arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 55 records · Page 3Linked to original sources

arXiv2026

Echoes of the Prior: A Computational Phenomenology of Forgetting

Memory is not merely the storage of data; it is the scaffolding of reality. When biological memory fades, the world does not simply turn black; it regresses into an unrecognizable chaos. Echoes of the Prior is an interactive installation that attempts to visualize this subjective phenomenology of forgetting. By inducing controlled synaptic decay within a Feed-Forward 3D Reconstruction model, we create an artistic analogy for the erosion of the brain's predictive priors. We position the Neural Network not as a tool for engineering, but as a cognitive proxy - a silicon brain whose structural degeneration evokes the disorienting, poetic, and terrifying experience of losing one's grip on the world. Ultimately, we offer this framework as a catalyst, inviting the wider community to explore the uncharted potential of neuromorphic aesthetics in visualizing the fragility of intelligence. Interactive demo see https://decart-4d.github.io/.

cs.CV↗

arXiv2026

PaperMentor: A Human-Centered Multi-Agent Writing Tutor for AI Research Papers on Overleaf

Expert writing feedback from experienced researchers is critical for early-career scholars to improve their manuscripts, yet high-quality feedback often remains scarce because reviewing research papers is labor-intensive. Emerging AI-powered writing assistants largely focus on grammar fixes or simulating peer review with final scores, yet they fall short of providing concrete, actionable suggestions that help students improve their papers during drafting. We present PaperMentor, a human-centered writing assistant system that delivers actionable suggestions as Overleaf-native inline comments while leaving the actual writing entirely to human authors. PaperMentor integrates an expert skill library carefully curated from established researchers' writing advice with 12 specialized agents covering different aspects of paper writing, such as formatting compliance, phrasing accuracy, and terminology consistency. In a user study (n=14), 90.6% of the generated comments were rated actionable and 67.5% were rated valid, significantly outperforming a GPT-5.2 baseline uswithout the skill library. We release PaperMentor as open source for public use. Our code is publicly available under the AGPL-3.0 license at https://github.com/jiarui-liu/overleaf

cs.CL↗

arXiv2026

Causality Is Key to Understand and Balance Multiple Goals in Trustworthy ML and Foundation Models

Ensuring trustworthiness in machine learning (ML) systems is crucial as they become increasingly embedded in high-stakes domains. This paper advocates for integrating causal methods into machine learning to navigate the trade-offs among key principles of trustworthy ML, including fairness, privacy, robustness, accuracy, and explainability. While these objectives should ideally be satisfied simultaneously, they are often addressed in isolation, leading to conflicts and suboptimal solutions. Drawing on existing applications of causality in ML that successfully align goals such as fairness and accuracy or privacy and robustness, this paper argues that a causal approach is essential for balancing multiple competing objectives in both trustworthy ML and foundation models. Beyond highlighting these trade-offs, we examine how causality can be practically integrated into ML and foundation models, offering solutions to enhance their reliability and interpretability. Finally, we discuss the challenges, limitations, and opportunities in adopting causal frameworks, paving the way for more accountable and ethically sound AI systems.

cs.LG↗

arXiv2026

STRIDE: Training Data Attribution via Sparse Recovery from Subset Perturbations

Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude ($13\times$) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.

cs.LG↗

arXiv2026

Trustworthy AI Suffers from Invariance Conflicts and Causality is The Solution

As artificial intelligence (AI), including machine learning (ML) models and foundation models (FMs), are increasingly deployed in high-stakes domains, ensuring their trustworthiness has become a central challenge. However, the core trustworthy AI objectives, such as fairness, robustness, privacy, and explainability, are hard to achieve simultaneously, especially while preserving utility. This position paper argues that causality is necessary to understand and balance trade-offs in performance and multiple objectives of trustworthy AI. We ground our arguments in re-interpreting trustworthy AI trade-offs as incompatible invariance requirements under different changes to the data-generating process. We then illustrate this argument through case-study analyses from the literature and a stylized synthetic-data simulation, showing that causality provides a unifying framework for understanding how trade-offs in trustworthy AI arise and how they can be softened or resolved through selective invariance. This perspective applies to both classical ML models and large-scale FMs. Finally, we outline open challenges and opportunities for using causality to build both trustworthy and high-performing AI.

