Papers

To deploy deep neural networks on edge hardware, highly efficient inference schemes are necessary that retain high accuracy. This work presents W16A16, a high precision (16-bit), fast speed, low energy quantization method. On a widely applied microcontroller architecture Armv7E-M, our proposed approach achieves faster speed and lower energy consumption on layer- and model-level compared to alternative quantization schemes. We analyze the architecture of Armv7E-M, explain the underlying principles behind the performance advantages of 16-bit approaches, and evaluate the empiric quantization errors for regression and classification tasks, as well as empiric time- and energy consumption in MCU deployment. We observe ca.\ 10 times lower quantization errors compared to 8-bit quantization schemes while achieving similar or better inference times and energy consumption.

Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.

Long-horizon tasks with sparse rewards pose an exploration bottleneck for goal-conditioned reinforcement learning: a policy started from the initial state rarely reaches the goal and receives no learning signal. Reference motions, hand-designed curricula, and shaped rewards supply this signal but require demonstrations or task-specific engineering; automatic start-state and goal curricula avoid this but typically expand from one side only, so the full distance to the target must be covered from that side. We propose the Bidirectional Voronoi-biased Exploration curriculum for Reinforcement learning (BVER), which expands from both ends at once. Inspired by bidirectional RRT planning, BVER grows start states outward from the goal and goals outward from the initial state distribution, biases both toward unexplored task space, and steers them toward each other, training one goal-conditioned policy on both. On point-mass mazes, quadrupedal box climbing, and robot-arm ring-on-peg transfer, BVER learns faster than all compared reference-free curricula. On box climbing, it reaches 95% success on a 0.4 m box in roughly 65% fewer iterations than the best of them, is the only one of them to learn to climb a 0.7 m box, and yields a policy robust to start, goal, and yaw variation. Without a demonstration, it approaches the sample efficiency of reference-based curricula on the 0.4 m box and on ring-on-peg transfer. Ablations show that expanding from both ends outperforms either direction alone.

Vision language models (VLMs) incur substantial inference cost because every visual token is processed by the attention and MLP projections of every decoder layer, even when token-specific visual computation is unnecessary at many depths. We introduce Patch-to-Prune (P2P), inspired by Mechanistic Interpretability, a training-free framework that converts activation patching from a diagnostic tool into an inference-time computation bypass. P2P performs validation-guided forward and backward layer sweeps to identify decoder regions whose visual-token projection outputs can be replaced by fixed neutral proxy activation vectors within a user-specified accuracy tolerance. Unlike conventional token-pruning methods, P2P preserves the sequence length, token order, positional information, attention mask, and residual pathways, thereby pruning computation without removing tokens or modifying the pretrained model weights. We evaluate P2P on four VLMs from the Qwen2.5-VL and LLaVA families across seven multi-modal benchmarks using mutually disjoint calibration, validation, and test partitions. P2P at a 3% tolerance retains around 94% of dense accuracy while reducing FLOPs by 55%. Beyond these efficiency gains, our layer-wise analysis suggests that visual processing in VLMs is non-uniformly distributed across decoder depth: early and late layers often require little token-specific visual computation, whereas intermediate layers appear to perform most task-relevant visual integration, enabling later reasoning to rely largely on visual information already embedded in shared residual and textual representations. This makes P2P both an efficient inference framework and a causal lens into visual information processing in VLMs.

Physics-Informed Neural Networks (PINNs) typically exhibit spectral bias, where some frequencies of the target function converge more slowly than others. In this work, we analyze the training dynamics of Fourier Feature PINNs in the Neural Tangent Kernel regime to address this limitation. We derive an explicit evolution equation to estimate the residual error in the frequency domain, demonstrating that the convergence rate of specific frequencies is primarily governed by the product of the differential operator's symbol and the spectral density of the initialization weights. Leveraging this theoretical insight, we propose an informative initialization strategy that tailors the initial weight distribution to the specific PDE being solved. With this method, we can diminish the operator-induced spectral bias, balancing the convergence rates across the frequency spectrum and achieving better prediction accuracy. Numerical experiments on linear and nonlinear partial differential equations confirm that this initialization strategy improves learning dynamics and approximation accuracy across frequencies compared to standard initialization methods, with no additional training cost.

