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01.
arXiv (CS.CL) 2026-06-17

GameCraft-Bench: Can Agents Build Playable Games End-to-End in a Real Game Engine?

Game generation is an emerging application of coding agents, requiring models to transform natural-language specifications into playable interactive systems. Unlike traditional coding tasks, game generation takes place within a game engine, where scripts, scenes, assets, rendering, and runtime interactions must jointly produce coherent gameplay. We formalize end-to-end game generation as the problem of producing a complete game artifact that realizes a specification through observable player-game interaction in a target environment. We argue that evaluating this setting requires three desiderata: Engine Grounding, Artifact Completeness, and Interactive Verification. We propose an interaction-grounded evaluation framework that assesses executable gameplay through replayed demonstrations and rubric-guided multimodal judging. We instantiate this framework as GameCraft-Bench, a benchmark comprising 140 Godot tasks across 15 game families. Evaluations of frontier coding agents show that end-to-end game generation remains highly challenging: the strongest agent achieves only 41.46%, and most agents score below 40%. Further analysis reveals that while agents often implement recognizable mechanics, they struggle to deliver complete games with sufficient content, functional visual feedback, and coherent presentation. See https://tongxuluo.github.io/gamecraft-bench-website for demos, code, and data.

02.
arXiv (CS.AI) 2026-06-19

Automating SKILL.md Generation for Computer-Using Agents via Interaction Trajectory Mining

arXiv:2606.20363v1 Announce Type: new Abstract: Explicit skill libraries make computer-using agents easier to inspect, but it remains unclear whether such libraries can be mined from interaction data in a way that improves downstream policies. We study this question through a three-stage pipeline that segments GUI trajectories, clusters segments into candidate skills, and trains a skill-aware policy from the resulting annotations. The mined clusters are readable on the source benchmark: five of eight clusters have at least 0.95 purity against InteraSkill Workflows labels. However, readability does not imply transfer. GRPO improves IW skill-step accuracy only from 18.5\% to 20.5\%, leaves BrowseComp+ essentially unchanged, and underperforms trivial frequency priors on key source-domain metrics. We therefore present the method as a diagnostic study: trajectory mining can expose inspectable skill structure, but the current boundary detector, orderless segment representation, and offline reward model are insufficient for reliable cross-domain policy improvement.

03.
arXiv (CS.AI) 2026-06-15

Moonlight in Latent Space: Chirality and Structural Correspondence Between Beethoven's Op. 27 No. 2 and Machine Learning Mechanisms

arXiv:2606.14612v1 Announce Type: cross Abstract: We show that the three movements of Beethoven's "Moonlight Sonata" (Op. 27 No. 2) instantiate three distinct machine learning architectures – not by analogy, but by structural correspondence. Through computational analysis of the score (entropy, Jensen-Shannon divergence, dissonance, hand distributional overlap, self-similarity matrices, temporal memory decay, and contextual pitch embeddings), we establish four counterintuitive findings: (1) perceived musical "temperature" is governed by throughput, not distributional width; (2) the lightest movement carries the highest dissonance; (3) the movements implement streaming, recurrent, and periodic positional encoding memory architectures; and (4) the same pitch class acquires different contextual identities across movements, analogous to contextual vs.static embeddings in NLP – and unsupervised clustering recovers the tonal structure without music-theoretic input. We construct a reverse sonification (decoding analytical features back into MIDI) and quantify the chirality of the encode-decode cycle: what distributions preserve and sequential ordering destroys. Prompted by a listener's observation that the decoded piece sounds like "mirror isomers that can't be superimposed," the chirality measurement reveals reconstruction loss increasing monotonically with n-gram order. Bootstrap baselines and subsample checks confirm all movements carry sequential information above noise, though raw values are confounded by sample size. Cross-domain comparison shows natural language has higher chirality than music, reflecting stronger sequential constraints.

