ed)}{1+(\log K)/d})\}$. Unrestricted computation followed by $K$-level encoding has rate $\min\{1,d/n+K^{-2/d}\}$. At a fixed sufficiently small error, statistically optimal sample size therefore requires order $d\log d$ working bits, while order $d$ bits suffice to store the answer. The lower bound tracks repeated state compression through an entropy potential obtained by Gaussian smoothing. A matching construction combines a multiscale modular counter with workspace reused across coordinate groups. In one dimension, it attains the terminal rate $n^{-1}+K^{-2}$. Any fixed confidence requirement that the realized loss not exceed the zero baseline preserves these rates. Increasing confidence creates a further memory requirement: at fixed nontrivial risk in every fixed dimension, failure probability $e^{-γn}$ requires and permits order $\log n$ working states for sufficiently small fixed $γ>0$. In the scalar problem, a fixed terminal alphabet suffices under the same protection. These bounds separate the memory needed to represent an answer from the memory needed to accumulate evidence and validate a decision.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39531

Conic-Lifting for Learning-rate-free Convex Optimization

Julien Grand-Clément, Joon Kwon, Francesco Orabona

原文摘要

A central topic in online and stochastic optimization is to design algorithms that do not require tuning of hyperparameters. Successful strategies in online learning include AdaGrad-style learning rates, Conic Blackwell algorithms, and parameter-free algorithms. However, these classes require different, often difficult, analyses. We develop a unifying family of Online Convex Optimization (OCO) algorithms that require no user-tuned learning rate on convex domains that may be unbounded. The construction lifts the domain to a cone by adding one scalar coordinate, an idea going back to Blackwell (1954). The lifted subgradients are orthogonal to the corresponding lifted decisions, leaving the comparator scale free to optimize in the regret analysis. Applying Follow-the-Regularized-Leader (FTRL) and Online Mirror Descent (OMD) on the cone recovers Conic Blackwell Algorithm (CBA) and Conic Blackwell Algorithm Plus (CBA$^+$) on bounded domains in Hilbert spaces and extends them to finite-dimensional normed spaces with a strongly convex squared norm. For arbitrary nonempty closed convex domains in these spaces, a known gradient bound yields parameter-free regret guarantees. Surprisingly, on an unconstrained Hilbert space, the construction recovers the Krichevsky--Trofimov (KT) coin-betting algorithm exactly. We also give a parameter-free algorithm for unconstrained domains that requires no gradient bound.

math.OC · cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2601.20251

Efficient Evaluation of LLM Performance with Statistical Guarantees

Skyler Wu, Yash Nair, Emmanuel J. Candès

原文摘要

Exhaustively evaluating many large language models (LLMs) on a large suite of benchmarks is expensive. We cast benchmarking as finite-population inference and, under a fixed query budget, seek tight confidence intervals (CIs) for model accuracy with asymptotic frequentist coverage. We propose Factorized Active Querying (FAQ), which (a) leverages historical information through a Bayesian factor model; (b) adaptively selects questions using a hybrid variance-reduction/active-learning sampling policy; and (c) maintains validity through Pro-Active Inference---a finite-population extension of active inference (Zrnic & Candès, 2024) that enables direct question selection while preserving asymptotic frequentist coverage. In our experiments, FAQ delivers up to $5\times$ effective sample size gains over strong baselines on two benchmark suites, across varying historical-data missingness levels, with negligible computational overhead: this means that it matches the CI width of uniform sampling while using up to $5\times$ fewer queries. We release our source code and our curated datasets to support reproducibility and future research.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2404.07661