Training long-horizon agents to solve complex tasks requires effective supervision over extended interaction sequences. However, sparse terminal rewards obscure intermediate contributions, while on-policy distillation can lose informative teacher guidance as student-generated histories grow. To address this problem, we introduce SCAD, which organizes interactions into planning and bounded subtask execution, distills execution in local contexts, and refines planning credit through cross-rollout subtask prefix trees, with planning receiving full terminal credit and execution receiving positive terminal credit and teacher guidance. Across all evaluated benchmarks, SCAD improves macro-average accuracy over the strongest training baseline by 4.48 percentage points for text tasks and 4.19 points for multimodal tasks. SCAD effectively combines outcome-based credit assignment with teacher-guided distillation to improve planning and execution in long-horizon agents.

Deep reinforcement-learning policies for order execution can vary substantially across training seeds, so apparent architectural gains may reflect favourable training realisations rather than reproducible properties of the architecture. We evaluate vanilla Double Deep Q-Learning (DDQL), K-means-partitioned mixtures of DDQL experts at $K \in \{2, 4, 8\}$, and dense networks parameter-matched to the $K{=}4$ and $K{=}8$ expert budgets on 5-minute mean-aggregated BTC/USDT limit order book data from Binance. No learned configuration significantly improves mean implementation shortfall over DDQL. Under the reported specification, all have higher mean shortfall than TWAP (0.39 bps) and immediate liquidation (0.21 bps) in an environment whose frictionless replay and terminal-urgency penalty make early liquidation nearly costless; 11/100 vanilla-DDQL runs, versus none in either MoE $K{\geq}4$ arm, converge to a policy that waits until forced liquidation. We then decompose this specification on a device-matched baseline. Annealed exploration alone eliminates observed collapses (12/100 to 0/100; exact McNemar $p{=}4.9{\times}10^{-4}$), matching the elimination under expert partitioning. Combining annealed exploration with the aligned reward restores collapse in 19/30 runs; with all three specification changes, it rises to 48/100. In this environment, expert partitioning is unnecessary to suppress collapse and appears to mask a training-specification failure rather than confer an intrinsic performance benefit. No MoE $K{=}8$ run collapses under any of the six specifications tested. Across-seed dispersion is lowest at $K{=}8$ but non-monotone and not robust to family-wise adjustment, while within-policy tail risk worsens monotonically with $K$. The apparent attribution of the failure mode reverses between 30 and 100 seeds, illustrating the importance of repeated-seed evaluation.

Critic-free reinforcement fine-tuning (RFT) for agentic large language models is often done through GRPO-style methods, which compute a group baseline over repeated rollouts to reduce target variance. However, this setup is ill-suited to agents acting in stateful environments such as live services or security sandboxes, where repeated rollouts are impractical to obtain and aggressive updates entrench the noise of long, sparsely verified trajectories. We propose Follow the Winners (FTW), a critic-free policy-learning algorithm that adapts the cross-entropy method to RFT, replacing group rollouts with an ordinal filter on replay-buffer samples that yields polynomial concentration in the order statistic of returns. We derive FTW through a control-as-inference lens, which also recovers GRPO and DPO as specific modelling choices, identifying GRPO as risk-neutral while DPO and FTW share a bounded risk-seeking offset that FTW controls. We identify this offset as an inherent trade-off of variance reduction through ordinal filters on samples, whereas a critic model induces a different trade-off between bias and variance. Scaled to agentic LLM post-training, FTW matches GRPO and PPO on Sokoban and Search-R1 baselines, showing a viable trade-off from a value model or group rollouts to CPU memory.