04.
arXiv (CS.CL) 2026-06-18

Improving Medical Communication using Rubric-Guided Counterfactual Recommendations

Text-based telemedicine increasingly relies on lightweight patient feedback, however, such feedback primarily reflects perceived communication quality rather than medical accuracy. We introduce an LM-guided counterfactual recommendation pipeline that discovers and refines interpretable communication features such as tone, personalization, actionability and completeness in addressing patient concerns, without interfering with the medical content. These features are used together with patient-doctor interaction metadata to estimate positive feedback. At inference time, the system searches over low-cost ordinal feature changes and recommends minimal communication changes predicted to increase the probability of positive feedback, while independent auditor models test whether these gains generalize beyond the selection model. Across interactions, recommendations yield a mean +6.41% gain in predicted positive feedback probability under independent auditors, and are non-negative for 93.31% of recommendations. These results suggest that small, interpretable communication changes can capture most predicted gains while preserving the doctor's control over medical reasoning and final wording.

05.
arXiv (CS.CV) 2026-06-16

R2RDreamer: 3D-aware Data Augmentation for Spatially-generalized 2D Manipulation Policies

Spatial generalization is critical for imitation-learned manipulation policies, but achieving it typically requires scaling demonstrations across diverse object poses, robot configurations, and camera viewpoints. Data augmentation from a few source demonstrations offers a practical alternative to costly real-world collection. Simulation-based augmentation can create controllable variation, but requires complex environment and object setup and may introduce a sim-to-real gap. Recent real-to-real methods avoid these issues by jointly editing 3D observations and action trajectories from real demonstrations, yet they still rely on strong 3D scene parsing and geometry completion, and often produce observations tailored to 3D pointcloud policies rather than RGB-based 2D policies. We propose R2RDreamer, a real-to-real demonstration augmentation framework that preserves the geometric consistency of 3D action-observation editing while moving visual completion to 2D video space. Specifically, R2RDreamer first performs lightweight 3D augmentation by editing incomplete object pointclouds and end-effector trajectories in a shared 3D frame; it then projects the edited scene into masked image-space control videos with occlusion-aware reasoning and uses a dense-control image-to-video model to complete temporally coherent RGB observations. Experiments on spatially shifted manipulation tasks with both 2D diffusion-style policies and vision-language-action policies show that R2RDreamer improves spatial generalization from limited source demonstrations, with analyses validating the contributions of 3D editing, occlusion-aware projection, and video completion.

06.
arXiv (CS.LG) 2026-06-18

A Guide to Estimating Conditional Average Treatment Effects in Competing Risks Settings

arXiv:2606.18281v1 Announce Type: cross Abstract: Conditional average treatment effects (CATEs) are central to treatment decision-making in personalized medicine. In competing risks settings, estimating CATEs from survival data allows for patient-specific assessments of treatment effectiveness for a specific event of interest while properly accounting for alternative event types. This distinction is essential in the presence of comorbidities, where competing causes of death may otherwise confound the therapeutic benefit. Focusing on right-censored survival times with binary treatment, we examine CATEs defined as covariate-conditional differences in the absolute risk for the event of interest at a fixed time. To this end, we study meta-learners which adapt machine learning algorithms for CATE estimation in competing risks scenarios. We systematically compare six meta-learners, combining Cox regression or random survival forests for risk modeling with elastic net regression or random forests for direct CATE modeling. To provide practical guidance on model selection, we evaluate their performance in multiple simulation settings, that differ in hazard complexity, treatment heterogeneity, treatment assignment, event type distribution and censoring. To facilitate applied use, we provide the R package, crsurvlearners, which implements all considered approaches.

