Papers

Generalist graph anomaly detection (GAD) aims to build a foundation model that detects anomalies on arbitrary unseen graphs without retraining or fine-tuning. Sufficient data are essential for foundation model training, yet generalist GAD still faces a data shortage, as real-world anomalous graphs are scarce and costly to collect and annotate. To fill this gap, we propose AG-FORGE, an Anomalous Graph generation Forge for automatic synthesis of anomalous graphs, exploring the feasibility of synthetic data-driven training for generalist GAD. Empirically, we find that synthetic data can achieve performance comparable to real-world training, but fail to push the performance boundary further due to the limited capacity of existing methods. To further unlock model capacity as training data scale up, we develop TS-GGAD, a Topology-Semantic coordinated Generalist GAD that captures complementary topological and semantic anomaly evidence, together with a curriculum learning strategy tailored to large-scale synthetic training. Extensive experiments on 14 real-world datasets demonstrate that TS-GGAD, trained on data generated by AG-FORGE, significantly outperforms state-of-the-art methods.

Generating large attributed graphs requires reproducing the topology, generating attributes jointly with the structure, and remaining scalable. Many real-world graphs exist as a single large graph, so a generative model has to generalize from the one graph it is fit on, without independent samples. We present Schema, which recursively decomposes a reference graph into a hierarchy of soft communities, assigning each node a membership distribution. Generation is then split into three stages, each trained independently: (1) synthesizing node attributes conditioned on soft memberships, (2) generating intra-community edges from local structural context, and (3) modeling inter-community connections over bridge nodes whose membership mass is distributed across several communities. No stage forms the full adjacency matrix, and each stage operates on a subgraph bounded by the community size. We also introduce an evaluation protocol that covers structural fidelity, memorization, downstream utility, and scalability. On four real-world attributed graphs, Schema recovers the balance between local and long-range structure more closely than any other model that generates attributes, while reproducing only a small fraction of the reference edges. It retains the downstream accuracy of the reference graph without raising it artificially above that level. Baselines that match its structural fidelity memorize the reference, while those with higher downstream accuracy either exceed the reference accuracy or fail to complete on the larger graphs. We measure scalability on six additional graphs with up to 10 million nodes.

Why does removing reference-policy KL regularization sometimes improve group policy optimization? This motivates studying how reference-policy information should enter group-relative updates. We analyze seven potential failure modes in the interactions between KL and rewards: residual KL updates after reward clipping, after gradient cancellation, and in groups with identical rewards; KL growth with response length and an imbalance in its relative contribution; KL concentration on a small number of tokens; and sampling noise when k1 is incorporated into rewards. We propose Zero-Sum Calibrated Policy Optimization (ZCPO), which uses relative drift measured by conditional KL to calibrate within-group reward coefficients and integrates them into the base surrogate. Mathematical reasoning experiments and ablations support this design's effectiveness in our settings.

We study episodic constrained Markov decision processes with adversarial losses under stochastic hard constraints. Specifically, starting from a known strictly feasible policy with margin $d$, we seek to obtain optimal regret while satisfying the expected cost constraints in every episode. In this setting, Stradi et al. (2025) show that a carefully designed mixing rule attains regret of order $\widetilde{\mathcal{O}}(\sqrt{T}/\min\{d,d^2\})$. Interestingly, they also provide a lower bound of order $\Omega(\sqrt{T}/\rho)$ for the same setting, where $\rho$ is the Slater margin of the offline problem and can be much larger than $d$. In this work, we build on their approach to obtain optimal regret dependence on these margins. Specifically, we propose MA-OPS, an algorithm that combines an optimistic search for the Slater margin with a pessimistic evaluation of the selected policies to safely learn a policy with a large feasibility margin. This policy is then used to minimize regret while satisfying the constraints at every episode. In particular, we show that MA-OPS attains regret $\widetilde{\mathcal{O}}(\sqrt{T}/\rho + 1/(d\rho))$. Finally, we provide a matching lower bound, showing that the dependence on $T$, $d$, $\rho$ in the regret bound is optimal up to logarithmic factors.