We consider a distributed learning task with agents that have correlated data. Specifically, the label of an agent depends on the input of other agents for the same sample, and these inputs are also correlated. Correlated data is the reality when agents share the same environment. Existing decentralized methods, such as federated learning, ignore the structure of the problem and perform poorly on correlated data. On the other hand, centralized approaches are infeasible due to privacy and communication constraints. We introduce cordial (correlated and distributed) learning to address this gap by sharing only low-dimensional outputs between the agents while training local models to extract informative signals from peers. This distributed learning induces a game in which the loss function of each agent depends on the models of others. Assuming a linear model, we prove that cordial learning converges with probability one to a globally optimal solution, despite the nonconvex global objective. Experiments on structured multi-digit MNIST tasks demonstrate that cordial learning remains highly effective even in highly nonlinear settings.

Large language models are increasingly used where small syntactic errors matter, yet character-level reasoning is still evaluated mostly through isolated probes and aggregate accuracy. We introduce SyntaxBench, a diagnostic benchmark and statistical evaluation framework for character-level reasoning. It contains five core tasks, character counting, letter containment, palindrome detection, edit distance, and longest-string selection, plus index_to_span, a harder substring-extraction stress test. The five core tasks use paired English and character-length-matched random-string inputs. index_to_span documents share a 200-500 word band and are not character-length matched. All six tasks use zero-, one-, and four-shot prompts. We evaluate eight open-weight models from 2B to 32B parameters across 11 reasoning-mode configurations. The framework reports exact-match and relaxed accuracy, Cohen's kappa, paired McNemar tests with odds ratios, bootstrap confidence intervals, Kendall's tau, class-conditional metrics, tokenization analysis, and multiple-comparison-corrected tests. Three findings stand out. First, tokenization shapes accuracy: random strings are more character-visible than English strings (1.892 vs. 3.169 characters per token), and character-counting accuracy falls as English words occupy more tokens. Second, reasoning mode is not uniformly helpful: Gemma4-31B is nearly unchanged across modes on the near-saturated tasks, while Qwen3.6-27B is worse with thinking on palindrome detection (0.952 non-thinking vs. 0.886 thinking at four-shot). Third, index_to_span remains largely unsolved; the best four-shot exact-match accuracy is 6.75%. Character-level evaluation needs controlled inputs, paired tests, and analyses of tokenization and reasoning mode rather than aggregate accuracy alone.

Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When combined with inference-time guidance, they offer a promising route to high-dimensional non-Gaussian data assimilation (DA), the problem of combining forecasts with observations to estimate latent system states. Existing filters, however, condition on a fixed history and assimilate only the most recent observation, leaving them unable to revise past states when new observations arrive. Estimates then stay tethered to a history that later observations may contradict, and errors accumulate over the assimilation run. To this end, we introduce **DAWIS**, a unified DA method covering filtering, fixed-lag smoothing, and block smoothing within a single framework. DAWIS replaces the single flow time of a state-level prior with a multitask stochastic interpolant over a window of consecutive states, assigning a separate flow time to each. An assimilation cycle inverts the window to a vector of per-state turning points and regenerates it under observation guidance, with the turning points controlling how strongly each state is held fixed, revised, or generated from scratch. The same construction can also absorb the forecast into the assimilation cycle, removing the need for a separate forecasting model. Experiments on challenging nonlinear systems show that DAWIS improves on both filtering and smoothing baselines under sparse, noisy, and nonlinear observations. The code for DAWIS is available at https://github.com/Erik-Wikingsson/DAWIS

Existing machine learning weather forecasting models typically generate forecasts through autoregressive rollouts at a fixed temporal resolution. While highly efficient for long-range prediction, this formulation can suffer from severe error accumulation when used with shorter time steps and does not explicitly encode the locality and temporal continuity of atmospheric dynamics. To address these limitations, we introduce **SDECast**, a Neural Stochastic Differential Equation (SDE) framework for continuous-time probabilistic weather forecasting. SDECast extends SDE Matching to learn stochastic dynamics directly in physical space, without requiring repeated SDE simulation during training. On a simulated geophysical flow, we show that SDECast recovers meaningful drift dynamics and faithfully reproduces the underlying continuous-time behavior. We then demonstrate its scalability to global weather forecasting at hourly resolution, where SDECast produces skillful probabilistic forecasts for lead times of up to five days.

Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton–Schulz polynomials, and guarantee only stationarity, so it is unresolved what Muon's five tuned Newton–Schulz steps preserve and whether that suffices to reach a prescribed neural-network training loss. We establish a finite-time training guarantee that accounts for both momentum accumulation before orthogonalization and the tuned finite-step update. For full-batch training of a sufficiently wide two-layer ReLU network with fixed random output weights and a positive-definite limiting neural tangent kernel, we prove that Muon reaches any target empirical squared loss $\varepsilon>0$ with high probability over initialization. For every momentum parameter $\mu\in[0,1)$, a target-dependent constant learning rate proportional to $(1-\mu)\sqrt{\varepsilon}$ yields a hitting-time bound of $O((1-\mu)^{-1}\varepsilon^{-1/2})$, with other problem parameters fixed. The sufficient width is independent of both target accuracy and momentum. The analysis shows that the tuned Newton–Schulz map preserves alignment with the momentum buffer while bounding the update's spectral norm. Control of gradient variation near initialization transfers this alignment to the current gradient, ensuring descent until the target is reached without requiring exact orthogonalization. Numerical experiments support these mechanisms at widths below the sufficient theoretical threshold: gradient-update alignment remains above the analytical reference, and all 30 runs across six widths and five student initializations on a fixed teacher-student dataset reach the target loss while maintaining kernel positivity.

Uncertainty 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 $u(t,\mathbf{x},\mathbf{Z})$ 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 $p=1.5\times10^{-5}$. 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.

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.

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.

GPU kernels generated by large language model (LLM) agents can remain less efficient than expert implementations, but runtime alone does not reveal how the gap relates to design discovery and implementation. We introduce D2K-Bench, a diagnostic benchmark of 26 tasks and 85 workloads that measures how effectively agents translate expert design guidance into efficient GPU kernels. The guidance covers L1: high-level algorithmic insights, L2: dataflow design, and L3: low-level optimization tricks, including dependencies among these levels. Pairwise runs with and without guidance share task descriptions, workloads, tools, hardware, and a 350-turn budget. Complementary assessments examine independently proposed designs and the design properties implemented in generated code. Across five models on NVIDIA B200 GPUs, guidance raises correctness over 130 model-task pairs from 93.1% to 98.5% and increases the Performance Score over all 26 tasks from 1.46 to 1.95. For the three frontier models with correct submissions on all 26 tasks in both runs (GPT-6-Astra, Claude-Opus-4.8, and GPT-5.6-Sol), geometric mean speedup increases from $1.69\times$ to $2.49\times$. Across all five models, the mean combined implementation score increases from 57 to 70 out of 100. These results show the value of expert design guidance while identifying design properties that remain unimplemented.

We present the Neuro-Physical Inverter (NPI), a modular, uncertainty-aware framework for geophysical inversion that couples ensemble-based conditioning with constrained residual learning, demonstrated in the 1D magnetotelluric (MT) setting as a controlled testbed. The framework operates in two stages. An Ensemble-Conditional Gaussian Process (EnsCGP) conditions a prior ensemble of resistivity models on the observed response, producing a physically admissible reference ensemble. A residual-learning neural network then predicts targeted corrections to this reference, trained on synthetic data and fine-tuned per station for field application through a physics-coupled objective. Because an ensemble is conditioned, refined, and propagated through both stages, every estimate carries an associated ensemble spread. Synthetic experiments show that NPI systematically reduces ensemble-mean error without destabilizing the ensemble. Applied to broadband MT data from the Gabbs Valley geothermal region (Nevada, USA), NPI reduces the across-station mean misfit over the mid-period band while retaining comparable ensemble spread. The propagated ensemble yields a factor of uncertainty that serves as an operational measure of constraint within the assumed model class. Both stages are dimension-agnostic in formulation, and the design principles established here are intended to scale to higher-dimensional parameterizations.

