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arXiv2026

AgenticEvolve: Evolutionary Program Search with Persistent Language Model Agents that Design and Run Experiments

Evolutionary program search with large language models keeps the structure of an evolutionary algorithm and uses the model as its variation operator. Typically, the model generates each candidate program in a single request from parent programs and their scores. We present AgenticEvolve, an evolutionary program search framework in which each island is run by a persistent large language model agent. Between evaluations, the agent designs and runs experiments on the candidate program. To measure the contribution of experimentation, we compare AgenticEvolve with No-analysis, an otherwise identical configuration with experiments disabled. On two heuristic design tasks with three large language models, AgenticEvolve produces better programs than No-analysis and OpenEvolve on both hidden and unseen instances. It reaches the baselines' final quality with far fewer evaluations and comparable cost. On twelve equation discovery problems, it recovers the ground-truth structure of more equations than No-analysis and existing language-model and genetic programming baselines.

cs.NE↗
arXiv2026

Typical periodic optimization and freezing phase transition: Dini potentials and beyond

We investigate the Typical Periodic Optimization (TPO) Conjecture and freezing phase transitions for Dini potentials and beyond. We show that the TPO conjecture fails already at Dini regularity. We identify a sharp regularity threshold for freezing phase transitions, which we call weak log-log Dini. Both results reveal the stability of aperiodic ground states. Moreover, we identify Dini regularity as the sharp threshold for a quantitatitve analog of the freezing phase transition.

math.DS↗
arXiv2026

Deep Learning for Random Objects in Metric Spaces: Beyond Manifold Assumptions

Deep learning (DL) methods have substantially improved predictive performance across a wide range of downstream prediction tasks, enabling new discoveries in multiple domains. However, principled DL methods for non-Euclidean random objects remain relatively scarce, despite the growing importance of modern biomedical outcomes taking the form of probability distributions, random graphs, functions, and other random objects in metric spaces. Motivated by a new generation of digital and clinical biomarkers, we propose a deep learning framework for regression with random objects in metric spaces. Our approach operates directly on the metric structure of the response space, avoiding restrictive manifold or Euclidean embedding assumptions imposed by many existing methods. At the same time, it retains modern statistical guarantees under the stated statistical assumptions. We establish statistical consistency and convergence rates for the proposed estimator, and characterize conditions under which it can mitigate the curse of dimensionality for hierarchically compositional regression functions. Extensive simulation studies demonstrate competitive predictive performance, with gains over several competing approaches in multiple Euclidean and non-Euclidean configurations. Finally, we demonstrate the practical utility of the proposed framework in two digital health case studies with distribution-valued outcomes in Wasserstein spaces, using high-resolution accelerometry and continuous glucose monitoring data. Embedding-based deep-learning methods may be less suitable when no informative low-dimensional representation exists or when the learned embedding does not adequately preserve the intrinsic geometry of the response space.

stat.ML↗
arXiv2026

WeVisOne-VL: Unified Visual Perception from Objects to Pixels

Existing vision-language models (VLMs) remain unreliable for fine-grained visual perception. In this report, we present WeVisOne-VL (WeChat Vision All-in-One), a powerful VLM that unifies object-level and pixel-level perception through structured next-token prediction. It supports multiple visual tasks including object detection, referring localization, counting, OCR, segmentation, and matting, enabling localization at any user-specific granularity, from points and boxes to masks and alpha mattes. Architecturally, we integrate a lightweight pixel decoder into the VLM via a special token to generate instance-level pixel outputs. We train the model with a three-stage curriculum SFT followed by mixed-task RL. Across over 30 benchmarks, WeVisOne-VL demonstrates leading performance on both object-level and pixel-level tasks, while maintaining robust rejection for object-absent queries. By releasing WeVisOne-VL to the open-source community, we hope to advance VLMs from broad visual understanding toward truly reliable perception systems for real-world deployment.

cs.CV↗
arXiv2026

Quantum Fokker-Planck solvers as trainable generative models

We develop and analyze generative models based on quantum solvers of stochastic differential equations. Unlike the common approach based on layered variational quantum circuits with parameterized rotations, we parameterize the potential of a Langevin process. The associated Fokker-Planck (FP) equations are Hermitianized and solved using a linear combination of cosine operators implemented through quantum singular value transformation. By encoding the square root of the stationary density, the model enables sampling through computational-basis measurements and is efficiently controlled by coefficients of the block-encoded diagonal potential. We train the proposed model to match empirical distributions within the family described by FP equations, demonstrating parameter recovery for multivariate probability distributions. Crucially, the model remains trainable at scale. Sample-efficient and convex optimization for in-distribution targets arises from a physics-informed inductive bias and holds regardless of the dimensionality of the problem. We provide circuit constructions and efficient block encodings of the main components of the algorithm and analyze resource requirements. Our approach frames quantum generative learning as quantum model discovery and provides a foundation for extending this framework to high-dimensional, strongly correlated scientific data.