In many engineering design problems, the objective and constraints depend on the state: the solution of a PDE determined by the design parameters. We consider improving a design while holding selected state observables near trusted values, which we call state preservation constraints. Constrained Bayesian optimisation handles these with a learnt feasibility model, but struggles with this problem's highly anisotropic feasible set. Our central idea is to pre-compute the set of controls whose linearised constraint response stays within tolerance, thereby pulling back the state-space constraint into design space. This linearisation defines an ellipsoid from which we can efficiently draw a large number of well-spread candidates. The underlying linear response map is refined online, and the ellipsoid is rebuilt accordingly. We demonstrate the method end-to-end on our key application - Tokamak divertor optimisation under plasma-boundary preservation.

Quantum machine learning, and quantum neural networks (QNNs) in particular, are advancing fields with growing potential. Although systematic comparisons of QNN configurations have been explored primarily for classification tasks, comparatively little attention has been given to regression problems, particularly financial time series forecasting. This study presents a large-scale systematic comparative evaluation of QNN component configurations for financial time series forecasting, using the GBP/USD spot exchange rate as a case study. A grid search across encoding methods, ansatz designs, qubit counts, layer depths, and cost functions yields 1,368 distinct model configurations, each evaluated in terms of prediction accuracy, computational cost, and convergence behaviour. The results reveal unique insights into how the choice of methods influences performance, such as that gate selection and arrangement are more critical to model success than raw parameter count, and that entanglement is a system-level property of the full circuit rather than solely at the ansatz level. The best-performing QNN configuration achieves an $R^2$ score of 0.985, outperforming a classical BiLSTM baseline. Additionally, the impact of real quantum hardware noise is assessed through execution on the IQM Emerald device, revealing that gate errors and decoherence represent a significant barrier to practical deployment, with gate selection and circuit depth identified as key determinants of hardware noise resilience. Overall, the findings provide practical architectural guidance for QNN design and establish a baseline characterisation of QNN noise sensitivity on near-term quantum devices.

Unauthorized model distillation, in which a model is trained on the outputs of a proprietary large language model (LLM), is a growing threat to model providers. We study distillation inference: determining whether a suspect model was distilled from another model or trained independently. We formulate this problem as a hypothesis test and estimate the behavior expected under each hypothesis by training shadow models: distilled shadow models learn from the teacher's reasoning traces, whereas independent shadow models learn only from reference answers. The auditor measures how closely each model predicts the teacher's reasoning outputs and then uses the shadow models to convert the suspect's score into a calibrated p-value. In a preliminary study using Qwen2.5-7B as the teacher and Llama-3.2-3B for the suspects, our test achieves a true positive rate of 1.0 at a significance level of 0.02. These results demonstrate the feasibility of using distillation inference to detect distillation attacks.

Many key-value (KV) caches are compressed before anyone knows what will be asked of them: a document cached for retrieval, a prompt prefix shared across requests, the memory of a long conversation. The prevailing approach scores KV entries by rehearsal: the model rereads the context and keeps the entries it attends to, assuming that the more completely a cache rehearses its context, the better it remembers it. We show that under tight budgets this assumption backfires: rehearse everything, remember nothing. At a 3% keep ratio, rereading the whole context keeps 31.5 of 96.5 points on RULER, and on LongBench's natural-text tasks it falls below methods that rehearse nothing at all. The cause is that a cache keeps what it rehearses: rereading spreads the budget across the whole context, so the answer's own entries survive at little more than chance. Like a student before an exam, a cache remembers more by testing itself than by rereading. Two principles follow: rehearse what will be read, and rehearse as much as there is. We instantiate them as Attic-KV (Attic for short), a training-free rehearsal in which the model quizzes itself with question-answer pairs that quote the context, alongside anchor tokens in a content-adaptive amount. Changing only the rehearsal lifts three hosts that score it in three different ways: Attic alone is the best training-free method in all eight settings we test on RULER and LongBench's natural-text tasks, and plugged into the gradient-based KVgrad and the trained RestoreKV+, it raises them by up to 17.1 and 28.1 points. Its advantage grows as the budget shrinks, reaching 41.9 points over full rereading at a 3% keep ratio, and on long documents it compresses faster than rereading them.