Robust performance metrics for imbalanced classification problems

Hajo Holzmann, Bernhard Klar

原文摘要

We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $κ$, the F-score or the Jaccard similarity coefficient are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics {becomes very small or even tends to $0$}. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate this issue we introduce robustified modifications of the MCC, of Cohen's $κ$ and of the F-score with an additional tuning parameter which allows to adapt the amount of robustness against class imbalance. As theoretical guarantee we show that the Bayes-optimal classifier for these robustified performance metrics, when expressed in terms of the density ratio $f_1/f_0$ of the class-conditional densities $f_i$, has a threshold parameter which is upper-bounded in terms of the tuning parameters. Therefore, even in strongly imbalanced settings, the TPR associated to this classifier will be bounded away from $0${, provided that $f_1/f_0$ exceeds this bound with positive probability under the positive class}. We numerically illustrate the behaviour of the various performance metrics and the effect of the tuning parameters in simulations as well as on a credit default data set. We also discuss connections to the receiver operating characteristic and precision-recall curves, which provide an alternative perspective on the proposed notion of robustness, and give recommendations on how to combine their usage with performance metrics.

stat.ML · cs.LG · stat.ME

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39409

Safe Multi-Objective Reinforcement Learning: Zero Constraint Violation and Primal-Averaging Convergence

Chenxi Li, Yao Shu, Siyang Gao, Shuang Qiu, Guangxin Jiang

原文摘要

Many applications of multi-objective reinforcement learning (MORL) require policies that balance conflicting objectives while satisfying safety constraints. We study safe MORL with zero constraint violation throughout learning, covering both cumulative and stepwise constraints. A key challenge is to explore sufficiently under unknown dynamics and constraint costs without violating the constraints. For a given preference over objectives, we develop an algorithm to learn a safe Pareto optimal policy by combining optimistic reward estimates with pessimistic cost bounds. With high probability, every policy executed over $T$ episodes incurs zero constraint violation. The algorithm returns a safe Markov policy induced by the averaged occupancy measure and achieves an $\widetilde{O}(1/\sqrt{T})$ suboptimality gap under smooth Tchebycheff scalarization. We further develop a preference-free algorithm that first explores safely without a prespecified preference and then computes a safe policy for any given preference without further interaction. Over $T$ exploration episodes and $K$ planning iterations, it retains the same safety guarantee and achieves an $\widetilde{O}(1/\sqrt{T}+1/\sqrt{K})$ suboptimality gap. Both algorithms require knowledge of a policy that strictly satisfies the constraints and its costs. We then relax these requirements, incurring at most constant cumulative violation. To our knowledge, we provide the first sample-efficient MORL algorithms that guarantee safety for every executed policy.

cs.LG · cs.AI · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.26676

Which Model for Which Role? Cost-Efficient Pareto Recommendation for LLM Agentic Workflows

Qian Xie, Wenyue Hua, Yueli He, Sripad Karne, Armaan Agrawal, Nikos Pagonas, Eugene Wu, Kostis Kaffes 等 10 位作者

原文摘要

LLM agentic workflows increasingly employ different models for specialized roles. Users may prefer different trade-offs between task quality and deployment cost, sometimes also considering latency. Finding good assignments incurs a separate search cost from evaluating multiple candidates. We introduce Cost-Coupled Gittins (CC-Gittins), a multi-objective extension of single-objective cost-aware Gittins search for Pareto recommendation. It exploits the coupling between evaluation and deployment costs: assignments that cost more to deploy also cost more to evaluate. The search alternates between seeking higher quality and lower deployment cost, reusing each evaluation to inform both searches. After each batch, CC-Gittins recommends assignments that are nondominated under uncertainty-adjusted estimates of quality and deployment cost. We evaluate CC-Gittins on eight quality--cost matrices from workflows with two to five roles and up to 1,681 candidate assignments. We also evaluate the method with latency as a third objective. Across the eight benchmarks, CC-Gittins recovers a substantial fraction of the true Pareto frontier at roughly 10% of the exhaustive-evaluation cost, and recovers most of the frontier with few false positives by 30%.

cs.LG · cs.CL · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.02959

The Direction of Ignorance: LLMs Encode and Temper a Unigram Prior

Toni J. B. Liu, Jiajun Bao, Gurbir Arora, Mitchell Ostrow, Yizhou Liu, Raphaël Sarfati, Nicolas Boullé, Christopher J. Earls

