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版本更新 · v2arXiv:2607.01266

Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks

Clemens Kinn, Philipp Petersen

原文摘要

We study binary classification tasks whose decision sets are given by definable sets in o-minimal expansions of the real field. Motivated by the cell decomposition theory of definable sets, we introduce traceable sets that isolate the analytical properties of definable sets used for fast approximation by ReLU neural networks. Under uniform bounds on the number of cells and a suitable extension assumption for the boundary functions, we prove that classifiers can be approximated in $L^p$ up to accuracy $\varepsilon>0$ by ReLU neural networks of size $\mathcal{O}(\varepsilon^{-p(n-1)/m})$, with depth independent of $\varepsilon$ and polynomially bounded weights. This establishes quantitative approximation rates for suitable definable collections in o-minimal structures using ReLU neural networks. Furthermore, the stated approximation rates are also derived for definable maps under similar geometric assumptions on their smoothness domains. We then obtain statistical learning rates for empirical risk minimization with hinge loss over the approximating ReLU neural network classes. For $N$ uniformly distributed samples, the predicted classifiers achieve expected misclassification error of order $N^{-m/(m+n-1)}$ up to an arbitrarily small polynomial loss.

math.LO · cs.LG · math.FA

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2506.06361

Tactile MNIST: Benchmarking Active Tactile Perception

Tim Schneider, Guillaume Duret, Cristiana de Farias, Roberto Calandra, Liming Chen, Jan Peters

原文摘要

Tactile perception has the potential to significantly enhance dexterous robotic manipulation by providing rich local information that can complement or substitute for other sensory modalities such as vision. However, tactile sensing is an inherently local sensor modality, providing information only at the points of contact. This strict locality necessitates the use of active perception techniques to acquire useful, task-relevant information from manipulated objects or the environment in general. Hence, the agent must actively guide sensors toward regions with more informative or significant features and integrate this information over time to understand a scene or complete a task. While active perception and tactile sensing methods have received significant attention recently, both fields lack standardized benchmarks. To bridge this gap, we introduce the Tactile MNIST Benchmark Suite, an open-source, Gymnasium-compatible benchmark specifically designed for active tactile perception tasks, including classification, localization, pose estimation, and volume estimation. Our benchmark suite offers diverse simulation scenarios, from simple toy environments to complex tactile perception tasks using vision-based tactile sensors. Furthermore, we offer a comprehensive dataset comprising 13,580 synthetic 3D MNIST digit models and 153,600 real-world tactile samples collected from 600 3D-printed digits. Using this dataset, we train a CycleGAN for realistic tactile simulation rendering. By providing standardized protocols and reproducible evaluation frameworks, our benchmark suite facilitates systematic progress in tactile sensing and active perception more broadly.

cs.RO · cs.AI · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.09887

关于 ReLU 网络集合的（非）闭性

On the (non-)closedness of the set of ReLU networks

Eloi Martinet, Leon Bungert

AI 速读 基于摘要

作者证明单隐层 ReLU 网络集合在 Sobolev 空间中是弱闭的，而宽度有界的双隐层 ReLU 网络集合在 Sobolev 空间与连续函数空间中均不闭。

cs.LG · math.CA · math.FA · math.NA · math.OC

arXiv ↗PDF ↗
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We prove that the set $\mathcal{N}_N$ of ReLU networks with one hidden layer and at most $N\in\mathbb N$ neurons is weakly closed in $W^{1,p}(Ω)$, for a bounded connected open set $Ω\subset\mathbb R^d$. Consequently, every coercive, weakly lower semicontinuous energy on this space attains its minimum over $\mathcal{N}_N$. This covers the Deep Ritz method with convex integrands, Sobolev training and Lipschitz learning. Moreover, as the weight decay parameter tends to zero, minimizers of the regularized problem converge, up to subsequences, to minimizers with minimal parameter norm. We also prove that the set of ReLU networks with two hidden layers of bounded widths is not closed in $W^{1,p}(Ω)$ or in $C(\overlineΩ)$. This disproves a conjecture of Petersen, Raslan and Voigtlaender.

新论文 · v1arXiv:2611.08857

STRIDE: Learning Humanoid Locomotion in Minutes with Acceleration-Based Rewards

Nico Bohlinger, Jan Peters

原文摘要

Learning locomotion directly on a humanoid robot is a promising direction to avoid the sim-to-real gap. However, locomotion rewards in Reinforcement Learning (RL) typically track the base velocity, which cannot be measured onboard without an external motion capture system or well-calibrated state estimator. This is why we introduce \method{}, which learns humanoid locomotion from minutes of samples with a reward that only requires the onboard Inertial Measurement Unit (IMU). Instead of tracking the base velocity, STRIDE rewards the robot for following a commanded acceleration profile. To learn efficiently from this reward, we use the off-policy RL algorithm XQC and combine a high gain setting for the joint position controllers with left-right symmetry augmentation. In simulation, STRIDE learns to walk on the Unitree G1 and Booster T1 humanoids within 14 minutes of samples. Compared to learning without these two components, it reduces the falls during training by 81%, while without them the robot learns only in over an hour.