Predicting the structure and response of inhomogeneous polymer electrolytes requires a description of ion correlations that retains molecular-scale accuracy while remaining transferable across spatial scales and geometries. We develop a neural density functional for electrolytes that preserves spatial symmetries, thermodynamic integrability and the Noether identities, with perfect screening recovered in stable, noncritical bulk states. Its nonlinear density dependence captures the concentration-dependent correlations missed by a pair closure, including a crossover from enhanced to suppressed long-wavelength number fluctuations at strong coupling. The functional describes density profiles at an untrained salt concentration and predicts bulk structure factors and the long-wavelength number response. Trained solely on planar density and internal-force profiles from molecular dynamics, the functional predicts ionic structure in larger domains and in two-dimensional external fields. On the same ion data, it is more accurate than three other neural density-functional architectures and keeps its accuracy with a quarter of the training runs, where the errors of the best alternative grow by about two thirds. The spatial transferability provides a necessary foundation for connecting molecular correlations to continuum predictions at larger scales.

Algorithm Selection is essential for efficient Constraint Programming. Over the years, many algorithm selectors based on machine learning methods have been successfully applied, yet traditional feature extraction methods often rely on manually decided instance-level statistics that fail to capture the underlying problem structure. In this paper we aim to bridge this gap by introducing a novel, automated feature extraction methodology that integrates graph conversion and Weisfeiler-Lehman graph kernels to generate robust structural representations of problem instances. The 1-WL test bounds the graph-distinguishing power of standard message-passing Graph Neural Networks (GNNs), and suitable GNN architectures match this bound \citep{Xuetal2018}. WL-based features offer an alternative that does not require training a GNN. Our primary contribution is a cut-based representation (WLc) designed to model structural partitions and provide a more nuanced predictive signal. We evaluate our approach on instances from the 2023–2025 MiniZinc Challenges across two tasks: maximizing Borda count scores and maximizing predictive accuracy. Experimental results across Support Vector Machines, Random Forests, and Multi-Layer Perceptrons demonstrate that cut-based features outperform fzn2feat with SVMs, while results with RFs and MLPs are closer.

In many machine learning applications, it is necessary to guard against worst-case scenarios and predictions that could result in substantial losses. In principle, this can be achieved by training risk-averse predictive models that minimize loss functions such as conditional value-at-risk (CVaR), rather than relying on models that perform well on average. In practice, however, the effectiveness of this approach to risk aversion is undermined by the learner's uncertainty regarding the true loss distribution and, consequently, the true CVaR. To achieve reliable risk-aversion, we propose a method in which this (epistemic) uncertainty is represented in terms of credal sets, i.e., sets of probability distributions. More specifically, we develop an efficient yet reliable learner that produces predictions in the form of credal sets and combine it with a novel decision rule that maps each credal set to a single predictive distribution for CVaR minimization. Across classification, under distribution shift, and in reinforcement learning, our approach reliably avoids catastrophic decisions, while sacrificing little in expected performance.

Off-policy actor–critic methods control overestimation bias by taking the minimum of two critics. This uses the same aggregation rule everywhere, regardless of how the critics disagree. We propose GeZo-SAC, which uses auxiliary geometric representations to adapt critic pessimism to the state and action. Alongside its scalar value, each critic predicts a set of generators defining a zonotope. Probing this zonotope along sampled directions provides a geometric width, "subtracted from each critic value as a pessimistic offset, and a measure of disagreement between the two critics, aggregated with log-sum-exp. This disagreement controls how the critics are combined, moving from a width-weighted average toward the usual minimum as disagreement increases. At inference, the deployed policy is an unmodified SAC actor, since the generators are used only on the critic side during training.Across four MuJoCo-v5 locomotion benchmarks and six off-policy baselines, GeZo-SAC achieves the highest mean return on Ant-v5 and Hopper-v5 and remains competitive with other methods on the remaining tasks. Our analysis further shows that GeZo-SAC achieves the lowest average actuator work and action effort per metre among the evaluated methods, while maintaining near-zero measured overestimation frequency across all four environments.