quant-ph↗
arXiv2026

Harmful Responses Are Jailbreak Templates: Transferring Autoregressive Jailbreaks to Diffusion Language Models

Diffusion large language models (dLLMs) enable flexible masked generation through bidirectional context modeling, but this capability also introduces a distinct jailbreak attack surface. We find that a harmful response to a given query naturally serves as an effective jailbreak template: simply masking a subset of its tokens can induce a dLLM to reconstruct harmful content. Based on this observation, we propose RMT-Jailbreak, a general framework that transfers existing autoregressive (AR) jailbreak attacks to dLLMs through their induced harmful responses. RMT-Jailbreak converts an AR-generated harmful response into a high-mask-ratio template using uniform token retention, and further applies prompt-based safety filtering to mask any remaining visible harmful content. The refined template is then provided to the target dLLM for bidirectional reconstruction. Extensive experiments across multiple AR jailbreak methods and target dLLMs demonstrate the effectiveness and generality of RMT-Jailbreak, revealing strong cross-paradigm transferability of jailbreak attacks.

cs.LG↗
arXiv2026

Convex-like Submanifolds, Caps and a Volume Comparison Theorem

Convex-like submanifolds in the Lorentz-Minkowski spaces are introduced in this paper as a natural and broad generalization of convex surfaces in the Euclidean space. Associated with such a convex-like submanifold in a Minkowski space, we define roofs (which resembles the supporting planes), caps (which are generated by the light rays in the normal bundle), and towers (which revives the notion of interior for such high codimensional objects). As a touchstone of this theory, a volume comparison theorem is proved, which is a non-trivial generalization of the obvious fact that among two nested convex surfaces, the outer one has larger volume. Finally we provide two important applications of this theorem.

math.DG↗
arXiv2026

Sketching Outside the Hilbert Space for the Infinite-Dimensional Randomised SVD

In randomised numerical linear algebra, common choices for distributions of sketch vectors $ω\in \mathbb R^n$ are isotropic, so that $\mathbb E[ωω^T]=I_n$. Unfortunately, the natural extension of an isotropic vector in $(\mathbb R^n, \|\cdot \|_{2})$ to an infinite-dimensional separable Hilbert space $\mathcal H$ may not exist as an element of the space, posing an obstacle for any attempt to lift the randomised SVD to infinite-dimensional target operators $A$. Current workarounds either forego isotropy and take $ω$ to be a continuous Gaussian process with trace-class covariance operators, or leave $ω$ implicit by instead sampling $Aω$ as if $ω$ were isotropic Gaussian. We unify their approaches by introducing "sketch functionals", an example of cylindrical random variables (Vakhania--Tarieladze--Chobanyan 1987) which allow us to treat general, non-Gaussian distributions with bounded covariance operators. To demonstrate the utility of the new theory, we apply it to develop novel bounds for the infinite-dimensional randomised SVD with a general class of sub-Gaussian sketch distributions.

math.NA↗
arXiv2026

GelSlim 5.0: Unifying Vision and Touch with a Single Fingertip Camera

Vision and touch provide complementary cues for object pose and local contact geometry, but external cameras are often occluded at the contact site. We present GelSlim 5.0, a fingertip sensor that acquires visual and tactile observations with one fixed camera and a continuous UV-responsive contact layer. By switching illumination, the camera sequentially acquires through-membrane visual images and contact-sensitive tactile images from a shared viewpoint, avoiding inter-camera extrinsic calibration. To combine these observations, we introduce VisTacFusion, a multimodal transformer with separate prediction paths for planar object pose and contact geometry. Asymmetric bottleneck fusion incorporates visual context while preserving tactile spatial features for depth and surface-normal estimation. Modality dropout enables inference with paired inputs or either modality alone. On real validation data from 12 known objects, paired inputs reduce depth MSE, angular error, and translation $L_1$ by 61.2%, 72.3%, and 61.3%, respectively, relative to tactile-only inference with the same model. Relative to visual-only inference, the corresponding reductions are 93.7%, 6.1%, and 8.6%.

cs.RO↗
arXiv2026

What the submission does not show: Complexifying cognitive offloading in students' mathematical work with LLMs

