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Ver preçosUncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S^{2}-PINN, that represents the solution u(t,x,Z) of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic basis, coupled by a low-rank Canonical Polyadic (CP) tensor decomposition core. The method is trained with a hybrid strong-form and gPC-projected residual loss. Our theoretical analysis establishes that the separable class is dense in L^2 under mild conditions, and the projected residual corresponds exactly to a stochastic Galerkin constraint. Furthermore, we show that mini-batch projection coefficients are logarithmically dependent on the number of gPC modes, and that the orthogonality penalty controls the conditioning of the learned spatial dictionary. Using four manufactured random PDE benchmarks, we show that S^{2}-PINN outperforms nine baselines in terms of mean and variance accuracy, as well as calibration, while using significantly fewer parameters. Further evaluations on non-manufactured Poisson and Darcy problems, a stochastic Navier--Stokes problem, a diffusion scaling study of higher random dimensions, and two stochastic inverse problems reveal the generalization capabilities of the proposed structure. Together, these results support stochastic separability as an effective design principle for physics-informed neural UQ. The code for the experiments can be found in https://github.com/DMax1314/s2pinn
Complex reasoning queries can be decomposed into directed acyclic task graphs and distributed across heterogeneous LLMs, reducing latency through parallelism and enabling smaller models to solve complex tasks. In practice, however, the suitability of an LLM for a given subtask may be a priori unknown, and execution alone does not reveal output correctness. We propose JOVE, an online framework that jointly assigns executor LLMs and selects intermediate outputs for paid verification. Verification runs asynchronously and is used to improve future allocations, so the system must balance spending on execution now against learning for later. We study how to optimize this trade-off under a long-term budget and a per-query latency constraint, with stochastic, initially unknown LLM service quality, invocation costs, and execution times. JOVE makes execution and verification decisions by solving a sequence of per-query mixed-integer linear programs. Online learning updates task-dependent estimates of LLM quality based on verification feedback, while an information-gain bonus incorporates the value of learning into allocation decisions. Under a natural set of assumptions, we establish sublinear quality-learning regret for JOVE. Across four reasoning benchmarks, JOVE achieves competitive accuracy against standard inference baselines while reducing average cost and latency by at least 3.17 times.
Lung ultrasound (LUS) is attractive for tuberculosis (TB) screening at primary-care level, but labelled cohorts are small. Echocardiography carries no such constraint, while sharing the same underlying ultrasound imaging physics, signal processing and B-mode appearance as LUS. We ask whether an encoder pretrained on that high-resource ultrasound domain carries representations that remain usable in the low-resource one. Only the encoder varies, across seventeen encoders spanning three architecture families. Among them, a latent-predictive video encoder pretrained on generic video (V-JEPA2-L) and its echocardiography counterpart (EchoJEPA-L) differ in pretraining corpus alone. The choice among these encoders does not resolve the classification, the whole family spanning 2.50 percentage points against a measurement resolution of 2.71. What moves the task instead is feature conditioning. Standardising the features between the encoder and the classifier improves all seventeen encoders by a mean of +1.23 percentage points at p=1.510^{-5}. On the held-out test set every encoder selected on the development folds stands above the baseline system by up to +2.57 percentage points of area under the receiver operating characteristic curve (AUROC), and specificity at 90% sensitivity reaches 79.3% against 60.3%. The contrast specified in advance, EchoJEPA-L against V-JEPA2-L, measures -0.16 percentage points at p=0.926. We therefore find no evidence that shared ultrasonic physics alone makes echocardiography a more productive pretraining corpus than generic video, and any advantage, if present, is smaller than this cohort can resolve. The video encoders receive replicated still images, however, so whether this absence of an effect reflects the pretraining domain or a video encoder applied to static frames cannot be separated. The limiting factor is the labelled cohort rather than the encoder.
Multimodal Large Language Models (MLLMs) achieve strong performance across vision-language tasks, yet the internal mechanisms by which visual and textual information are fused across layers remain insufficiently understood. We investigate representative MLLMs from two architectural paradigms: concatenation architectures and native multimodal architectures. We conduct three progressively connected analyses: alignment decoupling identifies which modality changes, attention routing and entropy characterize how cross-modal information is distributed, and intrinsic dimensionality examines how fusion reshapes feature spaces. Separately, we perform causal intervention experiments as a validation of the resulting interpretation. As a supplementary analysis, we use visual CKA to examine the Platonic Representation Hypothesis. Together, these analyses reveal two distinct fusion pathways: concatenation models follow a text-first, vision-later pathway, whereas native models exhibit earlier visual-textual co-adaptation and feature-space reorganization. This work provides a mechanistic perspective for understanding multimodal fusion and supports architecture-aware diagnostics of multimodal representations.
