UAI 2026 论文列表

We challenge the prevailing assumption that interpretability requires sacrificing accuracy in spatial-temporal forecasting. We propose STGNAM (Spatial-Temporal Graph Neural Additive Model), which enforces a strict additive decomposition: 𝐲̂ = f_node + f_temporal + f_spatial + f_interact + bias, where each component is independently evaluable and visualizable. Our central finding is that the additive inductive bias acts as an implicit regularizer: on PEMS-BAY, STGNAM *sets a new state of the art* (MAE 1.62), surpassing all black-box models including TITAN (1.69) and its own D2STGNN teacher (1.87)—even without knowledge distillation (KD). When combined with KD from a black-box teacher, STGNAM achieves 91–104

Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled Bayesian inference intractable. We propose the NonLocal Bayesian Spatio-Temporal model (NLBST), a hierarchical Bayesian framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time ODE whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural ODE residual captures additional nonlinear dynamics. A linear-Gaussian observation model enables Kalman-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a Bayesian hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.

The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection. However, a common assumption most methods make is that the conditional independencies in the distribution imply the same separation in the graphical structure—also known as the faithfulness assumption. Unfortunately, this assumption can be violated by higher-order dependencies such as XOR and parity-type relations, and—on finite samples—by empirical violations that, in extreme cases, even induce spurious dependencies absent from the true distribution. Therefore, in this paper we propose a “k-order” relaxation of the faithfulness assumption that captures parity type relationships between k+2 variables. We then propose a proof of concept algorithm called k-order Markov blanket (kOMB) that uses this relaxation for MB discovery. Finally, we empirically show how kOMB can recover the MB of a variable under both true and empirical violations of faithfulness. Code available at: https://github.com/lklee9/k-order-Markov-blanket.

We study k-means clustering of persistence diagrams through their Hilbert-space embeddings, focusing primarily on persistence landscapes. Although persistence landscapes are widely used in practice, it remains unclear when clustering them faithfully reflects clustering in the diagram space. We give simple, verifiable geometric conditions under which (i) nearest-center labels in the landscape space exactly agree with those in the diagram space, and (ii) the landscape k-means objective provably calibrates the diagram-space objective, leveraging tools from modern statistical learning theory. Combined with known fast rates for k-means in Hilbert spaces, our results show that landscape-based k-means provides a statistically and computationally efficient surrogate for diagram-space k-means with explicit performance guarantees and a controllable geometric distortion.

Conformal prediction is a distribution-free and model agnostic framework that can provide statistical guarantees to machine learning algorithms: a point-wise predictor is transformed into a conformal predictor that outputs sets of predictions which include the ground truth with a user defined confidence rate. In multi-label conformal classification however, the exponential growth of the output space makes confidence sets prohibitively complex to compute in the general case. In this paper, we analyze this challenge under the prism of enumeration complexity. We detail a general approach for confidence set enumeration based on the flashlight method, prove a sufficient condition for efficient enumeration and apply this method on three types of problems. First, we give an enumeration algorithm with linear delay for modular non-conformity losses. Then, we discuss informed conformal classification where a boolean circuit specifies a set of valid label combinations and prove a sufficient condition for efficient enumeration based on standard properties of the circuit. Moreover, we leverage our results on informed conformal classification to tackle label interactions in the loss. Finally, we illustrate the benefits of our approach with a few experiments.

Task-free continual learning (TFCL) aims to adapt models to non-stationary data streams without knowing task boundaries. In TFCL, catastrophic forgetting arises from both the evolving data distributions and the order-sensitive nature of batch-streaming optimization. To address these challenges, we propose a new TFCL framework that mitigates optimization-induced forgetting via order-invariant linearized adaptation during learning and accommodates evolving data distributions via density-guided adapter routing for more accurate and effective adapter retrieval during inference. We also provide a theoretical characterization of retrieval error in terms of density estimation quality and cross-adapter embedding separability. Experiments across multiple benchmarks demonstrate that our proposed method consistently achieves higher accuracy and lower forgetting than strong TFCL baselines under both standard and realistic streaming settings. For reproducibility, our experimental code is available at: https://github.com/Alisia0303/HESTIA.git .

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before changing its prediction. However, its applicability is more limited than some of its alternatives, since it requires the use of generative models and restricts the analyses either to specific model architectures or discrete features. In this work, we propose a new robustness metric applicable to any probabilistic discriminative classifier and any type of features. We demonstrate that this new metric is capable of distinguishing between reliable and unreliable predictions, and use this observation to develop new strategies for dynamic classifier selection.