Watermarking large language models is popular for tracing chatbot and agentic outputs, yet detectors remain unreleased since exposing them could let attackers do targeted edits with the detector's feedback. However, watermarks are already vulnerable to uninformed tampering attacks. We thus first quantify whether a public detector would be an additional liability in a deployment setting at varying levels of access, from token-level scores to a binary verdict. Second, we introduce a split-key public-private watermarking method that exposes one key through a public detector while keeping the other for full verification and forensics. An informed attacker can only move the public signal, creating an imbalance between public and private scores. We introduce a statistical test for this imbalance, and combine it with the full key verdict in a two-stage mechanism. Third, we evaluate the split-key method on a wide range of removal and forgery attacks, comparing the uninformed to detector-informed settings. Public detection improves removal only at small edit budgets, since plain rephrasing already strips the watermark at a lower quality cost, but it does enable forgery, which the private pipeline can identify. Overall, releasing half of the watermark enables transparency and interoperability, and tampering with the released half stays detectable. This bounds the provider's liability and questions the need to keep detectors fully private.

Flow matching has emerged as a scalable paradigm for training high-quality generative models, but sampling from the learned probability flow requires many network evaluations. Distillation can reduce this cost to one or a few evaluations; however, one-step generation often sacrifices quality, making few-step generation the practical operating regime. Existing few-step methods perform their iterative computation along the probability flow and therefore require a fixed, manually chosen timestep discretization. This discretization is often chosen heuristically and is expensive to tune; it may also be restrictive when refinement difficulty differs across samples or spatial locations. We introduce data-space iteration, a few-step generation framework that removes flow discretization altogether. Starting from noise, a shared generator directly refines its prediction in data space, with every iteration trained to produce the best sample permitted by its capacity. Our formulation integrates with distribution matching distillation (DMD) with minimal changes, enabling a controlled comparison between iteration methods under matched training settings. On class-conditional ImageNet 256x256, data-space iteration outperforms standard discretization baselines and matches or improves upon variants selected through schedule search, without requiring schedule-specific training. These results show that data-space iteration provides a simple and effective alternative to discretized flow-space iteration for fast generation.

Neural network-based predictive modeling with high-dimensional structured Gaussian targets requires an efficient and numerically stable, yet expressive approximation of the covariance matrix. We propose SCORE: a scalable framework, combining scoring rule training with an expressive covariance approximation learned in spectral space. For $d$-dimensional data, the learning task is decomposed into learning the marginal distributions and learning a structured correlation matrix, which enables dense dependencies with linear storage and $\mathcal{O}(d\log d)$ cost. We utilize the closed form Gaussian kernel score for training, which remains defined even for degenerate covariances and admits bounded gradients during optimization. We characterize kernel scores under invertible transforms and prove exact invariance under unitary transforms. At population level, our two-level objective recovers the true marginals and projects the target correlation onto the representable class; finite-sample PAC bounds show that the errors of the two stages enter additively. We evaluate our model on a variety of tasks with a commonly assumed Gaussian domain: Time-series forecasting, monocular depth estimation, and spatial weather prediction, showing improved performance at lower computational cost.

Few-shot learning aims to recognize novel categories from limited labeled examples. Recent studies incorporate textual semantics to compensate for limited visual observations and improve class representations. However, high image-text agreement may reflect both intrinsic object properties and incidental context, making support prototypes susceptible to contextual contamination. To address this problem, we propose DVLA-RL++, which extends DVLA-RL with complementary semantic purification (CSP) and counterfactual reinforcement-learning gating (CRG). Specifically, CSP generates intrinsic and nuisance descriptions from labeled supports and compares their agreement with each support token. An ambiguity-dependent rejection margin guides sparse evidence allocation, while an intrinsic semantic anchor fills the unassigned mass to provide a fallback when visual evidence is unreliable. CRG learns layer-wise semantic fusion strengths using a reward that balances recognition performance and nuisance exposure. An independently executed reference trajectory on the same episode provides a paired learning signal. Theoretical analysis relates retained evidence and anchor quality to prototype stability and establishes conditions for unbiased on-policy gradient estimation. Experiments on standard, fine-grained, and cross-domain benchmarks show state-of-the-art accuracy, with an average gain of 1.4% over DVLA-RL. The project page is available at https://peacelwh.github.io/TPAMI27-DVLA-RLpp/.

Particle filters are a standard tool for nonlinear state estimation, but their resampling step is discrete, preventing gradient-based learning in variational sequential Monte Carlo. We introduce Differentiable Systematic Resampling (DSR), a temperature-controlled relaxation of systematic resampling, that preserves the CDF-ordered, banded structure of systematic resampling while enabling full gradient flow. DSR converges to exact systematic resampling as the temperature vanishes, and we prove a pointwise exponential convergence rate for the induced bias. Compared to optimal-transport-based differentiable resampling, DSR avoids iterative solvers and has substantially lower computational overhead. Experiments on stochastic dynamical systems and real-world handwriting data show that DSR achieves comparable or superior filtering and dynamics learning performance.