Reinforcement learning (RL) for learning path recommendation (LPR) faces two coupled obstacles. First, the policy must commit to a sequence of L concepts without intermediate feedback, producing a combinatorial search space that grows super-exponentially with L and provides reward only at the final step. Second, expert learning paths would be the natural cure for sparse-reward RL, but they do not exist in educational data, because student logs record what learners did, not what they should have done. We address both obstacles by importing a recipe from simulator-based demonstration learning in robotics: the knowledge tracing simulator is used both to synthesize per-learner expert demonstrations through evolutionary search and to train a deployment-free policy that distills these demonstrations into a feed-forward learner. Our framework, EVOL, instantiates this pipeline with an asymmetric actor-critic where the actor commits to deployment-realistic blind planning while the critic exploits the privileged simulator state during training. Across three datasets (ASSIST15, Junyi, and EdNet; 39-189 concepts) and path lengths L = 5, 10, and 20, EVOL surpasses 8 baselines spanning heuristic, sequential, RL, graph-enhanced RL, and LLM-enhanced methods. We further compare three imitation strategies (BC, AWR, and DAPG) and show that final performance is governed by the quality of evolutionary experts rather than by the particular imitation objective.
Touché 2026 extends causality extraction to counter-causal claims: news sentences whose surface form appears causal but whose meaning denies the causation, as in "It is falsely believed that X caused Y." A system that relies on surface cues such as "caused" or "led to" will accept such a sentence as causal and give it the wrong polarity. On the Countercausal News Corpus (CCNC), the task has three subtasks: deciding whether a sentence is causal (detection), locating its cause and effect spans (extraction), and labeling its polarity as procausal, counter-causal, or uncausal. We build one model per subtask. Detection is a fine-tuned classifier with a single cross-task rule that uses the extracted spans to remove false positives. For extraction, we ensemble three RoBERTa-large BILOU+CRF taggers by averaging their token-level scores before decoding, rather than voting on the spans each tagger produces. For polarity, where labeled counter-causal examples are scarcest, we add training sentences generated by a large language model prompted with nine patterns of counter-causal expression adapted from Hagen et al., keeping only those that pass automatic structural checks. On the held-out CCNC test set, the system reaches F1 0.869 on detection and macro-F1 0.817 on polarity, and in the organizers' final causal-only evaluation of extraction it scores granularity-adjusted F1 0.728, the highest extraction score among all submissions including the organizers' baseline. The development split is used only for component selection and the ablations reported in the paper.
Large-scale pre-training has improved the generalization of neural operators across diverse PDEs. However, existing PDE foundation models still struggle with heterogeneous dynamics, where shared representations may cause knowledge interference, while mixture-of-experts (MoE) architectures suffer from increasing expert redundancy. We propose SPEAR, a spectral-disentangled MoE neural operator with knowledge-guided expert aggregation for large-scale PDE pre-training. SPEAR decouples latent features into low- and high-frequency components, enabling shared modeling of transferable dynamics and specialized learning of PDE-specific patterns. To address expert redundancy, we design a knowledge-guided expert aggregation strategy that measures expert similarity from dataset-specific learned knowledge and routing preferences, enabling the identification and consolidation of similar experts. Experiments on twelve PDE datasets and multiple downstream benchmarks demonstrate superior performance in pre-training, fine-tuning, and transfer learning. Furthermore, our aggregation strategy reduces the number of experts by 50\% while maintaining or improving prediction accuracy, achieving a balance between model efficiency and generalization for PDE foundation models.
Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.