cs.AI↗

arXiv2026

TabPFN-3: Technical Report

Tabular data underpins most high-value prediction problems in science and industry, and TabPFN has driven the foundation model revolution for this modality. Designed with feedback from our users, TabPFN-3 builds on this foundation to scale state-of-the-art performance to datasets with 1M training rows and substantially reduce training and inference time. Pretrained exclusively on synthetic data from our prior, TabPFN-3 dramatically pushes the frontier of tabular prediction and brings substantial gains on time series, relational, and tabular-text data. On the standard tabular benchmark TabArena, a forward pass of TabPFN-3 outperforms all other models, including tuned and ensembled baselines, by a significant margin, and pareto-dominates the speed/performance frontier. On more diverse datasets, TabPFN-3 ranks first on datasets with many classes, and beats 8-hour-tuned gradient-boosted-tree baselines on datasets up to 1M training rows and 200 features. TabPFN-3 introduces test-time compute scaling to tabular foundation models. Our API offering TabPFN-3-Plus (Thinking) exploits this to beat all non-TabPFN models by over 200 Elo on TabArena, rising to 420 Elo on the largest data subset, and outperforms AutoGluon 1.5 extreme while being 10x faster, without using LLMs, real data, internet search or any other model besides TabPFN. TabPFN-3 extends the capabilities of our models, enabling SOTA prediction on relational data (new SOTA foundation model on RelBenchV1) and tabular-text data (SOTA on TabSTAR via TabPFN-3-Plus); and improves existing integrations: a specialized checkpoint, TabPFN-TS-3, ranks 2nd on the time-series benchmark fev-bench, and SHAP-value computation is up to 120x faster. TabPFN-3 achieves this performance while being up to 20x faster than TabPFN-2.5. In addition, a reduced KV cache and row-chunking scale to 1M rows on one H100 with fast inference speed.

cs.LG↗

arXiv2026

PEFT-Arena: Understanding Parameter-Efficient Finetuning from a Stability-Plasticity Perspective

Parameter-efficient finetuning (PEFT) has become the standard approach for adapting large language models, yet evaluations largely emphasize downstream accuracy while overlooking the retention of pretrained capabilities. We argue that PEFT should be assessed through the stability-plasticity dilemma: the trade-off between target-task adaptation and resistance to forgetting. We introduce PEFT-Arena, a benchmark that jointly measures downstream performance and general capability retention. Across methods, we find distinct stability-plasticity profiles; under comparable parameter budgets, orthogonal finetuning achieves the most favorable Pareto frontier. To explain these differences, we analyze PEFT updates from two geometric perspectives. In weight space, spectral analysis reveals how parameterizations interact with the pretrained singular-value structure. In activation space, retention metrics show whether finetuning preserves or distorts general-capability representations, with forgetting linked to non-isometric representation distortion. Finally, an analysis shows that final SFT checkpoints often overshoot a better target-retention operating point. Inspired by this, we present case studies of a post-hoc improvement with path-wise rewinding.

cs.LG↗

arXiv2026

Intrinsically Interpretable Attention via Sparse Post-Training

We introduce a simple post-training method that makes transformer attention sparse without sacrificing performance. Applying a flexible sparsity regularisation under a constrained-loss objective, we show on models up to 7B parameters that it is possible to retain the original pretraining loss while reducing attention connectivity to $\approx 0.4 \%$ of its edges. Unlike sparse-attention methods designed for computational efficiency, our approach leverages sparsity as a structural prior: it preserves capability while exposing a more organized and interpretable connectivity pattern. We find that this local sparsity cascades into global circuit simplification: task-specific circuits involve far fewer components (attention heads and MLPs) with up to 100x fewer edges connecting them. Additionally, using cross-layer transcoders, we show that sparse attention substantially simplifies attention attribution, enabling a unified view of feature-based and circuit-based perspectives. These results demonstrate that transformer attention can be made orders of magnitude sparser, suggesting that much of its computation is redundant and that sparsity may serve as a guiding principle for more structured and interpretable models.

cs.LG↗

arXiv2026

Learning to Reason Efficiently with A* Post-Training

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid proof itself, requiring a reasoning procedure in which intermediate inferences are correct. Specifically, we investigate whether LLMs can learn to generate correct and efficient proofs with guidance from A* search -- an algorithm that guarantees an optimally efficient path to a goal. We explore two training techniques: supervised fine-tuning on execution traces from A* and reinforcement learning with A*-informed process reward models. Empirically, we find that Llama-3.2 models in the 1B--3B range benefit substantially from A* post training, going from near-zero accuracy to outperforming DeepSeek-V3.2 -- a much larger model. Our analysis uncovers a trade-off: while simple correctness rewards maximize accuracy, A*-informed signals strike a balance between accuracy and efficiency. Furthermore, we find that on larger search spaces, models trained with imperfect heuristics exhibit superior accuracy. Our results demonstrate a promising direction towards reasoning guided by principles derived from classical search algorithms.

cs.AI↗

arXiv2026

Riemannian Networks over Full-Rank Correlation Matrices

Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.

