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Tao Zhong, Kaison Fong, Keqin Wang, Christine Allen-Blanchette · 2026-10-21
Geometric algebra (GA) unifies geometric primitives and transformations in a single algebraic framework. Neural networks designed around this framework often represent features as multivectors and constrain layer operations to respect the algebraic structure, enabling principled …
Francesco Mori, Melanie Weber · 2026-10-21
The success of convolutional neural networks is often attributed to locality and weight sharing. However, how these two properties separately shape learning, and how their effects depend on the spatial correlations of natural images, remain poorly understood. We address these que…
Matteo Benati, Alessandro Londei, Denise Lanzieri, Raffaello Mastromarino, Vittorio Loreto · 2026-10-21
Training generative models on synthetic data causes loss of diversity and a decrease in performance, a phenomenon known as model collapse. We study this degeneration spectrally in a controlled Markov setting. The eigenvalue spectrum of the learned transition operator offers a dir…
Sharan Sahu, Martin T. Wells · 2026-10-21
Adaptive experiments use bandit algorithms to favor interventions with higher expected rewards. However, decision-makers also require reliable inference on current treatment effects: differences between intervention and reference-arm mean rewards at the present time, rather than …
Jiani Yan, Pengyun Wang, Klint Kanopka, Ben Domingue, Charles Rahal · 2026-10-21
Accuracy alone gives little information about which features or model components improve probabilistic fit, which outcomes benefit, or how fit changes during training. We introduce the InterModel Vigorish (IMV) into the Machine Intelligence space in order to express differences i…
Simon Martin, Francis Bach, Giulio Biroli · 2026-10-21
We study gradient flow in a two-layer linear network in the high-dimensional regime where the input, inner and output dimensions diverge proportionally. Under whitened inputs and isotropic imbalance, we combine a closed-form solution of the dynamics with prior random matrix theor…
Gyeonghun Kang, William Xingxu Chen, Xiang Cheng · 2026-10-21
How do diffusion transformers (DiTs) represent image content and learn rules for reusing it to generalize? We develop an aggregator--predictor view of DiTs as input-adaptive local denoisers, in which context aggregation and patch prediction provide functional roles for interpreti…
Gunjan Kumar, Yash Pote, Jonathan Scarlett · 2026-10-21
In likelihood-free hypothesis testing (LFHT), given samples from two unknown distributions $P,Q$ on $[n]$ with $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$, and from a third distribution $D\in\{P,Q\}$, the goal is to identify whether $D=P$ or $D=Q$. We study asymmetric likelihood-free h…
Johannes Keller, Albrecht M. Bloße, Adrian Lindenmeyer, Thomas Neumuth, Daniel Schneider · 2026-10-21
Vision-language-action (VLA) policies need to recognize gaps in their training knowledge to request useful demonstrations or assistance in new situations, especially when failures are costly. Disagreement within an ensemble of independently trained policies can guide these decisi…
Jérémie Bigot, Clément Bonet · 2026-10-21
Principal Component Analysis (PCA) is a fundamental tool for statistical dimension reduction, yet no canonical extension to distribution-valued data has emerged within the framework of optimal transport. While Wasserstein barycenters and Wasserstein least-squares regression provi…
Zijie Cheng, Zhihua Zhang · 2026-10-21
In this paper, we study quantile distributional policy evaluation, where the return distribution under a given policy is approximated by the quantile Bellman fixed point $\bmη_m$. We investigate the statistical accuracy of estimating $\bmη_m$ across quantile resolutions under Was…
Rafael Lopes Almeida, Ina Pöhner · 2026-10-21
Graph neural networks (GNNs) are among the standard tools for molecular property prediction, but the atom-level explanations of their predictions are hard for medicinal chemists to act on. We propose a change of input representation rather than a new model: molecules are encoded …
Bo Li, Peng Ye · 2026-10-21
We consider online prediction from experts, a fundamental problem in machine learning, under differential privacy constraints. Existing private algorithms achieve near-optimal regret $\tilde{O}(\sqrt{T})$, where $T$ is the time horizon. However, this bound becomes suboptimal when…