Continuing the Perception Test challenge series, we organised the fourth edition as a workshop at the European Conference on Computer Vision (ECCV) 2026 in Malmö, Sweden. This edition focused on spatial intelligence and featured four different tracks: unified multiple-choice videoQA and grounded videoQA from the original Perception Test benchmark, alongside two new tracks based on city-scale walking-tour videos (KilometerAudio and KilometerVision). In this report, we describe the new benchmarks used for the city-scale tracks and summarise the winning solutions across all tracks, including a generalist model that competed across all tracks with satisfactory performance. The winning solutions in the newly added city-scale tracks demonstrated that complex spatial and multimodal reasoning can be solved by expensive agentic pipelines, but remains difficult for multimodal models used standalone.

Simulators based on differential equations are ubiquitous in science and engineering. They are often used in simulation-based inference to evaluate the posterior distribution of the input parameters based on real-world observations of the simulator outputs. However, inference becomes challenging when individual simulator evaluations are computationally expensive. In such cases, a Bayesian optimization-based active learning approach with Gaussian process surrogate models has been used to maximize the information obtained from a limited simulation budget. Recently, gradients of simulator outputs with respect to input parameters have become increasingly available, yet they are rarely exploited for inference. Even though we only need to learn the simulator input-output relationship, gradient information can provide an additional valuable signal to guide the active learning procedure. This is of particular interest in the case of expensive simulators, when sample efficiency is crucial. In this paper, we demonstrate how incorporating gradient information into the Gaussian process surrogate accelerates Bayesian optimization-based inference under a limited simulation budget. Our results show significant improvement in convergence speed from using gradient information. For reverse-mode differentiation, the inference efficiency gains are maintained when accounting for the additional computational cost. In contrast, for forward-mode differentiation, the inference speed-up does not outweigh the computational costs. These results indicate that gradient-enhanced surrogates are beneficial primarily in problems where the number of parameters exceeds the output dimensionality, where reverse-mode differentiation is efficient.

Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear. In this work, we leverage Gaussian distributions to isolate this phenomenon. We establish 2-Wasserstein convergence bounds for optimized hyperparameters, showing that diffusion processes achieve a sampling error of $O(\sqrt{d\lambda_{\max}}\log N/N)$, where $d$ is the dimension, $N$ the number of sampling steps, and $\lambda_{\max}$ the largest eigenvalue of the target covariance matrix. Unadjusted and underdamped Langevin dynamics suffer from an additional $\sqrt\kappa$ factor, where $\kappa$ is the condition number. These rates follow from spectral bounds which are sharp: we confirm them via matching first-order asymptotics as $N\rightarrow\infty$. Our analysis provides a rigorous characterization, in the Gaussian setting, of how time-dependent score trajectories remove condition-number dependence during sampling. By contrast, in the learning phase, we show that estimating the unnoised score by gradient descent leads to essentially the same estimator as estimating a noisy score, which suggests that the benefits of noising do not come from the learning phase.

Graph neural networks (GNNs) predict molecular properties from chemical graph data, but predictive accuracy does not explain how graph information supports an individual decision. A compact prediction-preserving rationale does not necessarily reveal which changes reverse the decision or which modifications the model tolerates. We propose the Multi-Perspective Graph Explainer (MPGE), unifying factual support, counterfactual sensitivity, and exemplar tolerance for a frozen classifier. The factual view, originally termed prototype (PT), seeks a compact retained edge set with the same label and required confidence. Counterfactual (CF) explanations seek bounded prediction-changing deletions; exemplar (EXE) explanations seek non-trivial bounded deletions that preserve the label and confidence. A shared constrained formulation connects prediction behavior, compactness, and edit cost, while separate objectives generate the three views. Our graph-classification extension of CF-GNNExplainer learns symmetric edge rankings and verifies discrete candidates, recording unsuccessful searches. A separate BBBP fragment backend returns RDKit-sanitized molecules. We evaluate the primary GCN implementation on MUTAG, Mutagenicity, AIDS, COX2_MD, and BBBP using semantic coverage, conditional quality, stability, and runtime. Successful factual masks retained 8.6%–15.5% of input edges on average across datasets; bounded counterfactual coverage was 4.8%–67.6%, and exemplar preservation coverage was 98.9%–100.0%. Exploratory controls reveal the influence of hard projection and retained node information. Quantitative comparisons and molecular visualizations characterize model support, sensitivity, and tolerance without treating them as validated chemical mechanisms.

Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.

Large language models (LLMs) are increasingly deployed in sociotechnical systems where social attribution, the reasoning process attributing external events to the causes and reasons of agents' social behaviors, plays a critical role. These processes involve judgments of social cause, responsibility, and blame/credit to agents. Although attributional models are well-studied in social psychology and cognition through Attribution Theory, social attribution remains underexplored in AI, particularly LLM social reasoning. This paper provides the first systematic exploration of LLM social attribution. Our work focuses on responsibility and blame attributions, examining current LLMs' judgments and their underlying internal mechanisms. Guided by attribution theory, we construct a social attribution benchmark consisting of a Vignette subset based on classic scenarios from attribution theory research and a Reality subset based on real-world social narratives, yielding 7,639 responsibility/blame judgment questions. On this basis, we evaluate 32 representative LLMs and 5 basic non-LLM baselines. To further explore the internal mechanisms underlying the LLM judgment process, we develop a probing-based methodology to investigate the latent-space representations of 5 key attribution dimensions and the consistency of their influences on LLM judgments compared to those in human social attribution. Our research findings reveal that current LLMs exhibit measurable but incomplete agreement with human responsibility and blame judgments, and meanwhile, this agreement is positively correlated with model size. Some attribution dimensions are systematically decodable from specific positions in LLM hidden states, and their influences on the final judgment are consistent with those indicated by human Attribution Theory. The dataset and associated code are available at https://github.com/Yuzhaoxin946/SAB-Bench.

World models for control must capture which aspects of the environment respond to the agent's actions and which are relevant to reward. Generative world models such as Dreamer 4 consist of a video tokenizer, which encodes each frame into a latent, and a dynamics model, which is pretrained to predict future latents from past latents and actions. Yet the tokenizer is trained with a reconstruction objective, without action or reward supervision, so its latent provides no explicit mechanism to separate controllable, uncontrollable, reward-relevant, and reward-irrelevant information. We propose CausalDreamer, which keeps the tokenizer frozen and re-encodes its latent into a factored representation of four groups along two axes: controllability, where only the two controllable groups receive the action, and reward relevance, learned by predicting the reward from the two reward-relevant groups. The pretrained dynamics model is then fine-tuned to predict the factored representation. We evaluate CausalDreamer and the pretrained world model it starts from with model-predictive planning on 20 MMBench2 tasks: 10 clean tasks seen during training and 10 unseen tasks, of which 6 are manipulated variants of clean tasks with a changed background, object, or maze layout, and 4 are new environments. We normalize returns so that a policy taking uniformly random actions scores 0 and an expert scores 1. CausalDreamer achieves a 14% higher normalized score than the pretrained world model on the clean tasks (0.199 vs.\ 0.175) and a 25% higher score on the manipulated variants (0.307 vs.\ 0.246), while neither model scores meaningfully above the random policy in the new environments. Additionally, our analysis shows that the factored representation separates reward-irrelevant changes, such as a changed background, from its reward-relevant groups.

Physics-informed machine learning has gained significant attention in recent years. In regimes of limited data, parametrized Gaussian processes have become popular. Existing approaches, however, often face limitations, such as requiring parametrizable (also called controllable) systems or a large number of output tasks. In this work, we introduce a systematic procedure we call "ghost tasking", using auxiliary tasks to circumvent these limitations. We prove that such ghost tasks can render any non-parametrizable system effectively parametrizable, enabling algorithmic construction of parametrized Gaussian Processes while keeping the number of required tasks (i.e. output dimensions) and latent functions low. We find that ghost tasking performs especially well in an inverse problem setting, even with very few available data. We show the usage and power of ghost tasking in three experiments, providing systematic comparisons to the only other currently available method applicable to all experiments. We provide necessary syntax and explications for two computer algebra programs that compute parametrizations for systems with polynomial or rational coefficients. Our theoretical results extend to systems with meromorphic functions.