07.
arXiv (CS.AI) 2026-06-11

Position: Hippocampal Explicit Memory Is the Cornerstone for AGI

作者:

arXiv:2606.11245v1 Announce Type: new Abstract: Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, raising expectations for Artificial General Intelligence (AGI). This position paper argues that integrating explicit memory is the cornerstone for advancing LLMs toward AGI. The key reason is that the underlying learning mechanism of LLMs is highly analogous to human implicit memory. However, higher-order cognitive functions necessary for AGI, such as long-term strategic planning, metacognition, and symbolic reasoning, heavily rely on hippocampal explicit memory and cannot arise solely from implicit statistical learning. Drawing on findings from neuroscience, I advance this perspective and complement it with computational requirements for artificial explicit memory systems, hoping to foster further research and lay the groundwork for explicit memory integration.

08.
arXiv (CS.CL) 2026-06-18

Redact or Keep? A Fully Local AI Cascade for Educational Dialogue De-Identification

Educational dialogue is a valuable but sensitive resource for research: the same transcripts that capture authentic learning often capture personally identifiable information (PII) entangled with curricular content, where "Riemann" may refer to a real student or to a mathematical concept. Existing approaches force a tradeoff between governance and accuracy. Commercial Large Language Models (LLMs) can handle this ambiguity but require sending student data to third parties, while local named entity recognition (NER) systems preserve governance but over-redact curricular terms. We propose a fully local cascade framework that reframes de-identification from open-ended entity recognition to constrained privacy triage. A recall-first union proposer combines two lightweight encoders with deterministic rules to over-generate candidate spans; a context-aware reviewer then makes a binary Redact/Keep decision for each candidate using surrounding dialogue and speaker role. We evaluate three reviewer configurations against same-family LLM-only baselines and a commercial API on math tutoring transcripts from two large platforms. The strongest local configuration reaches 0.958 macro F1, compared with 0.767 for a same-family LLM-only baseline and 0.706 for the commercial API, while running entirely on a single laptop. On a targeted challenge set of curricular-personal name ambiguity, the same configuration degrades by only 0.03 F1 versus 0.19 to 0.25 for smaller reviewers. These results suggest that for educational de-identification, problem formulation matters more than model scale.

09.
arXiv (CS.AI) 2026-06-15

VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification

arXiv:2606.14176v1 Announce Type: new Abstract: Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent. Existing methods often trade off controllability and reliability: seed-based rewriting is flexible but weakly verifiable, whereas diagram-first construction improves validity but is less suited to arbitrary user-specified constraints. We introduce VeriGeo, a controllable geometry generation framework grounded in executable reasoning traces. Given user constraints such as target concepts and difficulty, an Author agent generates a problem and diagram, and a Solver agent produces a proof-aligned solution. Both agents use a shared action sequence that connects natural language, diagrams, geometric constraints, and proof steps into a verifiable representation. A three-stage pipeline checks numerical consistency, analytical realizability, and global consistency, using verification-guided reflection to repair recoverable failures and reject unrecoverable ones. Across five LLM backbones, raw generations frequently fail these checks, while VeriGeo repairs a substantial fraction of the invalid attempts. Supervised fine-tuning on 8.7k examples generated by VeriGeo achieves the best reported GeoQA performance among end-to-end multimodal LLM-based solvers, and obtains strong results on PGPS9K and MathVista-GPS, demonstrating the effectiveness of verified synthetic data for improving multimodal geometry reasoning.

10.
arXiv (math.PR) 2026-06-11

Convergence of a Critical Multitype Bellman–Harris Process with One Infinite-Mean Lifetime

arXiv:2606.11511v1 Announce Type: new Abstract: We study a critical multitype Bellman–Harris branching particle system in $\mathbb R^N$ with a finite type space $\mathbb K=\{1,\dots,K\}$. Particles of type $i$ move according to a symmetric $\alpha_i$-stable process and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The lifetime distribution of type $1$ is assumed to have infinite mean with regularly varying tail $$ 1-F_1(t)\sim c_1t^{-\gamma},\, 0 \frac{\gamma}{\beta}, $$ and a local increment condition on the heavy lifetime distribution, we prove convergence of the system to a Poisson random measure concentrated on the infinite-mean type.

