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arXiv2026

Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem

This paper addresses infinite-dimensional Bayesian inference for inverse problem of partial differential equations with model parameters in infinite-dimensional Hilbert space. To effectively incorporate prior information, we propose a novel continuous normalizing flows based infinite-dimensional model. Specifically, by introducing a well-defined neural ordinary differential equation in infinite-dimensional space, a simple reference measure can be transformed into a more complex measure which encodes the prior information. A corresponding theoretical framework is established to ensure the well-posedness of our proposed Bayesian prior in infinite-dimensional space. We also provide training methods of the prior for two distinct data settings, along with two sampling algorithms for the resulting Bayesian posterior. The proposed framework is applied to three representative inverse problems: the simple smooth inverse problem, inverse scattering problem, and the inverse heat conduction problem. Numerical experiments support the theoretical analysis and demonstrate the efficiency of the proposed algorithms.

math.NA↗

arXiv2026

Conditioning Degenerate Diffusion Models

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

cs.LG↗

arXiv2026

PhenoBench: Mapping What a Deeply Phenotyped Human Cohort Can Tell Us

Deeply phenotyped cohorts combine clinical, imaging, molecular, and wearable observations across timescales from seconds to years, but heterogeneous analyses are not directly comparable. We present PhenoBench, an executable benchmark that turns deep-phenotyping measurements into explicit questions and controlled comparisons of information sources and predictive models. It is built around the Human Phenotype Project, with more than 13,000 participants at the initial visit. Each question fixes the target, population, timing, and allowed information; its evaluation contract specifies the split, metric, baseline, and claim boundary. PhenoBench defines 90 clinically grounded tasks across 15 domains and 26 input modalities. Across 160 matched regression comparisons spanning 52 tasks, six pretrained tabular models ranked above the evaluated task-specific baselines, including XGBoost and CatBoost, under a fixed single-estimator protocol with bounded tuning. Giving each task equal weight, their mean advantage over ridge was 0.0103 $R^2$ (95% task-bootstrap interval, 0.0071-0.0136). We also evaluated 14 language models, collectively covering 40 tasks spanning phenotype recovery, classification, follow-up forecasting, and participant ordering. Without cohort-specific fitting, language models made informative predictions on some tasks but showed task-specific capability gaps, shared failures of scale, and rarely surpassed task-specific ridge or logistic regression models fitted on the same input fields. PhenoBench provides a versioned, auditable evaluation system where new questions, measurements, and models can be added without redefining existing comparisons.

cs.LG↗

arXiv2026

VERPO: Verified Evidence Regularized Policy Optimization

Verifiable rewards improve language models through reliable task-level feedback, but methods based on Group Relative Policy Optimization (GRPO) apply a sequence-level advantage uniformly across all tokens. This coarse credit assignment reinforces or penalizes entire responses without identifying which local decisions to preserve, reinforce, or revise. Conversely, evidence-conditioned self-distillation provides denser token-level supervision, yet teacher imitation can transfer stylistic artifacts and miscalibrated confidence that destabilize training when misaligned with task success. We introduce VERPO, which converts evidence-conditioned guidance into reward-aligned token-level credit assignment while retaining the outcome objective. VERPO decomposes teacher guidance into an evidence-free reference term and signed, evidence-induced corrections at each token. A stopped controller combines selective acceptance, token-wise localization, and cost-aware scaling by balancing alignment with the local GRPO update direction against Fisher movement cost. Furthermore, we introduce Fisher Evidence Contrast (FEC), which attenuates nuisance shifts along an estimated evidence-presence direction through a regularized projection. Across five scientific reasoning and tool-use tasks, VERPO prevents optimization collapse and consistently achieves the highest multi-task average across model backbones, yielding marked improvements particularly on smaller models over strong baselines. Qualitative diagnostics confirm that token acceptance selectively targets reasoning bottlenecks consistent with local reward alignment and Fisher movement cost.