Which forms of test-time compute improve the predictions of strong pretrained tabular foundation models (TFMs)? We systematically study this along three axes: adaptation, aggregation, and context construction. Our evaluation spans modern TFMs across the TabArena benchmark, supplemented by experiments on wide and large-scale tables from OpenML. For adaptation, we introduce DiagScale, a diagonal query-key similarity update. It trains only 0.003-0.03% of model parameters and achieves gains comparable to full fine-tuning across three independently pretrained backbones. For aggregation, both pool composition and selection strategy matter. TabPFN-3 already averages predictions from different preprocessing variants of the same data, and adding more such predictions yields diminishing returns. With a broader pool of 96 configurations, greedy selection reduces error by 2.4% relative to the default predictor, but uniform averaging increases error. For context construction, attention-guided retrieval improves TabPFN-3's predictions on some large tables and supports source pools beyond the full context memory limit. The context expansion methods we test yield no consistent improvement. Taken together, our results suggest that adaptation and selective aggregation yield consistent benchmark-level gains. The benefits of context construction depend more on the task and data regime. Adaptation and aggregation over the same backbone yield further gains when combined, but require substantially more computation than default inference. These trade-offs motivate choosing strategies according to the available computation budget. Code is available at https://github.com/kanghui-learning/test-time-compute-for-tabular-foundation-models.

Understanding how deep neural networks process information remains a central challenge. Existing interpretability methods often compromise structural fidelity, rely on prespecified corpora, or explain models post-hoc. We propose Polytopal Neural Networks (PNNs), a framework that extracts distinct layer-wise aspects by enforcing a polytope-based structure that is used directly in subsequent information processing. We scale our approach using learned corpus representations and an amortized simplex inference procedure and highlight how the framework also gives a direct route to vector quantized (VQ) training. In PNNs, observations are explicitly described by their alignment with layer-specific aspects. Empirical results show that imposing polytopal constraints on neural network representations preserves meaningful structures in the latent space with minimal degradation in performance, favorable compressed representations when compared to VQ representations in unsupervised learning, while also providing a performant new approach to VQ deep learning training. Our findings suggest that deep networks can enforce interpretable polytope-based representations, offering a principled path toward more transparent AI systems with minimal performance compromise.

Test-time training (TTT) adapts an LLM's parameters using signals derived from test inputs, and can make striking improvements in pre-specified settings such as IMO competitions or designated open problems. By turning deployment experience into parameter updates, TTT provides a direct mechanism for model-level self-improvement. Yet TTT is not universally beneficial: each TTT algorithm works in different settings, and applying an ill-suited method could waste test-time compute or even damage model performance. Therefore, such parameter-level self-improvement requires agency: the model must decide when TTT is warranted, which algorithm to invoke, and whether an existing skill can be reused. To fill this gap, we introduce Agentic-TTT, which learns a test-time policy to govern those decisions. Agentic-TTT turns TTT procedures into callable tools, treats accumulated skills as an evolving deployment environment, and trains its policy using the observed utility gains from its decisions. On our benchmark, Agentic-TTT nearly doubles the utility over the backbone model, learns to trade off utility against compute, and generalizes to domains unseen during training. Together, these results point toward autonomous self-improvement: models that can decide how to learn from their own deployment experience.

Bayesian optimisation is the natural tool for shape design when objectives are expensive and non-differentiable, but it needs a compact yet expressive parameterisation of the search space. Hand-crafting one is a complex endeavour requiring domain expertise, and often yields implicit infeasible regions, artificial bounds, and coupled, unordered coordinates. We instead learn the parameterisation from a collection of existing designs, applying principal component analysis to the deformations between shapes. The result is a linear, interpretable search space in which the number of components explicitly trades expressivity against dimensionality. Across aerofoils, wings, and radio-frequency cavities, spanning 2D geometry to 3D aerodynamics and electromagnetics, we show improved sample efficiency and the ability to explore beyond the confines of hand-crafted baselines.

We detail scalable methods for approximating the quadratic entropy $p^T d p$ for arbitrary distributions $p$ and common distances $d$ of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where $d$ is held constant while $p$ varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.