11.
arXiv (CS.CV) 2026-06-11

Bridging the Modality Gap in Forensic Image Retrieval

Automated image retrieval plays an increasingly critical role in modern forensic analysis, supporting investigative workflows that rely on efficient comparison of visual evidence. While prior work has focused primarily on developing and optimizing multimodal retrieval systems, limited attention has been paid to evaluating the forensic applicability of these technologies across diverse real-world scenarios. In this study, we present a unified retrieval framework adapted to four key forensic tasks: (1) tattoo image retrieval given a tattoo query image; (2) tattoo retrieval guided by human-expert textual descriptions, modelling the common situation where a witness verbally describes a tattoo; (3) tattoo retrieval from hand-drawn sketches; and (4) face retrieval from forensic face sketches. Our system leverages a multimodal large language model (MLLM) to automatically generate structured textual descriptions for all queries and gallery images, followed by sentence-transformer embedding for text-based comparison. We evaluate retrieval using visual-only embeddings, text-only embeddings and a multimodal fusion strategy that combines text- and image-based similarity scores derived from state-of-the-art visual feature extractors relevant to each task. The fusion of modalities consistently improves retrieval precision and robustness, especially in scenarios where visual information is limited or noisy (e.g., sketches, partial tattoos, or fragmented witness statements). This work highlights the forensic value of a unified multimodal retrieval pipeline and demonstrates how modern MLLMs can operationalize challenging forensic tasks that traditionally rely on manual expert analysis. Our results position multimodal retrieval as a promising tool for supporting investigative workflows involving tattoos, facial composites, and witness descriptions.

12.
arXiv (CS.CV) 2026-06-15

Gefen: Optimized Stochastic Optimizer

AdamW is a default optimizer for modern deep learning, but its first and second moment states add roughly two parameter-sized buffers to training memory. We propose Gefen, a memory-efficient optimizer that automatically shares second-moment estimates across parameter blocks and quantizes the first moment using a learned codebook, thereby reducing AdamW's memory footprint by ~8x while maintaining the same performance, corresponding to a reduction of 6.5 GiB per billion parameters. The method is motivated by a theoretical result showing that large mixed Hessian entries constrain the ratio of squared gradients toward one, suggesting that Hessian-aligned parameters are natural candidates for sharing second-moment statistics. Since computing Hessians is impractical at scale, Gefen infers block structure from the initial squared gradients, requiring no architecture-specific metadata or hyperparameters beyond AdamW defaults. Gefen learns an exact histogram-based dynamic-programming quantization codebook and reuses the same blocks for first-moment scaling. Across diverse experiments, Gefen achieves the lowest peak optimizer memory among the compared AdamW-like methods while maintaining AdamW-level performance. In FSDP and DDP training, the reduced memory footprint enables larger microbatches and improves throughput significantly over AdamW, providing a practical drop-in replacement with lower memory usage that can increase throughput and enable training larger models or using larger batch sizes. We provide the complete Python implementation, including fused CUDA kernels at https://github.com/ndvbd/Gefen

13.
arXiv (CS.LG) 2026-06-15

Muon$^p$: Muon with Fractional Spectral Powers

arXiv:2606.13867v1 Announce Type: new Abstract: Muon is an increasingly widely used optimizer that replaces a gradient $G=USV^\top$ with its polar factor $UV^\top$, thereby flattening the singular spectrum. However, full flattening discards singular-value information that may matter for adaptation. We introduce Muon$^p$, a Muon-style optimizer that instead uses fractional spectral-power updates $US^pV^\top$ for rational $p\in(0,1)$, interpolating between Muon and gradient descent. To make it practical, we prove that fractional spectral powers cannot be computed by any fixed univariate polynomial iteration, and furthermore derive low-degree odd bivariate recurrences that approximate $US^pV^\top$ using only matrix multiplications, preserving Muon's matrix-multiplication-only structure and compute complexity. We show that Muon$^p$ maximizes the linear improvement in loss under the Schatten $q$-norm for $q=1+\frac{1}{p}$. Empirically, Muon$^p$ is especially effective for finetuning: on billion-scale models, Muon$^p$ improves validation perplexity and downstream task performance. We further analyze when Muon$^p$ is less suitable, through the lens of spectral geometry. Our results reveal important insights on when preserving the singular spectrum can bring significant gains, and introduce a principled way to achieve them.