原文摘要

What does a language model predict when it has few clues?The answer lies in its unembedding geometry: a single direction of the unembedding matrix encodes the unigram distribution of the training corpus, which serves as the Bayesian prior the model falls back on when uncertain. This structure, termed the direction of ignorance, appears across all model families examined (Llama, Qwen, Gemma, and Pythia), ranging from 0.4B to 405B parameters. Projecting the final prediction state onto this direction yields a per-token prior loading factor $λ$, which declines steadily as the context becomes more informative. Formally, the same projection decomposes the prediction state into two orthogonal vectors interpretable as the two components of a tempered Bayesian update: a unigram prior raised to the exponent $λ$ and a context-driven likelihood. This geometric probabilistic connection makes $λ$ meaningfully comparable across model sizes and families. Larger models generally exhibit lower prior reliance, and reasoning models exhibit lower reliance than their base counterparts. Finally, we show that $λ$ serves as a causal, inference-time control: reducing it can promote context-driven continuations and improve Llama-3.2-3B-Instruct on GSM8K, whereas amplifying it or applying matched perturbations along random directions degrades performance.

cs.LG · cs.AI · cs.CL · stat.ML

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新论文 · v1arXiv:2610.39321

Satisficing Regret Minimization in Bandits with Knapsacks

Qing Feng, Tianyi Ma, Ruihao Zhu

原文摘要

We study satisficing regret minimization in bandits with knapsacks (BwK), where a learner sequentially selects randomized policies, i.e., distributions over arms, to obtain mean rewards above a satisficing threshold as frequently as possible while respecting finite resource budgets. The performance is measured by satisficing regret, the cumulative deficits of the selected policies' mean rewards below this threshold. Resource constraints introduce two difficulties: an algorithm can incur linear satisficing regret even with small standard regret as deficits to the threshold cannot be compensated, and random consumption can cause early resource depletion even when policies are feasible in expectation. To address these challenges, we propose SELECTwK, a general algorithmic template that uses a BwK learning oracle algorithm with sub-linear expected (standard) regret upper bound to search for and test candidate satisficing policies (i.e., policies whose mean rewards exceed satisficing threshold and whose expected resource consumption is feasible over the time horizon). Our regret analysis, supported by an LP-duality argument, establishes that SELECTwK attains constant expected satisficing regret when a satisficing policy exists. We further introduce a stronger regret condition that bounds the expected sum of positive reward deficits to the optimal one at each time step, under which SELECTwK achieves a sharper constant bound together with a sub-linear bound in the time horizon. As a complement, SELECTwK still preserves the oracle's sub-linear expected standard regret bound if the satisficing threshold is unattainable. Finally, we establish the oracle conditions and corresponding satisficing regret bound for existing finite-armed BwK and dynamic pricing algorithms, and conduct numerical experiments on dynamic pricing with limited inventory to demonstrate the empirical performance of SELECTwK.

stat.ML · cs.LG

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版本更新 · v2arXiv:2610.36633

Deep Bayesian Filtering for Nonlinear Structural System Identification: A Tutorial on Structural and Physical Inductive Biases