We release PaMIR (Public Arrival-ordered Measurement for Inference in Risk), an open benchmark for credit-default prediction when labels are scarce and arrive late. The field's reference benchmark studies use eight datasets each, only two or four of them public. PaMIR brings together 19 public datasets with binary default labels -- 1.24M loans, firms and card accounts from nine countries -- rebuilt from pinned source snapshots by one leakage-audited recipe and never redistributed; to our knowledge it is the one of its kind as of today. Every model is a single function, scored under a repeated i.i.d. split and a label-delayed stream in which each application is scored on arrival, with AUC reported by label budget; fleet means are withheld unless every dataset is scored. A synthetic-data harness tests generated training rows without letting a generator see held-out rows. This report describes release 0.4.0 of this living benchmark.
Scalable nonlinear causal discovery requires methods that combine flexible mechanism estimators with efficient search over large graph spaces. Several algorithmic families have been proposed to address this challenge, yet their accuracy-runtime trade-offs remain poorly understood. We empirically compare the four major approaches: differentiable structure learning, amortized structure learning, score-matching, and combinatorial search. Our results reveal complementary bottlenecks: differentiable and amortized methods scale well but exhibit an accuracy gap, score-matching methods can be accurate in low dimensions but degrade quickly for increasing feature sizes, and combinatorial methods remain accurate but are slowed by repeated and redundant local scoring. Motivated by this bottleneck, we develop SPADE, a spline-based score-evaluation scheme that compiles sufficient statistics once and reuses them throughout combinatorial search. Under bounded indegree, its Gaussian variant reduces algorithmic complexity from O(nd^3) to O(nd^2+d^3). Empirically, SPADE shifts the observed scalability-accuracy frontier by orders of magnitude: it solves 100-variable problems with 160K samples in seconds and 1600-variable problems with 2.5K samples in minutes, while retaining high structural accuracy across synthetic and real-world benchmarks. These results reveal a substantial shift in the practical scale of combinatorial search and highlight the importance of evaluating scalable causal-discovery methods along the full accuracy-runtime frontier.
We present a first evaluation of machine learning applied to patient clinical and demographic data gathered in two different countries for the purpose of tuberculosis (TB) screening to identify people who would benefit from expensive molecular testing. Experiments are based on the recently-compiled CAGE-TB dataset, which includes sub-cohorts of people with presumptive TB presenting at community health care centres in South Africa and Uganda. Three neural network architectures (logistic regression (LR), multilayer perceptrons (MLP) and convolutional neural networks (CNN)) are considered in conjunction with greedy feature selection. For the convolutional neural network, a strategy that jointly optimises feature selection and feature ordering is proposed and shown to lead to consistent development and test set improvements. For all three models, development set area under the receiver operating characteristic (AUROC) curve is improved by 2-7% using feature selection. LR after feature selection achieves an AUROC of 0.8 [0.75,0.86] (95% CI) and 0.84 [0.78,0.9] when testing on the held-out Ugandan and South African data respectively. Although outperforming LR on the development cohort, the deeper networks (MLP, CNN) show inconsistent trends on the held-out cohorts, while LR achieves performance within 1-2% of the best achieved in terms of AUROC. LR narrowly misses the WHO minimum requirements by 4-9% in sensitivity even though the network is being evaluated on a completely held-out cohort. The development of neural-network based classifiers for TB screening therefore appears viable.
Local AI is becoming more useful by the token. As AI agents move from experiments into everyday development, increasingly capable open models are shrinking to fit on more devices, giving builders more to run locally. Coming this month, NVIDIA DGX Spark will be available with 64GB of unified memory from top manufacturer partners — Acer, […]
A model trained on "The capital of X is Y" may produce "Y" after "The capital of X is" but fail after "The capital of X:". We call these different ways of eliciting the same fact request forms. To separate learning a fact from retrieving it, we train two models in two stages. In the first stage (request-form training), one model sees each fact in five forms and the other sees the same facts only as statements. In the second stage (target-fact training), both receive identical training on new facts, all as statements. Both then retrieve the new facts almost equally well from statements, but differ sharply on other request forms. Thus, a model can learn how to retrieve through a request form before it learns the facts. To understand this difference, we examine the hidden state immediately before the answer, which we call the context state. When given two different request forms for the same fact, the model trained on five forms in stage one produces more similar context states than the model trained on statements alone in that stage. Changing this state at retrieval time can enable or prevent retrieval of an already learned fact, and the same effect transfers across facts and factual relations, such as capitals and currencies. To test its role during learning, we change the context state only during target-fact training. This intervention changes later retrieval without intervention at test time. Together, these results show that later retrieval depends on earlier request-form experience and the context state during fact learning.