14.
arXiv (CS.LG) 2026-06-17

Beyond Independent Genes: Learning Module-Inductive Representations for Single-Cell Gene Perturbation Prediction

arXiv:2602.04901v2 Announce Type: replace-cross Abstract: Predicting transcriptional responses to genetic perturbations is a central problem in functional genomics. In practice, perturbation responses are rarely gene-independent but instead manifest as coordinated, program-level transcriptional changes among functionally related genes. However, most existing methods do not explicitly model such coordination, due to gene-wise modeling paradigms and reliance on static biological priors that cannot capture dynamic program reorganization. To address these limitations, we propose scBIG, a module-inductive perturbation prediction framework that explicitly models coordinated gene programs. scBIG induces coherent gene programs from data via Gene-Relation Clustering, captures inter-program interactions through a Gene-Cluster-Aware Encoder, and preserves modular coordination using structure-aware alignment objectives. These structured representations are then modeled using conditional flow matching to enable flexible and generalizable perturbation prediction. Extensive experiments on multiple single-cell perturbation benchmarks show that scBIG consistently outperforms state-of-the-art methods, particularly on unseen and combinatorial perturbation settings, achieving an average improvement of 6.7% over the strongest baselines. The code is available at https://github.com/ttruan2426-dot/scBIG.

15.
arXiv (CS.CL) 2026-06-16

Connecting Speech to Words through Images

How can we learn the mapping between written words and their spoken counterparts in the absence of explicit textual supervision? We present a visually grounded method for building a vocabulary of spoken words using only images and their spoken descriptions. First, image captioning systems are used to build a vocabulary of written words representing salient visual concepts in the images. For each word, we then find utterances whose image captions contain that word. Then we use an unsupervised word discovery technique to align these utterances to locate instances of the target word. The result is spoken word segments that are linked to written words – all accomplished without any text supervision. In spoken word retrieval and keyword spotting experiments, the proposed approach outperforms a strong neural baseline while being more interpretable. These results demonstrate the feasibility of the approach in English and motivate future work on low-resource languages without transcripts.

16.
arXiv (CS.LG) 2026-06-15

Arbitrary control over multimode wave propagation for machine learning

arXiv:2402.17750v2 Announce Type: replace-cross Abstract: Controlled multimode wave propagation can enable more space-efficient photonic processors than architectures based on discrete components connected by single-mode waveguides. Instead of defining discrete elements, one can sculpt the continuous substrate of a photonic processor to perform computations through multimode interference in two dimensions. Here we designed and demonstrated a device with a refractive index that can be rapidly reprogrammed across space, allowing arbitrary control of wave propagation. The device, a two-dimensional programmable waveguide, uses parallel electro-optic modulation of the refractive index of a slab waveguide with about $10^4$ programmable spatial degrees of freedom. We implemented neural network inference on benchmark tasks with up to $49$-dimensional vectors in a single pass, without digital pre-processing or post-processing. Theoretical and numerical analyses further indicated that two-dimensional programmable waveguides may offer not only a constant-factor reduction in device area but also a scaling benefit, with the area required growing as $N^{1.5}$ rather than $N^2$.