cs.LG↗

arXiv2026

The Alien Space of Science: Sampling Coherent but Cognitively Unavailable Research Directions

Scientific discovery is constrained not only by what is true, but by what is cognitively available to the researchers currently exploring a field. Many directions are coherent in light of the literature yet unlikely to be proposed because no existing community occupies the right combination of concepts, methods, and intuitions. Modern language models inherit this bias, recombining high-density regions of the literature when prompted for novel ideas. We introduce a framework that targets the complementary region, which we call the alien space of science, where directions are plausible under the structure of existing knowledge but unlikely under the distribution of existing researchers. Our method first decomposes papers into granular conceptual units and clusters them into a shared vocabulary of idea atoms. It then learns two complementary models over this vocabulary. A coherence model scores whether a combination of atoms forms a viable research direction, and an availability model scores whether any existing author community is positioned to produce a given combination. Sampling alien directions then reduces to ranking atom combinations that maximize coherence while minimizing availability. On a corpus of 16,068 peer-reviewed LLM papers from NeurIPS, ICLR, ICML, and major NLP venues, the resulting sampler explores a 3.5 - 7 x broader effective atom vocabulary than frontier LLM ideation baselines without sacrificing coherence, and produces ideas that match or exceed those baselines under blind LLM, human, and downstream experimental evaluation. By separating scientific plausibility from community availability, our framework points toward AI ideation that complements rather than merely accelerates human science, expanding exploration into coherent directions that the current community may overlook.

cs.AI↗

arXiv2026

Test of Time: Rethinking Temporal Signal of Benchmark Contamination

Post-cutoff performance decay of LLMs has been widely interpreted as a temporal signal for benchmark contamination, where public information released before the training cutoff may have been included into training corpora and inflated model performance by memorization. We critically examine this view and demonstrate that this temporal signal is highly sensitive to how benchmark questions are constructed, even if the underlying source material remains invariant. Specifically, we show that LLM-transformed questions can produce remarkably different temporal patterns compared to fill-in-the-blank (cloze) questions directly retrieved from the very same documents. We validate this effect on prior benchmarks that report clear post-cutoff decay (LiveCodeBench), and show that a simple LLM-driven transformation of the same problems can effectively remove the temporal pattern. We further provide a mechanistic understanding of this phenomenon using influence function analysis. Overall, our results suggest that post-cutoff performance decay is a sensitive contamination signal, motivating more robust contamination probes for reliable LLM evaluation.

cs.AI↗

arXiv2026

Learning POMDP World Models from Observations with Language-Model Priors

Whether navigating a building, operating a robot, or playing a game, an agent that acts effectively in an environment must first learn an internal model of how that environment works. Partially-observable Markov decision processes (POMDPs) provide a flexible modeling class for such internal world models, but learning them from observation-action trajectories alone is challenging and typically requires extensive environment interaction. We ask whether language-model priors can reduce costly interaction by leveraging prior knowledge, and introduce \emph{Pinductor} (POMDP-inductor): an LLM proposes candidate POMDP models from a few observation-action trajectories and iteratively refines them to optimize a belief-based likelihood score. Despite using strictly less information, \emph{Pinductor} matches the performance and sample efficiency of LLM-based POMDP learning methods that assume privileged access to the hidden state, while significantly surpassing the sample efficiency of tabular POMDP baselines. Further results show that performance scales with LLM capability and degrades gracefully as semantic information about the environment is withheld. Together, these results position language-model priors as a practical tool for sample-efficient world-model learning under partial observability, and a step toward generalist agents in real-world environments. Code is available at https://github.com/atomresearch/pinductor.

cs.LG↗

arXiv2026

PENEX: AdaBoost-Inspired Neural Network Regularization

AdaBoost sequentially fits so-called weak learners to minimize an exponential loss, which penalizes misclassified data points more severely than other loss functions like cross-entropy. Paradoxically, AdaBoost generalizes well in practice as the number of weak learners grows. In the present work, we introduce Penalized Exponential Loss (PENEX), a new formulation of the multi-class exponential loss that is theoretically grounded and, in contrast to the existing formulation, amenable to optimization via first-order methods, making it a practical objective for training neural networks. We demonstrate that PENEX effectively increases margins of data points, which can be translated into a generalization bound. Empirically, across computer vision and language tasks, PENEX improves neural network generalization in low-data regimes, matching and in some settings outperforming established regularizers at comparable computational cost. Our results highlight the potential of the exponential loss beyond its application in AdaBoost.

cs.LG↗

arXiv2026

Stargazer: A Scalable Model-Fitting Benchmark Environment for AI Agents under Astrophysical Constraints