cs.LG↗

arXiv2026

Parameter-Free Dynamic Regret under Heavy-Tailed Noise

We study online convex optimization with one unbiased stochastic subgradient per round and noise having a finite $p$-th central moment, where $p\in(1,2]$ is unknown. For a bounded convex domain of diameter $D$, subgradients bounded by $G$, noise scale $σ$, and comparator path length $P_T$, let $Λ_T=1+P_T/D$. A single algorithm, using none of $G,σ,p,P_T$, attains expected dynamic regret $O_p\left(\min\{GD\sqrt{TΛ_T}+σDT^{1/p}Λ_T^{(p-1)/p},\,GDT\}\right)$ against every fixed comparator sequence. Restarted AdaGrad experts produce the noise-path exponent $(p-1)/p$, and a prior favoring longer restart intervals removes horizon-dependent logarithmic overhead. We give an explicit bound uniform in $p$; its logarithm-free form has noise coefficient $O(1+\log(p/(p-1)))$, while the static-regret constant is universal. The analysis requires only marginal noise moments and permits dependent errors. Complete pathwise proofs retain both the expert-loss range and the gradient energies preceding comparator movement. Matching lower bounds hold on every bounded convex domain of positive diameter, under the same gradient-only information model. Together with a path-budget-tuned upper bound, they characterize the minimax rate with universal constants, including its linear-regret saturation.

cs.LG↗

arXiv2026

The Illusion of Replacement: Rethinking Specialized Machine Learning Models in the Foundation Model Era

Specialized machine learning architectures encode structural assumptions (equivariance, permutation invariance, relational structure) that language-based foundation models lack by design. This review asks whether such assumptions can instead be acquired through language, drawing on a corpus of 186 papers published between 2016 and 2026 across nine modalities: tabular data, graphs, time series, vision, chemistry, code, knowledge graphs, point clouds, and protein structure. Methods are organized into eight representational regimes, ranging from language-only prompting to fully specialized architectures, and are assessed not only on predictive accuracy but on whether structural information is preserved by the representation and computed by the model. Language-mediated models prove competitive in extreme few-shot prediction, discretized symbolic tasks, and textually annotated knowledge graphs. No evidence of general replacement survives once structure itself is evaluated: where direct tests exist, apparent parity is traceable to information asymmetry, benchmark contamination, or computation performed outside the language model. Across independent research communities, missing structural inductive biases are reintroduced through graph modules, structure-aware tokens, or specialized attention, indicating that specialization is relocated rather than eliminated. The review closes by specifying a falsifiable controlled experiment that would measure the remaining gap directly. The derived data supporting the findings of this review are openly available in the repository at https://github.com/kiyan-rezaee/language-vs-structure.

cs.CL↗

arXiv2026

Tree species mapping in Denmark: A comparison of spectral-temporal features with geospatial foundation model embeddings

We map tree species across Denmark using National Forest Inventory plots and EO data, while evaluating the potential of foundation models for large-scale forest characterization. We compare two alternative input representations for tree species classification: (i) manually engineered spectral-temporal features (STF) derived from multi-temporal Sentinel-1 and Sentinel-2 observations, and (ii) embeddings generated by the EO FMs TESSERA and AlphaEarth. Both representations are complemented with canopy height information. Random forest, XGBoost, and Multi-Layer Perceptron (MLP) classifiers are evaluated for all input representations, with separate assessments for pure and mixed forest stands. The STF-based MLP achieves the highest classification performance, yielding macro F1 scores of 0.843 and 0.653 for pure and mixed stands, respectively. The MLP trained on TESSERA embeddings delivers competitive performance for pure stands, achieving results within 1.1 percentage points of the best-performing model. TESSERA consistently outperforms STF-based models when fewer than approximately 25% of training plots are available, demonstrating a substantial advantage under limited training data. Multi-year observations systematically improve classification accuracy relative to single-year inputs, while ablation experiments reveal the complementary contributions of Sentinel-1 backscatter, spectral indices, and canopy height data. The best-performing model is subsequently applied at the national scale to generate a 10 m tree species map of Denmark. Area-adjusted validation indicates an overall map accuracy of 79.9%. The resulting map, released as an open-access product, is the first high-resolution national tree species map of Denmark and provides a valuable resource for forest monitoring, ecological research, and land management applications.