Long-horizon LLM agents are typically trained with sparse outcome rewards, making trajectory-level objectives too coarse to distinguish the contribution of individual decisions. Step-level credit assignment provides finer-grained supervision, but its estimates can be unreliable because observed returns also depend on subsequent actions, environment transitions, and trajectory length. We propose AdaStep, an Adaptive Step-credit weighting method that controls how strongly each group-derived local advantage modifies the trajectory-level signal. We formulate this weighting as a mean-squared-error estimation problem for the latent step advantage and, under an explicit conditional sampling assumption, derive an optimal per-state shrinkage coefficient. The coefficient admits a signal-to-total-variance interpretation: it preserves local credit when return variation is attributable to the selected action and suppresses it when variation is dominated by downstream randomness. AdaStep requires only lightweight scalar computation, with no critic, additional rollouts, or extra model inference. Experiments with three model backbones on ALFWorld, WebShop, and ScienceWorld show consistent improvements over baselines at low computational cost.

This paper studies the complexity of convex optimization using lazy second-order oracles (Doikov, Chayti, and Jaggi, ICML 2023), where an algorithm queries gradients every iteration and Hessians once per $m$ iterations. Under this setting, we show a lower bound of $\Omega(m+ m^{1/7} \epsilon^{-2/7})$ on the number of total iterations to find an $\epsilon$-solution using a novel block zero-chain construction. Then we propose a novel method that achieves a new upper bound of $\tilde{\mathcal{O}}(m+ m^{1/7} \epsilon^{-2/7})$, which significantly improves the prior one (Chen, Liu, Luo, and Zhang, COLT 2026) of $\tilde{\mathcal{O}}(m+ m^{13/21} \epsilon^{-2/7})$ and is tight up to logarithmic factors.

Hybrid quantum classical neural networks integrate parameterized quantum circuits (PQCs) with established deep learning architectures, but their performance depends strongly on the choice of quantum circuit architecture, a choice that remains largely manual. Most existing approaches rely on hand-designed or fixed circuit ansätze, requiring circuit structure, gate composition, and qubit connectivity to be specified in advance with no guarantee that they suit the task. This limitation is especially acute in image classification, where quantum circuits must transform features extracted by classical networks while remaining compact enough for practical training, requirements that generic, task-agnostic ansätze are unlikely to satisfy simultaneously. We extend EXAQC, an evolutionary framework for automated quantum circuit discovery, to image classification. EXAQC evolves PQCs as intermediate processing modules while retaining classical feature-extraction and prediction layers. On MNIST, Fashion-MNIST, and CIFAR-10, EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy, respectively, while using comparable gate counts to other quantum architecture-search methods. Against classical networks, evolved hybrid models maintain comparable accuracy with substantially fewer trainable parameters, reaching 85.68% on CIFAR-10 with over 25$\times$ fewer parameters than a 10-layer CNN. Encoding choice also matters: rotation-based encodings (RX, RY, U3) outperform amplitude encoding by 22-25 points on CIFAR-10. These results demonstrate that automated circuit discovery yields compact quantum modules that can replace larger classical components in vision architectures while retaining competitive accuracy.