A common concern is that using large language models (LLMs) lets students offload mathematical work that tasks are designed to elicit. Yet such claims often rest on outcomes (e.g., submitted solutions), rather than on evidence of students' work with LLMs. We followed 23 first-year linear algebra students as they solved three differently designed homework tasks with LLMs. Drawing on self-regulated learning and choice-affluent environments, we interpreted each of 429 prompts as a trace of a regulatory event and compared 59 chatlogs with the problem solutions the students submitted. Prompts formed five structures, casting the LLM mainly as a solver, explainer, or validator. The mix of structures shifted across the tasks, and ten of the 15 students who completed all three tasks changed their dominant structure. Most final submissions stayed close to LLM output, including those that followed exchanges in which students had explained, conjectured, and checked their own ideas. We conclude that an LLM-aided submission is not a trustworthy marker of students' offloading of the mathematical work, and that offloading needs to be examined in each regulatory space and part by part rather than as a whole.

math.HO↗
arXiv2026

Metric Conformal Prediction via the Conditional Expected Local Radius

We introduce the conditional expected local radius (CELR) and develop a new conformal prediction method for non-Euclidean responses in general metric spaces. CELR measures local conditional probability concentration, allowing prediction sets to accommodate heterogeneity and multimodality without requiring densities or a vector space structure. Its conditional distribution yields a nonconformity score that is comparable across covariate values and avoids costly transport comparisons between distance profiles. We further adapt a metric distributional random forest that handles multivariate covariates and nonlinear interactions, while a single forest fit supplies all score components, reducing computation by eliminating repeated local fitting. We establish uniform consistency of the estimators and asymptotic conditional validity under suitable regularity conditions, together with finite-sample marginal coverage under exchangeability. Numerical studies demonstrate effective uncertainty quantification across different metric spaces and substantial computational savings over the conditional profile score method.

stat.ML↗
arXiv2026

Generalized Infinite Hidden Markov Models

We introduce a flexible Bayesian nonparametric hidden Markov model for longitudinal data based on the hidden hierarchical Dirichlet process. Unlike the classical infinite hidden Markov model, the proposed model allows transition probabilities to change over time. In particular, this model provides a framework that operates between homogeneous and heterogeneous Markov model formulations, allowing the rows of the transition probability matrix to be clustered ac- cording to their temporal evolution. Inference is performed through a Markov chain Monte Carlo algorithm, which enables the joint estimation of model parameters, latent variables, and number of states, within a unified framework. Simulation studies under both homogeneous and heterogeneous transition regimes show that the proposed model tends to recover the true latent structure, whereas the infinite hidden Markov model tends to overestimate the number of states when transitions vary over time. Two applications illustrate the ability of the model to detect changes in the transition dynamics.

stat.ME↗
arXiv2026

ValuSpec: Plug-and-Play Candidate Valuation before Target Verification for Tree-Based Speculative Decoding

Tree-based speculative decoding accelerates large language model inference by verifying multiple candidate branches in parallel. However, in practical serving scenarios, similar requests repeatedly induce overlapping candidate branches. While retrieval-based methods mitigate this by reusing historical drafts, the resulting candidate trees often contain many low-quality branches as the candidate tree grows, which reduces verification efficiency and wastes target-side computation. To address this, we propose ValuSpec, a plug-and-play candidate valuation mechanism that filters low-quality branches from a supplied candidate tree before expensive target-side verification. ValuSpec introduces transfer-based supervision to align filtering with the target model's behavior. A filtering threshold is estimated from the target model's greedy trajectories on a calibration split, without any parameter training. The target model then verifies the filtered tree under the output-identical greedy rule, so accepted tokens are guaranteed to match standard autoregressive decoding exactly. Experimental results on HumanEval, GSM8K, Dolly, and SpecBench show that, in our main evaluation, ValuSpec achieves up to 2.38x end-to-end speedup in retrieval-based tree settings. Furthermore, integrating ValuSpec into the EAGLE-3 dynamic tree framework yields up to 2.78x end-to-end speedup without modifying its tree construction strategy, demonstrating that ValuSpec serves as a generally applicable and plug-and-play candidate valuation module.

cs.AI↗
arXiv2026

First hardware demonstration of a continuous-state probabilistic computer with programmable energy-defined sampling

Probabilistic computing has proved useful for combinatorial optimization, but conventional implementations rely on binary stochastic units and sigmoid-based updates. Extending these systems to continuous variables requires binary encoding. Here we introduce a continuous probabilistic computer (CPC) whose continuous probabilistic bits sample bounded states from conditional distributions defined by local energies. Separating random-source generation from conditional sampling provides a route to using physical random sources with different native distributions. A field-programmable gate array (FPGA) prototype updates finite-precision states using digital randomness. The same framework supports product constraints, memory recovery and solution-space exploration. For the tested 7-bit factorization case, fixed-temperature FPGA CPC reduces mean core solving time approximately 33,000-fold relative to the evaluated quadratic unconstrained binary optimization software implementation. The FPGA recovers stored MNIST patterns without pretrained networks, achieving final success rates of 100%. Software CPC reaches 90% reference coverage of the feasible area in approximately 18% of the time required by restarted Adam.