cs.CV↗

arXiv2026

MARBO: Relational Belief Grounding for LLM Agents in Social Deduction Games

Social deduction games (SDGs) require agents to reason under partial observability by maintaining relational beliefs about hidden roles and team alignments. While recent LLM-agent approaches improve gameplay through prompting and preference optimization, they often optimize actions and in-game speech without explicitly grounding them in such beliefs. This frequently leads to strategically inconsistent behavior, especially for compact LLM agents. We introduce Multi-Agent Relational Belief Optimization (MARBO), a belief-grounded preference optimization framework that leverages relational beliefs to guide strategic decisions and in-game speech. MARBO provides preference feedback only when behaviors are supported by reliable relational beliefs and lead to strategically favorable social outcomes, encouraging more consistent learning under uncertainty. Experiments on representative SDGs show that MARBO enables compact LLM agents to consistently outperform existing baselines. The Code is available on https://github.com/PleaseTakemeAway/MARBO.

cs.AI↗

arXiv2026

Exact-Form Regret for Gradient Descent, Mirror Descent and Follow-the-Regularized-Leader

Online gradient descent is usually studied through external regret, where the learner competes with fixed alternatives. Recent work shows that first-order methods control richer action-dependent deviations. We ask for a geometric characterization of the deviations with respect to which online gradient descent, mirror descent, and follow-the-regularized-leader (FTRL) achieve no regret. We identify exactness as the common principle. Exactness means that the relevant displacement field is generated by a scalar potential, or equivalently that the associated one-form is exact in the geometry used by the algorithm. This geometry depends on the algorithm. For gradient descent it is Euclidean geometry, for mirror descent it is the geometry induced by the regularizer, and for FTRL it is the cumulative dual state. Under mild regularity conditions, exactness yields sublinear regret, while nonzero circulation provides the complementary obstruction and leads to linear regret. This gives a unified geometric framework for understanding the deviation classes controlled by these algorithms and reveals that different first-order methods can control genuinely different classes of deviations. These deviation classes have direct consequences for learning, particularly in games. We study the equilibrium notions induced by exact-form deviations and introduce conservative correlated equilibrium, reflecting both the conservative geometry of the underlying displacement fields and the restricted family of deviations available to the players. We characterize its relation to correlated equilibrium, determine when the resulting equilibrium notions coincide and when they separate, and show how these relationships depend on the geometry and the learning algorithm. Overall, this work gives a unified geometric account of what first-order online learning algorithms are no-regret with respect to, beyond fixed comparators.

cs.LG↗

arXiv2026

SingProbe Technical Report

We present SingProbe, an open intrinsic guardrail framework for generation-time monitoring of LLMs. Intrinsic guardrails reuse hidden states already produced by the base model during autoregressive decoding, rather than relying on an independent model to repeatedly process generated text. While this route has been explored in industrial systems, the community lacks a broadly reusable open stack that combines cross-model guard adaptations, unified training methods, serving integrations, and systematic evaluation resources. SingProbe is designed to provide this missing layer and uses a lightweight probe to continuously produce query-intent, response-safety, and hallucination-risk signals during decoding. This report describes the full intrinsic-guardrail stack: training methods, serving integrations with SGLang and vLLM, and adapted guard models for 29 open-source base models across diverse families and scales. We also introduce SingStreamBench, a benchmark that measures whether streaming guardrails remain inactive on benign prefixes while promptly detecting emerging unsafe content. Across evaluations of safety, streaming detection, hallucination detection, false-positive robustness, online monitoring, and runtime overhead, SingProbe provides performance competitive with, and in several settings stronger than, state-of-the-art standalone guardrails and specialized hallucination detectors, while adding less than 0.5% serving overhead in our implementation. Beyond passive monitoring, we show that intrinsic guard signals can guide constrained decoding and selectively activate medical-risk interventions in SingProbe-Med. By open-sourcing our infrastructure, training methods, and model adaptations, we aim to facilitate the broader adoption and deployment of intrinsic guardrails, as well as further research in this direction.