The rise of autonomous AI agents suggests that dynamic benchmark environments with built-in feedback on scientifically grounded tasks are needed to evaluate the capabilities of these agents in research work. We introduce Stargazer, a scalable environment for evaluating AI agents on dynamic, iterative physics-grounded model-fitting tasks using inference on radial-velocity (RV) time series data. Stargazer comprises 120 tasks across three difficulty tiers, including 20 real archival cases, covering diverse scenarios ranging from high-SNR single-planet systems to complex multi-planetary configurations requiring involved low-SNR analysis. Our evaluation of eight frontier agents reveals a gap between numerical optimization and adherence to physical constraints: although agents often achieve a good statistical fit, they frequently fail to recover correct physical system parameters, a limitation that persists even when agents are equipped with vanilla skills. Furthermore, increasing test-time compute yields only marginal gains, with excessive token usage often reflecting recursive failure loops rather than meaningful exploration. Stargazer presents an opportunity to train, evaluate, scaffold, and scale strategies on a model-fitting problem of practical research relevance today. Our methodology to design a simulation-driven environment for AI agents presumably generalizes to many other model-fitting problems across scientific domains. Source code and the project website are available at https://github.com/AIPS-UofT/Stargazer and https://aips-uoft.github.io/Stargazer/, respectively.

cs.LG↗

arXiv2026

Drifting Fields are not Conservative

Drifting models have recently gained attention for generating high-quality samples in a single forward pass. During training, they learn a push-forward map by following a vector-valued field, the drift field. We ask whether this procedure is equivalent to optimizing a scalar loss and find that, in general, it is not: drift fields are not conservative and cannot be written as the gradient of any scalar potential. We identify the position-dependent normalization as the source of non-conservatism, with the Gaussian kernel as the unique radial exception. Guided by this, we introduce the sharp kernel $k^\#$ and a sharp-normalized drift field that is conservative for general radial kernels. The resulting vector field is the gradient of a scalar potential that can be optimized directly using stochastic gradient descent. Moreover, the field has the form of a score difference of kernel density estimates, and gives exact equilibrium identifiability. Thus, sharp normalization closes the gap to related literature, such as Wasserstein gradient-flows and denoising score matching, also for non-Gaussian kernels. Empirically, sharp normalization preserves the performance of the original drifting objective, suggesting that the non-conservative flexibility is not required for high-quality generation.

cs.LG↗

arXiv2026

Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA

Binary black holes (BBHs) in eccentric orbits produce distinct modulations in gravitational waves (GWs); measuring orbital eccentricity provides evidence for dynamical binary formation channels. We analyze 57 GW events from the LIGO-Virgo-KAGRA (LVK) O1-O3 observing runs using a multipolar aligned-spin inspiral-merger-ringdown waveform with two eccentric parameters: eccentricity and relativistic anomaly (assuming a quasi-circular merger-ringdown), made computationally feasible by the machine-learning code \texttt{DINGO}, which accelerates inference by 2-3 orders of magnitude. First, with a uniform eccentricity prior, eccentric vs. quasi-circular aligned-spin $\log_{10}$ Bayes factors are 1.84-4.75 (depending on glitch mitigation) for GW200129, 3.0 for GW190701 and 1.77 for GW200208_22. We infer $e_{\text{gw, 10Hz}}$ $(e_{\text{gw, 20Hz}})$ to be $0.27_{-0.12}^{+0.10}$ ($0.16_{-0.05}^{+0.04}$) to $0.17_{-0.13}^{+0.14}$ ($0.1_{-0.04}^{+0.05}$) for GW200129, $0.54_{-0.30}^{+0.12}$ ($0.31_{-0.13}^{+0.12}$) for GW190701 and $0.39_{-0.23}^{+0.23}$ ($0.21_{-0.08}^{+0.08}$) for GW200208_22. Second, eccentric aligned-spin vs. quasi-circular precessing-spin $\log_{10}$ Bayes factors are 1.43-4.92 for GW200129, 2.61 for GW190701 and 1.23 for GW200208_22. Third, GW190521 shows no evidence for eccentricity ($\log_{10}$ Bayes factor 0.04). Fourth, neglecting spin-precession with an astrophysically-motivated prior on the eccentric BBH rate, the probability of one of the 57 events being eccentric exceeds 99.5\% or $(100-8.4\times10^{-4})$\% (depending on glitch mitigation). Fifth, we study parameter estimation impacts of neglecting eccentricity in quasi-circular models or higher modes in eccentric models. These results underscore the inclusion of eccentric parameters in BBH characterization for upcoming LVK runs and future ground- and space-based detectors probing more diverse BBH populations.

gr-qc↗

arXiv2026

Bounded Ratio Reinforcement Learning

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

cs.LG↗