17.
arXiv (CS.AI) 2026-06-19

Speeding up the annotation process in semantic segmentation industrial applications

arXiv:2606.19934v1 Announce Type: cross Abstract: Current machine learning models commonly require large and well-annotated datasets. However, the annotation process often becomes a bottleneck, with increased complexity leading to higher chances of human errors. Within this context, our goal in this paper is to leverage unsupervised algorithms to improve data annotation efficiency for complex semantic segmentation problems in industrial materials science. Previous research has quantified labeling time and others explored unsupervised methods. However, to the best of our knowledge, this is the first study to quantify how much unsupervised algorithms accelerate the labeling process. We aim to validate the extent to which this laborious process can be accelerated, focusing on semantic segmentation tasks that involve annotating each pixel of high-resolution images, such as the microstructure characterization challenge in materials science. Specifically, we demonstrate that by using unsupervised computer vision algorithms, the time required for the labeling process can be reduced from 170 hours to 37 hours, achieving an approximate reduction of 78\%. The dataset we work with includes large images of dimensions 1280x959 and 960x703, which further increases the complexity of the annotation task. Despite these challenges, we create and share the largest public steel microstructure segmentation dataset to date, available under MIT License with permanent DOI, contributing a fully annotated, high-resolution dataset to the field. Additionally, this is the first work to compare the labeling time from scratch (a common approach in previous studies) to the labeling time when using these unsupervised algorithms as a pre-annotation step. Furthermore, we provide a Deep Learning model trained on this dataset, validated by field experts, and deployed in an industrial setting, serving as an initial benchmark for this public dataset.

18.
bioRxiv (Bioinfo) 2026-06-15

Inferring Cell Fate Trajectories in Time-Resolved Metabolic RNA Labeling data

Single-cell RNA sequencing provides high-resolution snapshots of cellular states but lacks direct information about transcriptional dynamics. Metabolic RNA labeling addresses this limitation by distinguishing newly synthesized RNA, offering insight into the direction of cell state changes, and providing valuable information when attempting to recover the underlying continuous dynamics from static snapshots of cell distributions. However, existing trajectory inference methods do not fully exploit this additional signal. Here, we propose FLOWSATATE, a framework for single-cell trajectory inference that leverages time-resolved RNA labeling within an Optimal Transport setting. We model cell dynamics as a gradient flow in an inferred potential landscape parameterized by a neural network, integrating both total and labeled RNA across time points. The learned potential enables identification of key genes and transcription factors driving cell fate decisions and supports prediction of future cellular states. We benchmark our approach on its ability to generalize unseen data and recover coherent trajectories. We also apply it to study colorectal cancer response to demethylation treatment as well as neuronal differentiation of embryonic stem cells.

19.
arXiv (CS.CL) 2026-06-12

Zero-source LLM Hallucination Detection with Human-like Criteria Probing

Large language models (LLMs) often hallucinate by generating factually incorrect or unfaithful content, posing significant risks to their safe use. Detecting such hallucinations is particularly challenging under the zero-source constraint, where no model internals or external references are available, and detection must rely solely on the textual query-answer pair. In this paper, we propose Human-like Criteria Probing for Hallucination Detection (HCPD), a paradigm that emulates the multi-faceted reasoning of human evaluators. Its core is a Human-like Criteria Probing (HCP) mechanism, in which a LLM agent adaptively decomposes its judgment into a weighted set of interpretable criteria and aggregates criterion-specific scores into a final truthfulness measure. To achieve this adaptive capability, we introduce a reward-based alignment scheme using only weak supervision from semantic consistency. At inference, we employ a multi-sampling aggregation strategy to ensure robust decisions while preserving full interpretability. We further provide theoretical analysis supporting the reliability of our approach. Extensive experiments show that HCPD consistently outperforms state-of-the-art baselines, offering an effective and explainable solution for zero-source hallucination detection. Code is available at https://github.com/TRISKEL10N/HCPD.