cs.CR↗

arXiv2026

HBQ: Hierarchical Scaling Block Quantization with Hardware-Efficiency-Aware Design for Accurate LLM Inference

Block Quantization (BQ) enables efficient LLM inference by quantizing both weights and activations, but its design space remains underexplored. Through hardware-accuracy design space exploration, we identify block size as a key trade-off: larger blocks improve hardware efficiency by amortizing dequantization and accumulation costs, but degrade accuracy. Motivated by this insight, we propose Hierarchical Block Quantization (HBQ), which combines large blocks with low-overhead significand (SIG) scaling for second-level quantization. SIG scaling effectively compensates for large-block quantization errors while accounting for distinct weight and activation distributions. HBQ-A achieves W4A16-level accuracy with W4A5 and lower area than NVFP4, while HBQ-E further reduces hardware cost by 17% while outperforming existing BQ methods in accuracy. We implement HBQ for weights, activations, and KV cache in a 28nm ASIC accelerator and introduce partial-sum BQ to reduce EMA energy. At comparable accuracy, HBQ achieves 2.3x/4.6x higher area/energy efficiency than state-of-the-art weight-only quantization and 1.6-3.3x lower system energy with 1.5-3x speedup over prior BQ methods. Our implementation is publicly available at: https://github.com/SeoLabCornell/HBQ.git.

cs.LG↗

arXiv2026

FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions

Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.

cond-mat.mtrl-sci↗

arXiv2026

Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus

Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.

math.OC↗

arXiv2026

Infrequent Resolving Algorithm for Online Linear Programming

Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications such as online auctions, network revenue management, order fulfillment and advertising. Existing OLP algorithms fall into two categories: LP-based algorithms and LP-free algorithms. The former typically guarantees better performance but requires solving a large number of LPs, which could be computationally expensive. In contrast, LP-free algorithms only require first-order computations but induce a worse performance. In this work, we bridge the gap between these two extremes by proposing a well-performing algorithm that solves LPs at a few selected time points and conducts first-order computations at other time points. Specifically, for the case where the inputs are drawn from an unknown finite-support distribution, the proposed algorithm achieves a constant regret (even for the hard "degenerate" case) while solving LPs only $O(\log\log T)$ times over the time horizon $T$. Moreover, when we are allowed to solve LPs only $M$ times, we design the corresponding schedule such that the proposed algorithm can guarantee a nearly $O\left(T^{(1/2)^{M-1}}\right)$ regret. Our work highlights the value of resolving both at the beginning and the end of the selling horizon, and provides a novel framework to prove the performance guarantee of the proposed policy under different infrequent resolving schedules. Numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms. The code is available at https://github.com/guokai-li/infrequent_resolving_olp.

cs.DS↗

arXiv2026

The Axiomatic Trader: Latent Regularity, Information Budgets, and the Canonical Form of a Quantitative Investment System

Systematic trading rests on one article of faith: that regularities found in the past persist. This paper does three things. First, it states that faith as five axioms, each a commonplace practitioners already accept: (A1) a decision may use only what was known when it was made; (A2) what looks like the market changing its rules is the market changing its unobserved state, the machinery being the same in every era; (A3) the future may replay stretches of the past, though not in history's proportions; (A4) states persist for a while; (A5) whatever predictability exists is slight, even for a rule that knows the state. What turns these into axioms is quantification, and the quantities are declared rather than estimated: an invariance defect $\varepsilon_0$, a recurrence bound $Λ$ at a block scale $b$ (one declaration in two parts), coherence times $\ell_i$, a signal ceiling $ρ$ and an invariance ratio $κ$. These five declarations are the whole of the premises' empirical content. Second, it proves that the axioms force a five-stage canonical form for a quantitative investment system -- a declared representation, a predictor within a capacity ceiling, contiguous purged block evaluation aggregated by $\mathrm{CVaR}_{1/Λ}$, a budgeted and deflated search, robust sizing at a fraction of the estimate that the budget bounds -- each stage necessary: a procedure omitting it does strictly worse under a law the axioms admit. Third, it tests the axioms where they are falsifiable, each only at its declared constants, on real market series: no axiom is so far overturned.