cs.NE↗
arXiv2026

Direct Production of Ultra-High Radioisotopic Pure $^{64}$Cu from Natural Zinc Metal via D-D Fusion Narrowband Fast Neutron Source Irradiation

Copper-64 radiopharmaceuticals have seen limited clinical deployment primarily due to the high cost of the isotopically enriched $^{64}$Ni metal required for its production. In this work we demonstrate that ultra-high radioisotopic pure $^{64}$Cu can be directly produced in a no-carrier-added-form from natural zinc metal through irradiation with D-D fusion narrowband fast neutron sources. A highly controlled D-D fusion narrowband fast neutron source at the ELI-ALPS Laser Facility was deployed to irradiate encapsulated 99.995\% pure natural zinc for 1 hour. Time-resolved gamma-ray spectroscopy of the irradiated sample over 72 hours was deployed to assess copper radioisotope activity. $^{64}$Cu was the only copper radioisotope detected within the irradiated sample, with a minimum and Minimum Detection Activity (MDA) threshold-corrected $^{64}$Cu radioisotopic purity of 99.62\% and 99.97\% respectively. Our result illustrates that highly controlled D-D fusion narrowband fast neutron sources have the potential to reduce the raw material production costs for $^{64}$Cu radiopharmaceuticals on the order of 2000 times. Cheaper $^{64}$Cu radiopharmaceuticals will increase their use in clinical practice, and, in-turn, increase outcomes for cancer patients receiving radionuclide therapy.

physics.med-ph↗
arXiv2026

Lawlor's curvature criterion and topologically trivial area-minimizing hypercones of Hsiang type

For a closed embedded minimal hypersurface in a unit sphere, we show that the existence of a uniform vanishing angle in Lawlor's criterion suffices for its cone to minimize area. The normal-wedge condition follows from Howard's rolling theorem. We derive explicit curvature bounds and apply them to the reported Hsiang-Sterling curvature estimates for topologically trivial cones. The resulting area-minimizing cones give an affirmative answer to the existence question raised by Ilmanen and White (Camb. J. Math., 2015).

math.DG↗
arXiv2026

Typed Template Fuzzing

Fuzzing software with complex inputs has been a longstanding challenge. Traditionally, fuzzers either programmatically encode language constraints, requiring significant engineering effort, or rely on users to declare grammars and constraints. Recent LLM-based fuzzers address these drawbacks but introduce new issues. Some use LLMs for test generation, sacrificing throughput and producing invalid inputs when the LLM makes mistakes. Others rely on language-specific parsers, static analysis, and AST manipulation libraries. We introduce Typed Template Fuzzing (TTF), a lightweight LLM-based fuzzing methodology. The key idea is to use LLMs in a preprocessing step to transform seeds into typed templates. The typed templates then enable semantically aware, mutation-based fuzzing without language-specific parsers, type checkers, or further LLM queries during fuzzing. By exploiting the correspondence between seeds and templates, TTF can moreover repair LLM mistakes. We have implemented TTF in our tool Typos, which we evaluate across 21 input languages, including C, C++, Go, Rust, SystemVerilog, Scala, and Java, as well as libraries such as PyTorch and Qiskit. In a six-month fuzzing campaign, we reported 135 bugs, 128 of which were previously unknown. Perhaps most notably, on average 96% of Typos's mutants are valid, coming close to the validity rates of domain-specific fuzzers. Our evaluation further shows Typos's benefits over the state of the art.

cs.SE↗
arXiv2026

A sharp diameter-mass inequality on Einstein manifolds and ADM mass

Let $(M^n,g), n\geq 4$ be a close Einstein manifold with positive scalar curvature and $G$ be the Green function of the conformal Laplacian. The ADM mass of the asymptotically flat metric $\hat g:=G^{4/(n-2)} g$ is an important geometric invariant. When either $n=5$ or $n\geq 6$ with Weyl vanishing condition, we prove a mass formula, generalizing Gursky-Malchiodi's formula in dimension $4$. An important step is an extension of Viaclovsky's Green function expansion in higher dimensions. Next we prove a sharp diameter-mass inequality on Einstein manifolds. Finally we present two applications. First, we prove a mass gap theorem for Einstein manifolds. Second, for Collins-Székelyhidi's family of Sasaki-Einstein metrics $g_i$ on $\mathbb{S}^5$ with volume going to zero, the sequence of the masses $m(\hat{g_i})$ blows up uniformly as $i\to\infty$.

math.DG↗