20.
arXiv (CS.CV) 2026-06-16

ResEdit: Residual embeddings for precise generative image editing

Conditional diffusion image generators can be repurposed for editing through inversion, without the need for large-scale paired fine-tuning data. However, producing high-quality, targeted edits while maintaining image identity and global consistency remains challenging, as weakly conditioned inversion often embeds conflicting image features into the noise. We demonstrate that incorporating a residual image encoding as additional conditioning enables both improved identity preservation and better editability. We optimize this residual encoding to provide a strong conditioning signal for reconstruction, thereby reducing the reliance on inversion and susceptibility to its aforementioned pitfalls. To ensure this residual does not interfere with desired edits, we incorporate a gradient reversal-based optimization strategy that disentangles the residual from the edited condition. We illustrate our method's ability to produce high-fidelity results across precise intrinsic-based editing and relighting, and show proof-of-concept text-guided manipulation.

21.
arXiv (CS.LG) 2026-06-11

Discovery and inference beyond linearity for epidemiological data by integrating Bayesian regression, tree ensembles and Shapley values

arXiv:2505.00571v3 Announce Type: replace-cross Abstract: Machine Learning (ML) is gaining popularity in epidemiology and healthcare studies for hypothesis-free discovery of risk and protective factors. ML is strong at discovering nonlinearities and interactions, but this power is compromised by a lack of reliable inference. Although Shapley values provide local measures of features' effects, valid uncertainty quantification for these effects is typically lacking, thus precluding statistical inference. We propose RuleSHAP, a framework that addresses this limitation by combining a dedicated Bayesian sparse regression model with an improved tree-based rule generator and Shapley value attribution. RuleSHAP provides detection of nonlinear and interaction effects, with uncertainty quantification at the individual level as a key contribution. We derive an efficient formula for computing marginal Shapley values within this framework. We apply RuleSHAP to data from an epidemiological cohort to detect and infer several effects for high cholesterol and blood pressure, such as nonlinear interaction effects between features like age, sex, ethnicity, BMI and glucose level. To conclude, we demonstrate the validity of our framework on simulated data.

22.
arXiv (math.PR) 2026-06-17

Optional Stopping for Superhedging Supermartingales

arXiv:2606.17452v1 Announce Type: new Abstract: Superhedging supermartingales, introduced by the authors in previous work, are non-probabilistic processes defined via subadditive outer integrals that carry a purely financial interpretation in terms of superhedging cost. Building on the Leinert-König theory of non-lattice integration, the present paper establishes several results that are classical in probability theory but whose non-probabilistic proofs require fundamentally new arguments: (i) a tower inequality for the conditional outer integral \overline{\sigma}_j applied at stopping times, reducing to equality when the integrand is conditionally integrable; (ii) three versions of Doob's optional stopping theorem, organised by the class of supermartingale and the range of the stopping times; and (iii) Dubins' upcrossing inequality in both finite- and infinite-time horizons. A key structural result, property (K)-a.e., identifies conditions under which the two superhedging operators \overline{\sigma}_j and \overline{I}_j coincide on non-negative functions, extending the scope of all preceding results to the positive operator \overline{I}_j. None of the proofs invoke classical measure-theoretic tools; in particular, (classical) integrability and measurability are not assumed. The analogues of classical stochastic results acquire a purely financial interpretation and, in this way, gain depth and generality by providing a context that is independent of any a priori probabilistic structure.

23.
arXiv (CS.LG) 2026-06-16

Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

arXiv:2605.31027v2 Announce Type: replace Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional input, it employs $d$ independent subnetworks – each acting on a single coordinate – and constructs basis functions via element-wise multiplication of their outputs. The PDE solution is approximated as a linear combination of these basis functions, with coefficients determined by least squares. Critically, all network weights and biases are randomly initialized once, from a uniform distribution with unit variance, and remain fixed thereafter. To enhance expressivity, a tunable scaling factor is introduced in each subnetwork to modulate the frequency content of the resulting basis functions. Fourier features are explicitly embedded through cosine activations, endowing the method with strong spectral approximation capabilities. To mitigate the memory bottleneck associated with dense collocation in high-frequency or three-dimensional problems, we replace automatic differentiation with analytically derived basis function derivatives and develop a memory-efficient batched QR decomposition algorithm for solving large-scale least-squares systems. Numerical experiments demonstrate that MS-SFNN achieves unprecedented accuracy across a range of challenging PDEs, significantly outperforming state-of-the-art methods such as Physics-Informed Neural Networks (PINN) and Separated-Variable Spectral Neural Networks (SV-SNN).