Daniel Klippert, Quang Nhat Huynh, Alexander Marx · 2026-10-21
Residual-based causal discovery assumes that each variable is generated from its parents and an independent noise source. It estimates this noise and tests its independence from candidate causes. For identifiable functions such as additive-noise models (ANMs) and the broader clas…
Dwi Sunaryono · 2026-10-21
Models are updated repeatedly, and an update that looks better on validation data but not on new data is a false improvement that can misguide clinical decisions. The naive rule accepts every positive validation gain and is optimistic when the same data choose and judge the updat…
Mitsuki Nagai, Keisuke Yano · 2026-10-21
In this paper, we develop a unified framework connecting proper scoring rules and Stein's method for the estimation of unnormalized models. We construct a class of proper scoring rules that encompasses score matching, ratio matching, pseudolikelihood, and noise contrastive estima…
Mathias Grau, Pierre Henry-Labordère · 2026-10-21
We propose a new generative modeling framework grounded in forward-backward partial differential equations (PDEs). These equations arise naturally in mean-field game (MFG) theory, and are closely related to nonlinear Schrödinger systems. Our main contribution is to reinterpret th…
Ewsey Obzherin, Valentin Khrulkov · 2026-10-21
Low-NFE generative ODE sampling is constrained not only by solver order, but also by how a fixed budget of network evaluations is distributed along the flow. We develop a density-level backward-error framework that identifies the component of a solver's modified-equation defect t…
Shaojin Ma, Ruitao Wang, Pengyi Li, Jie Yang, Liangyu Chen and others · 2026-10-21
Recent advances in multi-turn reinforcement learning (RL) have substantially improved the performance of LLM agents on complex, long-horizon interactive tasks. However, despite progress in fine-grained credit assignment, policy optimization still applies these learning signals th…
Leon Chlon, Julie Huang · 2026-10-21
We are the first to give a certified rule for whether unseen data belong in a pretrained model's context or its weights, built on an exact law for their information value. That value, the code length saved on held-out queries, equals in expectation the bits stored about the query…
Qicheng Zou, Biao Yuan, Siyu Song, Wentao Liu, Xiaokun Wang · 2026-10-21
Outcome-predictive signals are often treated as promising optimization targets in reinforcement learning, but predictive validity and optimization utility are different claims. We expose this distinction in GuanDan, a multi-round imperfect-information game in which the implicatio…
Yashaswini Kaluguri, Nikhil Karamchandani · 2026-10-21
We propose a novel stochastic cascading bandit setup where probing an ordered shortlist of $K$ out of $L$ arms incurs position-dependent costs, and the learner observes only noisy feedback regarding each arm's true output. We identify a sub-class of noise models for which the opt…
Donghyun Jeong, Yoon-Yeong Kim · 2026-10-21
Sparse Mixture-of-Experts (SMoE) models improve scalability by routing input tokens to only a subset of expert networks, but they often suffer from representation collapse, in which multiple experts converge toward similar functions and lose their intended diversity. Prior work h…
Yongqiang Chen, Chenxi Liu, Deyu Zou, Zhenhao Chen, Tongliang Liu and others · 2026-10-21
Evolutionary coding agents such as AlphaEvolve are one of the notable successes in using Large Language Models (LLMs) to build AI Scientists. These agents tackle open-ended scientific problems by iteratively improving and evolving programs, leveraging the prior knowledge and reas…
Qian Li, Shang-Hua Teng · 2026-10-21
Why large language models trained via log-loss minimization over massive and diverse datasets exhibit broad capabilities and generalizable skills is not yet fully understood. Grau-Moya et al. (ICML 2024) offer a conceptual explanation through the lens of meta-learning: if sequenc…
Ngoc-Hai Nguyen, Thuan Nguyen, Prakash Ishwar, Shuchin Aeron · 2026-10-21
Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual d…
Dimitris Oikonomou, Nicolas Loizou · 2026-10-21
Sharpness-Aware Minimization (SAM) has established itself as a widely used method for training deep neural networks. Despite its popularity, existing convergence guarantees for SAM-type methods require smoothness, a restrictive assumption. Generalized smoothness conditions have r…