cs.RO · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2601.21623

LAMP: Look-Ahead Mixed-Precision Inference of Large Language Models

Stanislav Budzinskiy, Marian Gloser, Tolunay Yilmaz, Ying Hong Tham, Yuanyi Lin, Wenyi Fang, Fan Wu, Philipp Petersen

原文摘要

Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of compositionally-rich functions, concentrating on transformer inference. Based on the rounding error analysis of a composition $f(g(\mathrm{x}))$, we provide an adaptive strategy that selects a small subset of components of $g(\mathrm{x})$ to be computed more accurately while all other computations can be carried out with lower accuracy. We then explain how this strategy can be applied to different compositions within a transformer and illustrate its overall effect on transformer inference. We study the effectiveness of this algorithm numerically on GPT-2 models and demonstrate that already very low recomputation rates allow for improvements of up to two orders of magnitude in accuracy.

cs.LG · math.NA

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.16828

Prediction-Intervention Games and Invariant Sets

Linus Kühne, Felix Schur, Jonas Peters

原文摘要

We consider the following two-player game: using observational data, the leader chooses a prediction function for a response variable $Y$ from given covariates. The follower then reacts with an intervention on some covariates in the underlying structural causal model to maximize their own objective. The leader knows the intervention targets, but may have limited knowledge of the follower's objective. We call this setup a prediction-intervention game, a special case of a Stackelberg game. Finding an optimal strategy for the leader is generally difficult. To avoid severe performance loss, the leader may base their prediction on the causal parents of $Y$, or more generally on an invariant subset of covariates. We prove, for two common classes of follower objectives, that predictors based on the stable blanket, an invariant subset, are at least as good as those based on the causal parents. We further upper bound the leader's post-intervention risk by a worst-case risk over allowed interventions and strengthen existing distribution generalization results to analyze this bound: we give sufficient conditions under which stable-blanket predictors are worst-case optimal, and show by examples that these conditions cannot in general be dropped. Finally, we discuss practical strategies for settings with known and unknown graph, and test them on simulated and real-world data.

stat.ML · cs.AI · cs.LG · stat.ME

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2606.06233

Anchor PCA

Benedikt Seiter, Anya Fries, Julius von Kügelgen, Jonas Peters

原文摘要

Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data. However, this approach can focus on spurious directions that exhibit high variation in only a few domains. To find a robust embedding that still explains most variance in unseen but similar domains, we propose instead to focus on shared directions of variation. To this end, we introduce Anchor PCA which trades off overall explained variance with agreement between the shared and domain-specific low-rank embeddings. Anchor PCA amounts to PCA on a modified target matrix and thus can be solved efficiently. Moreover, we show that Anchor PCA recovers a maximal invariant subspace and admits a minimax reconstruction interpretation under bounded domain-specific covariance inflations. On simulated and real-world data with temporal distribution shift, we demonstrate, respectively, that Anchor PCA recovers the maximal invariant subspace and yields embeddings that explain more variance on unseen domains than the pooling baseline and a worst-case alternative. Taken together, these findings establish Anchor PCA as a promising approach to robust unsupervised dimension reduction from multi-domain data.

stat.ML · cs.LG · stat.ME

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2606.02194

Coherent Off-Policy Improvement of Large Behavior Models with Learned Rewards

Christian Scherer, Joe Watson, Theo Gruner, Daniel Palenicek, Ingmar Posner, Jan Peters

原文摘要

Distilling expert demonstration data into large generative models using behavioral cloning is a scalable approach to learning capable policies for robotic control, particularly for dexterous manipulation. Reinforcement learning (RL) can be used as a means to finetune these policies further using additional experience. An open question is whether RL is more sample-efficient than collecting more expert demonstrations. Prior work has finetuned large pretrained policies in a scalable fashion by applying RL to a smaller residual policy that corrects the pretrained model. However, for typical sparse reward tasks, RL algorithms can struggle to optimize the behavior in a sample-efficient manner. We explore inverse reinforcement learning, where a dense reward function is learned from expert demonstrations, potentially reducing the challenge of RL finetuning. We specifically consider coherent imitation learning, an IRL method that facilitates improvement of the BC policy by using a specific learned reward formulation with theoretical guarantees for imitation learning. We show that our IRL method maintains or improves the performance of pi-0.5 on all six sparse manipulation tasks and achieves a $\geq 90\%$ success rate on five out of six complex manipulation tasks, outperforming RL-based baselines using sparse rewards. We also demonstrate real-world learning on a robot manipulation task, finetuning pi-0.5 to success with less than 30 minutes of environment interaction time. By ensuring our initial pretrained finetuning policy is optimal for our initial reward and critic, our method circumvents the initial drop commonly seen in RL finetuning and enables faster improvement.

cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.02681

HistoTx: Early fusion of H&E images and spatial transcriptomics at varying spatial transcriptomics resolution with self-supervised learning

Alice Driessen, Emil Malmsten, Steffen Wolf, Bernd Illing, Isinsu Katircioglu, Adriano Martinelli, Rolf Stahel, Solange Peters 等 14 位作者

原文摘要

Spatial transcriptomics maps gene expression across tissue sections and, when integrated with whole slide images, jointly captures both morphological architecture and molecular activity to provide a rich, multimodal view of tissue biology. ML approaches combining spatial transcriptomics and WSIs typically learn a mapping from morphological features to molecular profiles via contrastive alignment or supervised fine-tuning of pathology foundation models. In both cases, transcriptomics serves as a training signal rather than a true input modality, leaving inference fundamentally image-driven. We propose an early-fusion vision transformer architecture in which transcript tokens are constructed at arbitrary spatial resolution, merged with image patch tokens, and jointly processed through a shared transformer stack for deep cross-modal interaction. Starting from a pretrained vision-only pathology foundation model, we train HistoTx by continuing self-supervised pretraining on paired image and spatial transcriptomics data and demonstrate that: 1) at inference with image only, performance remains on par with the baseline on most tasks while improving on tasks that inherently benefit from molecular knowledge, such as gene expression prediction; 2) when both modalities are available at inference, jointly providing image and transcript inputs outperforms either modality alone.

cs.LG · cs.AI · q-bio.GN · q-bio.QM

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37965

Meta-Initialization of Implicit Neural Representations to Accelerate Deformable Medical Image Registration

Marat O. Zinovev, Dmitry V. Sorokin

原文摘要

Implicit neural representation (INR) methods for deformable medical image registration require the network parameters to be optimized for each new image pair, making adaptation speed a practical limitation. This work investigates whether early adaptation can be accelerated using an initialization learned from a collection of previously solved registration tasks. We examine two schemes: Reptile meta-initialization and STRAINER transfer of the shared component of a coordinate network. KAN-IDIR is used as the base INR displacement-field model. Experiments are conducted on OASIS-1, with 364 consecutive pairs used for training and 49 pairs for test-time adaptation. Registration quality is evaluated using mean Dice and HD95, together with the fraction of voxels with a negative Jacobian determinant at iteration 1500. In the configurations studied, both schemes yield higher Dice and lower HD95 at early iterations than random initialization. Reptile numerically outperforms STRAINER under a small iteration budget, although their pretraining budgets are not matched. As the number of iterations increases, the differences between the schemes shrink. STRAINER pretraining takes 39-40 minutes, compared with 44.98 hours for Reptile.

cs.CV · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2505.13231

Investigating Active Sampling for Hardness Classification with Vision-Based Tactile Sensors

Junyi Chen, Frederik Heller, Mario Gómez Andreu, Boris Belousov, Tim Schneider, Lisa P. Y. Lin, Katja Doerschner, Knut Drewing 等 10 位作者

原文摘要

Hardness is one of the most important object properties that humans and robots perceive through touch. This paper investigates active sampling strategies for sample-efficient hardness classification with vision-based tactile sensors (VBTS), using information-theoretic measures of model uncertainty. We evaluated three probabilistic classifier models and two active sampling strategies and a random sampling baseline on a hardness classification task, with our own dataset of VBTS samples collected by a robot and a previously published dataset. In addition, we conducted a human study on the hardness classification task with the same objects as our dataset. Our findings indicate that the active sampling approaches, driven by variance and entropy as measures of model uncertainty, perform best with accuracy reaching 90%, compared to human accuracy of 48%, demonstrating the effectiveness of using VBTS for hardness classification. More information can be found at: https://fheller1.github.io/ActiveHardness

cs.RO · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36452

Whole-Body Humanoid Control via Stochastic Motion Tokenization

Michael Drolet, Oleg Arenz, Jan Peters

原文摘要

While velocity-commanded RL policies are effective for controlling quadrupeds, they are a limited interface for humanoids that need to perform complex whole-body motions. Furthermore, RL tracking policies for whole-body motions typically have limited information about the desired future motion, preventing them from performing controlled deviations to achieve long-term task success; such information is particularly relevant when a controller must prepare for transitions between behaviors. We address these challenges using concise motion representations that can be generated by a high-level controller, given a behavior label or text command. These representations can be fed directly into a tracking policy to provide a detailed motion reference. Our method exhibits a high degree of flexibility in performing real-world robot motions such as dancing, fighting, or walking based on conditional information. At matched capacity, our adopted stochastic motion tokenizer reconstructs motions from the Unitree G1 at a level that exceeds state-of-the-art approaches such as finite scalar quantization (FSQ) and the vector-quantized autoencoder (VQ-VAE). The resulting discrete interface conditions whole-body tracking policies that execute generated dance, fight, and walk motions lasting 16.8 s each and a 35 s fight-to-dance sequence on a physical Unitree G1.

cs.RO · cs.LG

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arXiv ↗PDF ↗