Uncertainty quantification is essential for deploying machine learning models in high-stakes domains such as scientific discovery and healthcare. Conformal Prediction (CP) provides finite-sample coverage guarantees under exchangeability, an assumption often violated in practice due to distribution shift. Under covariate shift, restoring validity requires importance weighting, yet accurate density-ratio estimation becomes unstable when training and test distributions exhibit limited support overlap. We propose KMM-CP, a conformal prediction framework based on Kernel Mean Matching (KMM) for covariate-shift correction. We show that KMM directly controls the bias–variance components governing conformal coverage error by minimizing RKHS moment discrepancy under explicit weight constraints, and establish asymptotic coverage guarantees under mild conditions. We then introduce a selective extension that identifies regions of reliable support overlap and restricts conformal correction to this subset, further improving stability in low-overlap regimes. Experiments on molecular property prediction benchmarks with realistic distribution shifts show that KMM-CP reduces coverage gap by over 50

Machine unlearning aims to selectively remove the influence of designated training data from a trained model. Gradient ascent-based unlearning methods are widely used in machine unlearning, but are often observed to exhibit instability and sensitivity to optimization hyperparameters. In this work, we show that the ordering of forget-set samples during ascent materially influences the resulting optimization trajectory, yielding markedly different forgetting–retention trade-offs under identical optimization budgets. We provide a local second-order analysis illustrating how non-commutativity of ascent updates induces path dependence, and we propose a simple ordering strategy that processes forget samples from low to high predictive uncertainty. By deferring high-uncertainty samples, this strategy attenuates early parameter drift and leads to more stable trajectories. Across image classification benchmarks with convolutional and vision transformer architectures, as well as text classification tasks, we observe that this ordering consistently achieves effective forgetting while better preserving retain-set utility compared to random ordering. In the retain-data-free regime, this trajectory-aware modification substantially strengthens vanilla gradient ascent, improving its position on the forgetting–retention Pareto frontier relative to naive ascent and several retain-data-free unlearning baselines. In general, our results identify sample ordering as a practically meaningful and previously under explored degree of freedom in machine unlearning, highlighting the importance of trajectory-aware design and evaluation.

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale Lorenz ’96 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel Bayesian and flow-based approaches. Our results show that ensemble perturbations do not increase the system’s long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.

Federated Distillation enables distributed learning for clients with heterogeneous model architectures. In this paradigm, the server and clients exchange predictions on a shared unlabeled public dataset, rather than model parameters or gradients.

Multi-agent language systems are increasingly relied upon for high-stakes decision support. Many systems use consensus among agents as a measure of confidence. However, such a model is prone to failure if aligned agents have the same biases and propagate the same error. Under sycophantic consensus, correlated errors resemble strong agreement, and hallucination manifests as a consequence of uncalibrated uncertainty. While current measures provide useful heuristics, they lack statistical safety bounds at deployment time. This work reinterprets hallucination control as an uncertainty quantification problem. We contribute a Score Deviation penalty that directly lowers confidence when the factual disagreement within the ensemble rises. A Learn-Then-Test calibration procedure converts these penalized scores into a certified decision threshold that provably bounds the expected False Discovery Rate. The results show that this deviation-penalized method reduces the conservatism of the calibration process, achieving 71.7

Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use.In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.

Benchmark scores are the dominant lens through which progress in large language models is assessed, yet the implicit assumption that different benchmarks read out a shared internal structure has never been verified at the representation level. We introduce readout subspace analysis, a framework that extracts the low-dimensional subspace a benchmark uses to linearly discriminate correct answers from a model’s frozen hidden representations, and compares these subspaces across models and tasks via a coordinate-invariant Gram cosine metric. Analyzing 50 models spanning six architecture families and varied fine-tuning strategies (SFT, DPO, RLHF, model merging) on three benchmarks (MMLU, MedQA, AGIEval), we find that readout geometry is governed by the benchmark, not the model. Within the same benchmark, readout subspaces are strongly aligned even across architecturally unrelated models (Gram cosine up to 0.87 versus a random baseline of ∼10^-3), while subspaces across different benchmarks are nearly orthogonal. This convergence is graded: benchmarks sharing cognitive demands partially overlap in readout subspace, whereas those requiring qualitatively different reasoning occupy orthogonal regions. Furthermore, probe accuracy consistently meets or exceeds generation accuracy, indicating that benchmark scores reflect not only representational structure but also decoding efficiency. These findings recast benchmarks from passive measurement instruments to active structural constraints that selectively activate specific regions of representation space.