cs.LG↗

arXiv2026

Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits

While parameterized quantum computations have shown success in standard reinforcement learning (RL), whether these advantages adapt to hierarchical RL (HRL) remains a critical open question. This work demonstrates that variational quantum circuits (VQCs) can effectively enhance HRL agents based on the option-critic architecture. Evaluated in standard environments, a hybrid HRL agent with a quantum feature extractor outperforms classical baselines while using fewer parameters. We also identify an architectural bottleneck: using VQCs for option-value estimation severely degrades learning. Further ablations reveal how quantum circuit design affects performance. Our work establishes design principles for parameter-efficient hybrid HRL agents.

cs.LG↗

arXiv2026

D-TAIA: Domain-Aware LLM Adaptation for Multi-Task Predictive Process Monitoring

Predictive Process Monitoring (PPM) enables organizations to forecast future process behavior, such as the next activity and remaining time of ongoing cases. In practice, three conditions cause existing methods to degrade, namely data scarcity, high process entropy and distributional shift. While Foundation Models (FMs), especially Large Language Models (LLMs), offer a new paradigm through broad sequential reasoning, adapting them to multi-task PPM under these conditions remains an open challenge. Existing FM-based approaches either lack mechanisms for handling distributional shift or rely on direct regression heads that can be structurally misaligned with continuous time prediction tasks. This paper introduces D-TAIA (Domain-aware Training and Attention-based Inference Architecture), a framework for a joint next activity and remaining time prediction task via parameter-efficient fine-tuning of an FM backbone. Our approach combines domain-aware triplet loss (DATL) pre-training with FAISS-based nearest neighbor retrieval for remaining time prediction, and adopts the TAIA inference strategy to preserve pre-trained sequential reasoning during fine-tuning. Evaluated across four real-world event logs, D-TAIA consistently shows SOTA or competitive performance compared to a fine-tuned LLM and a recurrent neural network baseline. Ablation studies confirm that techniques from NLP and computer vision can be transferred effectively to PPM with only a 10M-parameter backbone, though component contributions vary by dataset entropy.

cs.LG↗

arXiv2026

Toward Physically Grounded JEPA World Models for Goal-Conditioned Robotic Planning

Action-conditioned JEPA world models enable planning toward visually specified goals without reconstructing future pixels, yet latent prediction alone does not explicitly encourage the learned representations to retain information relevant to robotic control. We introduce an end-to-end JEPA world model that augments latent prediction with inverse dynamics (IDM) and state alignment (SA). While inverse dynamics discourages latent collapse and makes latent transitions informative of the actions that produced them, state alignment grounds consecutive representations in their associated physical configuration and motion. Across four benchmark tasks, our model attains the highest success rates on TwoRoom (100%), PushT (98%), and OGBench-Cube (87%), while performing comparably to LeWorldModel on Reacher. Our ablation further shows that adding state alignment consistently improves planning success over IDM alone across all four tasks. Although LeWorldModel, our primary baseline, attains higher average straightening on OGBench-Cube, transition-subspace analysis shows that its transition energy is concentrated in a substantially lower-dimensional subspace. Our state-aligned model exhibits a higher effective transition dimension than LeWorldModel and improves planning over IDM alone, supporting state alignment as an effective complement to inverse dynamics for robotic planning.

cs.RO↗