Wei Liu, Konstantinos Vlachas, Eleni Chatzi

原文摘要

Nonlinear structural system identification remains challenging when governing physics is only partially known and measurements are sparse. Deep Bayesian filtering addresses these challenges by combining learnable dynamical representations with probabilistic state-space models, physical inductive biases, and uncertainty-aware inference. This paper presents, for the first time, a unified tutorial treatment of deep Bayesian filtering for nonlinear structural system identification, connecting model formulation, learning, posterior inference, and evaluation. Amortized variational inference and differentiable Kalman filtering are introduced as complementary strategies within this broader framework. The Deep Markov Model (DMM) provides a data-driven reference, while the Physics-guided Deep Markov Model (PgDMM) and Neural Extended Kalman Filter (Neural EKF) serve as illustrative instances through which methodological choices and their implications are examined. Dynamic state estimation and joint state and parameter estimation are demonstrated on a three-dimensional shear-frame benchmark with hysteretic Bouc-Wen connections and sparse acceleration measurements. The comparative analysis yields new observations concerning the relationships among reconstruction accuracy, predictive fidelity, physical interpretability, and estimation robustness. Physical structure improves latent-state interpretability without necessarily ensuring faithful predictive dynamics, while comparable typical reconstruction accuracy can conceal substantial differences in estimation robustness. These findings motivate practical guidelines for model construction, training, and evaluation that distinguish reconstruction, forecasting, state recovery, and parameter identification. The tutorial concludes by outlining challenges in uncertainty calibration, identifiability, and validation on real structures.

cs.LG · cs.CE · stat.ML

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新论文 · v1arXiv:2610.39302HF 社区推荐

Proving and Improving the Platonic Representation Hypothesis with JEPAs

Randall Balestriero, Yann LeCun

原文摘要

Whether models trained on different modalities converge to the same representation of the world is central to AI. The Platonic Representation Hypothesis (PRH) conjectures that they do as they scale, but without a proof it offers neither a guarantee nor a recipe. We turn the hypothesis into a theorem. First, we prove a \emph{Platonic Representation Theorem}: Joint-Embedding Predictive Architectures (JEPAs) trained separately on any number of modalities learn the same representation up to one rotation whenever their positive pairs are two observations of one scene--\emph{good views}--and their misalignment is bounded otherwise. Second, we show that next-token prediction is a JEPA with \emph{bad views}, parts of a single document, which explains why language models align with vision only through scale. Third, we validate the theory from 145k captions to the texts of 940M web images, and uncover a scaling law of alignment that predicts unseen runs within seed noise. Good views need 42 times fewer training samples than next-token prediction on the same corpus to reach the same alignment, and a 109M-parameter text JEPA aligns with DINOv2 and CLIP's image encoders better than every language model we evaluated, up to 72B parameters, and than CLIP's text encoder: next-token prediction is a remarkably inefficient route to platonic representations. As a showcase, one rotation turns separately trained encoders into an image captioner (CIDEr .838 on COCO). Even that rotation needs no pair: on the latest pair-free benchmark, our text JEPA beats every zero-shot accuracy reported with language models up to 8B parameters, e.g., 64\% against at most 56\% top-5 on ImageNet-100. Positive views, and not scale alone, are thus the lever to build platonic representations.

cs.AI · cs.CV · stat.ML

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新论文 · v1arXiv:2610.39295

There Is No Free Lunch in RLVR: Every pass@1 Gain Has a pass@k Price

Yinuo Liu

原文摘要

Reinforcement learning with verifiable rewards (RLVR) makes a language model solve more problems on the first try and fewer when given many tries: it raises pass@1 while the base model overtakes it at large sampling budget k. Is this a failure of RL to add reasoning, or a transient that more training removes? We settle the question with a theorem. The reversal is a price, and we compute its exact rate. Modeling RLVR as an exponential tilt of a base policy over strategies shared across prompts, we prove that under exclusive specialization every update that raises pass@1 strictly lowers the success of some prompt; a strictly positive price on prompts (Stiemke duality) is the exact condition, and being merely the best strategy on a prompt is provably not enough. When the loss reaches the hardest prompts, it forces a pass@k crossover, and the number of crossings is at most the sign variation of the shift in per-prompt success, a totally positive bound that is tight and that recovers the known single-crossover result as its order-preserving case. The crossover is not a bug to patch: a constrained update traces the exact pass@1 versus pass@k frontier, and removing the crossover entirely costs the entire pass@1 gain. The same tilt identity yields entropy collapse and the entropy-performance law with an identifiable exponent, unifying two literatures under one mechanism. Reinforcement cannot widen the reasoning frontier; it can only move along it, at a price we make measurable by a diagnostic that reads the bound, the order-preserving test, and the price from any evaluation log. There is no free lunch, only a price.