Kernel Singular Value Decomposition (KSVD) learns a pair of singular vectors w.r.t. an asymmetric kernel matrix, which can be induced by two data sources, e.g., the queries and keys in self-attention or the rows and columns of a given matrix. In this work, we extend KSVD to multiple data sources, namely eKSVD, which conducts joint nonlinear feature learning upon asymmetric kernels. In the primal formulation, the projections associated with each data source are jointly learned to capture maximal information, while incorporating pair-wise couplings. With the Lagrangian and its Karush-Kuhn-Tucker (KKT) conditions, the optimization in the dual leads to a generalization of the shifted eigenvalue problem in Lanczos decomposition theorem of KSVD. Further, a covariance-based framework is derived together with using neural networks (NNs) for explicit feature mappings, complementary to the kernel-based interpretation and optimization. Numerical experiments verify the effectiveness of our eKSVD compared to methods based on Mercer kernels for tackling multiple data sources, and our innovation of deploying NNs demonstrates great flexibility for kernel methods.

Self-supervised hypergraph representation learning can produce informative node embeddings, but existing methods often require deep encoders trained for hundreds of epochs, making embedding generation costly even for hypergraphs with a few thousand nodes. This limits applications requiring embeddings for many or evolving hypergraphs. We present HyperFuse, a label-free pipeline for fast hypergraph representation learning. HyperFuse (i) computes structural node coordinates by maximizing a spectral relaxation of hypergraph modularity using Banerjee's hypergraph adjacency and a matrix-free operator with cost linear in node-hyperedge incidences; (ii) constructs multi-scale feature summaries and assigns bounded utility weights to hyperedges based on member stability under feature and membership masking; and (iii) trains a lightweight utility-weighted hypergraph encoder for 100 epochs using an invariance-decorrelation objective. We compare HyperFuse with TriCL, SE-HSSL, VilLain, and HypeBoy on nine public hypergraphs using six downstream classifiers and k-means clustering. On the eight datasets where all methods completed, HyperFuse required 8.7 s per dataset on average, achieving 13-179x geometric-mean speed-ups over the baselines. It achieved the highest average accuracy with five of six classifiers, while classification and clustering performance was not significantly different from TriCL and SE-HSSL. Compared with HypeBoy, HyperFuse was 13x faster and 2.1-4.1 percentage points more accurate across all classifiers. HyperFuse provides a practical approach for fast, repeated hypergraph embedding generation.

We establish lower bounds for Hamiltonian property testing with access to the time-evolution operator but not its inverse. Each experiment may query the time-evolution operator multiple times, and distances between Hamiltonians are measured in the normalized Frobenius norm. In this model, we show that testing whether a Hamiltonian is $k$-local or $\varepsilon$-far from every $k$-local Hamiltonian requires $\Omega(1/\varepsilon^2)$ total evolution time, matching the upper bound of Kallaugher and Liang (TQC'25). We also prove that testing whether an unknown Hamiltonian equals a target Hamiltonian or is $\varepsilon$-far from it requires $\Omega(1/\varepsilon^2)$ total evolution time, matching the upper bound of Sinha and Tong (2025). These are the first lower bounds for natural problems in Hamiltonian learning and testing that rule out Heisenberg-limited scaling of $1/\varepsilon$. As a third result, we show that amplitude estimation to precision $\varepsilon$ requires $\Omega(1/\varepsilon^2)$ total time evolution, recovering the result of Tang and Wright (QIP'26) in the continuous-time query model. All three results follow from the hardness of distinguishing the zero Hamiltonian from a suitably chosen ensemble of random Hamiltonians. We establish this hardness by adapting the continuous-time adversary method to forward Hamiltonian evolution.

Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitioners to make a number of design decisions, such as the choice of the kernel and the observation model. Suboptimal choices can produce misspecified models that do not capture the underlying data generating process. We introduce Predictively Oriented Gaussian Processes (PrO-GPs), which treat predictive uncertainty as the primary inferential target and provide a robust alternative to standard GPs. Although direct computation of a PrO posterior for nonparametric models is intractable, we derive a reduced formulation and practical sampling scheme for efficient computation. Through synthetic and real data experiments, we show that PrO-GPs produce better calibrated predictive distributions under model misspecification compared to standard GP approaches.