Curtis McDonald, Peter Bartlett · 2026-10-21
Reward guidance methods sample an exponential tilt of a base density using a diffusion model trained with only samples from the base distribution. Existing methods use what we call external guidance: additive terms in the drift or multiplicative terms on the transition probabilit…
Ansh Desai, Jason Liu, Srujan Roplekar, Matthew Rosenzweig · 2026-10-21
We study a jump-modified Wasserstein gradient flow of the squared maximum mean discrepancy generated by the energy kernels $K(z)=-|z|^q$, $0<q<2$, in every dimension $d\ge2$ as well as the one-dimensional range $1\le q<2$. Under subcritical density and finite-moment assu…
Paris A. Karakasis, Walid Saad · 2026-10-20
Many problems in signal processing, machine learning, and neuroimaging provide several jointly observed measurements of one process, each mixing a component common to all of them with a component private to itself, and require the common component to be recovered without supervis…
Weiqin Chen, Xinlong Du, Gesualdo Scutari, Harsha Honnappa · 2026-10-20
In-context reinforcement learning (ICRL) exploits the impressive in-context learning ability of large language models to zero-shot generalize to new, unseen tasks at inference time without any parameter updates. Among many approaches, the Decision-Pretrained Transformer (DPT) is …
Achref Doula, Max Mühlhäuser · 2026-10-20
Conformal prediction (CP) for language models is typically evaluated under a matched protocol, in which calibration and deployment use the same post-training inference configuration, such as quantization mode and inference temperature. In deployment, these choices often differ fr…
Jose M. Peña · 2026-10-20
Natural direct and indirect effects are defined through cross-world interventional counterfactuals. We propose an alternative construction based on backtracking counterfactuals. Rather than intervening on the treatment or mediator, we use a backtracking conditional distribution t…
Mohammad Afzali, Hassan Ashtiani, Alex Bie, Gautam Kamath, Peihan Liu and others · 2026-10-20
We show that every class of distributions that is learnable up to arbitrarily small target error in total variation distance with finitely many samples is also learnable under ($\varepsilon, δ$)-differential privacy up to arbitrarily small target error with finitely many samples.…
Cynthia Bortolotto, Francisco Ganacim, Roberto I. Oliveira · 2026-10-20
We revisit the problem of depth separation for neural networks, as studied by Eldan and Shamir, Daniely, and others. Specifically, we consider the natural setting of $L^2$ approximation of radial functions under the standard Gaussian measure in $d$ dimensions. We show that there …
Nghi Dao, Calder Morton-Ferguson, Noah Golowich, Adam Block · 2026-10-20
RLVR improves language-model reasoning, but commonly relies on independent stochastic rollouts for exploration, which can repeatedly sample similar failed strategies. Prior work has seen success with approaches that guide exploration by introducing dependence into the sampling pr…
Rakesh Sengupta · 2026-10-20
Gold's theorem shows that no learner can identify an arbitrary language in a superfinite class from positive presentations alone. We prove a positive result of a different shape. Fix an innate \emph{recursive contrast operator} $R$ mapping any string to a finite set of structural…
Rodrigo Casado Noguerales, Dimitri von Rütte, Bernhard Schölkopf, Thomas Hofmann, Aran Raoufi · 2026-10-20
Discrete diffusion models iteratively denoise a noisy sequence of categorical data such as text, enabling any-order generation with self-correction and in-filling capabilities. This makes them promising candidates for reasoning, planning, and constrained-generation tasks like cod…
Recep Yusuf Bekci, Stefanus Jasin, Joline Uichanco · 2026-10-20
Large retail chains must tailor assortment and pricing decisions to local customer preferences, yet even retailers with extensive sales records often have limited data for estimating demand at the store or local market level, particularly in product categories with short selling …
Alvaro Ribot, Yulia Alexandr, Anna Seigal · 2026-10-20
A neural model is the set of functions that can be expressed by a given neural network architecture. Neural models contain natural submodels, such as those obtained by setting some neurons to be inactive. We study the geometry of neural models and ask whether they prefer their su…
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