Certifying the IID generalisation ability of deep networks is the first of many requirements for trusting AI in high-stakes applications from medicine to security. However, when instantiating generalisation bounds for deep networks it remains challenging to obtain non-vacuous guarantees, especially when applying contemporary large models on the small scale data prevalent in such high-stakes fields. In this paper, we draw a novel connection between a family of learning methods based on model fusion and generalisation certificates, and surprisingly show that with minor adjustment several existing learning strategies already provide non-trivial generalisation guarantees. Essentially, by focusing on data-driven learning of downstream tasks by fusion rather than fine-tuning, the certified generalisation gap becomes tiny and independent of the base network size, facilitating its certification. Our results show for the first time non-trivial generalisation guarantees for learning with as low as 100 examples, while using vision models such as VIT-B and language models such as mistral-7B. This observation is significant as it has immediate implications for facilitating the certification of existing systems as trustworthy, and opens up new directions for research at the intersection of practice and theory.

Causal representation learning typically achieves identifiability using auxiliary variables external to the mixing process. This fails when observable sources act as internal mixing inputs whose entanglement invalidates standard volume-change proofs. We introduce a framework that treats observable sources as internal auxiliaries. We establish identifiability when all observed internal sources are used as conditioning variables. Under a volume-preserving mixing assumption, suitable variability conditions, and additional alignment conditions on the learned model, the unobserved source subspaces are identifiable up to an Independent Subspace Analysis (ISA)-style equivalence class—a permutation of conditionally independent subspaces with within-subspace invertible transformations. In practice, we approximate the volume-preserving restriction with encoders that stabilize the induced distortion. Leveraging the known causal graph, we further propose a scheme that selects conditioning sources so as to preserve fine-grained factorizations of the unobserved sources. Experiments show improved recovery over representative auxiliary-based baselines in settings where treating internal sources as external conditioners can induce cross-factor leakage.

Training divergence in transformers wastes compute, yet practitioners discover instability only after expensive runs begin. They therefore need an initialization-time signal for identifying risky training configurations. We study Residual Koopman Spectral Profiling (RKSP), a fixed, single-forward-pass spectral risk score. RKSP extracts Koopman spectral features by applying whitened dynamic mode decomposition to layer-wise residual snapshots. Our central diagnostic, the near-unit spectral mass, quantifies the fraction of modes concentrated near the unit circle, which captures instability risk. For predicting divergence across extensive configurations, this score achieves an AUROC of 0.995, outperforming the best gradient baseline. When calibrated probabilities are required for a target configuration distribution, a held-out one-dimensional calibrator maps the same scalar score to probabilities. We further make the diagnostic actionable through Koopman Spectral Shaping (KSS), which reshapes spectra during training. In the challenging high learning rate regime without normalization layers, KSS reduces the divergence rate from 66.7

In general reinforcement learning, all established optimal agents, including AIXI, are model-based, explicitly maintaining and using environment models. This paper introduces Universal AI with Q-Induction (AIQI), the first model-free agent proven to be asymptotically ε-optimal in general RL. AIQI performs universal induction over distributional action-value functions, instead of policies or environments like previous works. Under a grain of truth condition, we prove that AIQI is strong asymptotically ε-optimal and asymptotically ε-Bayes-optimal. We also apply our novel proof techniques to show asymptotic ε-optimality of Self-AIXI without any ad-hoc assumptions. Our results significantly expand the diversity of known universal agents.

Counterfactual fairness is a rigorous criterion for algorithmic decision-making but remains fundamentally unidentifiable from observational data alone. Existing partial identification methods address this by deriving bounds for fairness measures; however, these intervals are often wide, limiting their practical utility. To address this limitation, we propose a framework that quantifies the probability that a black-box model satisfies counterfactual fairness, under a stated prior over the structural causal models compatible with the observed data. By exploiting conditional independencies to reduce the parameter space, we demonstrate that the set of causal parameters compatible with the observed data forms a convex polytope. We further show that, given domain-specific priors on exogenous distributions, this prior-dependent probability can be estimated via Hit-and-Run Monte Carlo integration. Our approach provides a practical tool that complements worst-case bounds, offering a prior-dependent probabilistic summary for auditing model fairness.