cs.LG · cs.AI · math.OC · stat.ML

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版本更新 · v2arXiv:2609.17474

Iterative Calibration and Learning: Mitigating Teacher Bias in LLM Distillation without Target-Domain Reward Feedback

Haichen Hu, Yuheng Zhang, David Simchi-Levi

原文摘要

Large language model (LLM) distillation can propagate teacher bias under covariate shift when target reward feedback is unavailable. We propose Iterative Calibration and Learning (IterCaL), which alternates source-reward teacher calibration through token-level branching with student learning on target prompts. We prove polynomial convergence in expected average KL to the oracle student, the reference-regularized target-reward maximizer within a potentially misspecified student class; a quantified source-to-target calibration discrepancy gives an explicit additive true-return term. Our separation shows that regularized direct teacher matching retains positive oracle-KL error at its population optimum for every shared reference penalty, even when the teacher is stronger than every student. On the same instance, IterCaL converges to the oracle using source rewards alone.

cs.LG · cs.AI · math.ST · stat.ML

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新论文 · v1arXiv:2610.39223

Where Position Matters: Profiling-Guided Layer-Wise RoPE Allocation in Transformers

Zhiwei Liu, Boao Kong, Bing Liu

原文摘要

Rotary Position Embedding (RoPE) typically uses uniform coverage across Transformer layers despite heterogeneous positional requirements. Phase-off interventions reveal non-uniform, model-specific rotary-phase dependence, while coverage interventions relate it to coverage-upgrade benefits. We propose profiling-guided layer-wise RoPE allocation, assigning high/low coverage under a fixed budget using early coverage-benefit profiles. The framework supports fixed-width query/key representations and physical rotary-dimension allocation in Multi-head Latent Attention (MLA). Normalized-depth mapping transfers profiles within model families, enabling small-model measurements to guide larger-model allocations before pretraining. A brief analysis relates selection and transfer to score calibration and inter-layer interactions. From-scratch experiments demonstrate validation-loss improvements over available budget-matched baselines, while analytical resource accounting identifies favorable quality--storage--compute trade-offs for physical MLA. These results connect positional demand to transferable, efficient architecture design.

cs.LG · cs.AI · stat.ML

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版本更新 · v2arXiv:2407.05302

Mamba Hawkes Process for Event Sequence Modeling

Shan Dai, Yuyang Shen, Yuyang Liang, Chenhao Ma, Anningzhe Gao

原文摘要

Modeling asynchronous event sequences is crucial in numerous real-world applications such as healthcare monitoring, financial transaction analysis, and so on. Traditional temporal point processes, including Hawkes Processes, often fail to capture complex dependencies due to their parametric limitations. While neural approaches like RNNs and Transformers have improved flexibility, they struggle with computational inefficiency, and attention saturation. In this paper, we introduce the Mamba Hawkes Process (MHP), the first framework to integrate selective state space model (Mamba) with temporal point processes. MHP leverages time-varying state transitions and input-dependent gating to efficiently encode event history and capture long-term dependencies with linear complexity. Importantly, we provide theoretical guarantees showing that MHP generalizes both classical multi-exponential Hawkes processes and exponential-decay gated RNNs, underscoring its expressive power and theoretical soundness. To address the inherent constraints of pure state space models in handling heterogeneous event interactions, we further develop Adaptive Mamba Hawkes Process (A-MHP) that incorporates two novel mechanisms: a Time-Scaling Mechanism that adaptively weights time intervals based on event type and history, and a Dual-Channel State Transition that adaptively processes event content and temporal dynamics for more refined state updates. Extensive experiments on synthetic and realworld datasets demonstrate that MHP and A-MHP consistently outperform state-of-the-art baselines in event prediction tasks, particularly in long-sequence scenarios. Our work establishes a scalable and theoretically grounded paradigm for event sequence modeling, with practical implications for predictive maintenance, anomaly detection, and dynamic system analysis.

cs.LG · stat.ML

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