24.
arXiv (CS.LG) 2026-06-17

On Randomized Algorithms in Online Strategic Classification

arXiv:2602.06257v2 Announce Type: replace Abstract: Online strategic classification studies settings in which agents strategically modify their features to obtain favorable predictions. For example, given a classifier that determines loan approval based on credit scores, applicants may open or close credit cards and bank accounts to obtain a positive prediction. The learning goal is to achieve low mistake or regret bounds despite such behavior. While randomized algorithms have the potential to offer advantages to the learner in strategic settings, they have been largely underexplored. In the realizable setting, no lower bound is known for randomized algorithms, and existing lower bound constructions for deterministic learners can be circumvented by randomization. In the agnostic setting, the best known regret upper bound is $O(T^{3/4}\log^{1/4}T|\mathcal H|)$, which is far from the standard online learning rate of $O(\sqrt{T\log|\mathcal H|})$. In this work, we provide refined bounds for online strategic classification in both settings; our bounds depend on the Littlestone dimension $\mathrm{Ldim}(\mathcal H)$ of the hypothesis class $\mathcal H$ and the maximum degree $\Delta$ of the manipulation graph. In the realizable setting, we extend, for $T > \mathrm{Ldim}(\mathcal H) \Delta^2$, the existing lower bound $\Omega(\mathrm{Ldim}(\mathcal H) \Delta)$ for deterministic learners to all learners. This yields the first lower bound that applies to randomized learners. We then provide the first randomized learner that improves the known (deterministic) upper bound of $O(\mathrm{Ldim}(\mathcal H) \cdot \Delta \log \Delta)$. In the agnostic setting, we give an improper randomized learner that improves the regret upper bound to $O(\sqrt{T\log|\mathcal H|})$, matching the standard online learning rate. We also show a larger lower bound for all proper learning rules, demonstrating that improperness is necessary to achieve the optimal rate.

25.
arXiv (CS.CV) 2026-06-12

Skill-3D: Evolving Scene-Aware Skills for Agentic 3D Spatial Reasoning

This paper explores agentic 3D spatial understanding, i.e., MLLM agents performing 3D reasoning through tool use. Existing methods often misuse tools and exhibit biased tool preferences under 3D scenarios, leaving the agentic paradigm with only marginal gains over non-agentic strategies. We reveal that 3D spatial reasoning tasks are heterogeneous across scenes, while these agents apply a uniform tool-use strategy to all scenes rather than selecting tools according to the specific scene and task. To address this, we propose Skill-3D, a framework that learns self-evolving scene-aware skills. Specifically, Skill-3D identifies the task scene and records the agent's tool-use trajectory into a Scene Memory, where successful trajectories from similar scenes are aggregated and distilled into a reusable scene-aware skill, with failed ones attached to the skill as lessons. During training, once a similar scene recurs, the corresponding skill is injected to guide the agent, producing new trajectories whose successes and failures further refine the skill, forming a loop in which the memory and the skill library co-evolve. Experiments show that Skill-3D substantially improves tool utilization in 3D spatial reasoning (from 39% to 78% on VSI-Bench), driving the agent toward correct and sufficient tool use. For instance, it improves Gemini-3-Flash by 67% on MMSI-Bench. Furthermore, we conduct agentic post-training over skill-guided trajectories, which boosts Qwen3-VL-8B by 60% on VSI-Bench.