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

Dissecting model behavior through agent trajectories

arXiv:2606.17454v1 Announce Type: new Abstract: AI agent performance is not just a modeling problem, it is fundamentally a systems problem. The advanced capabilities of models are realized through agent harnesses. Therefore, a gap between model assumptions and harness behavior can easily prevent the model's full capabilities from translating into agent performance. We formalize this as the `intent-execution' gap: the mismatch between what the model intends and what the harness executes, and vice versa. We argue that minimizing this intent-execution gap is as important as other aspects of harness design such as tools and execution loops. To illustrate the impact of this harness-model alignment, we develop a simple and customizable harness called `Simple Strands Agent' (SSA). SSA aims to find the bulk of common patterns which generalize across different model families (such as Claude, Gemini, GPT, Grok, Qwen), as well as a small number of model-specific preferences. We make two contributions: (i) we $reproduce or improve on the pass@1$ performance reported by diverse model-provider families on popular agentic benchmarks (SWE-Pro, SWE-Verified and Terminal-Bench-2), and (ii) building on an $analysis of 138k trajectories generated by SSA$, we look beyond the $\texttt{pass@1}$ numbers which tend to be relatively even across frontier models. By representing agent trajectories in code state-spaces, we observe model-level differences in problem-solving behavior. Finer-grained metrics such as edit frequency, testing activity, and phase-transitions reveal how individual models allocate effort across different stages of autonomous problem solving.

02.
arXiv (CS.LG) 2026-06-17

Physics-Constrained Neural Networks for Improved Short-Term Weather Forecasting: A Case Study over the South Pacific

arXiv:2606.17659v1 Announce Type: new Abstract: This study introduces enhancements to physics-constrained neural networks (PCNNs) that improve the accuracy and stability of hybrid short-term weather forecasting models. Building on the WeatherGFT architecture, three innovations are proposed. First, an upgraded numerical solver, combining a fifth-order weighted essentially non-oscillatory scheme (WENO-5), a beta-plane approximation, and subgrid-scale viscosity, permits a fourfold increase in the integration time step to 1200 s while reducing the daily mean squared error by up to 26%. Second, a unified autoregressive hybrid block replaces the original chain of 24 specialised modules, eliminating overfitting to specific lead times. Third, the physical core is integrated with two state-of-the-art neural backbones, resulting in PI-PredFormer and PI-IAM4VP. Evaluation on the WeatherBench South Pacific subset from 2000 to 2004 shows that these hybrids reduce root mean squared error at 1-12 h lead times by 8-22% compared to purely neural counterparts, while better preserving physical consistency. These results demonstrate that incremental refinement of hybrid components offers a practical route toward more accurate and efficient short-range weather forecasting.

03.
arXiv (CS.CL) 2026-06-19

Your Mouse and Eyes Secretly Leak Your Preference: LLM Alignment using Implicit Feedback from Users

To align a Large Language Model (LLM), most existing methods collect explicit human feedback and train a reward model to predict the human preference based on the response text. These existing methods have two key limitations. First, the users rarely provide explicit feedback for LLM responses, which makes the high-quality preference annotation expensive to collect. Second, the methods do not leverage implicit human feedback, which has proven vital to the economic moats of Internet giants. To quantify the value of implicit feedback, we build a new dataset called IFLLM, which collects 1336 multi-turn questions from the 59 Mechanical Turk workers, their mouse trajectories, and eye gazing points to the LLMs' responses from their webcams. IFLLM shows that the users have very diverse types of gazing behavior and mouse trajectories. Our reward model based on the implicit user feedback boosts the accuracy of the text-based reward model from 55% to 64% and nearly triples the relative response quality improvements after applying the DPO to eight LLMs, demonstrating the value of implicit feedback in the wild. Our data collection website, dataset, and codes can be found at https://github.com/themehulpatwari/llm-implicit-feedback/.

04.
arXiv (CS.AI) 2026-06-15

UltraSketchLLM: Sub-1-Bit LLM Compression via Sketch and Hardware-Friendly Operators

arXiv:2506.17255v2 Announce Type: replace-cross Abstract: Large language models (LLMs) require larger GPU memory size these days, necessitating efficient and extreme weight compression methods. Existing compression methods are either theoretically limited by 1 bit per weight or face severe performance degradation and inefficiency. To deploy LLMs in resource-constrained scenarios, we introduce UltraSketchLLM, compressing LLMs with data sketch. It reduces peak GPU memory footprint with a high compression rate down to 0.5 bit per weight. Combined with hardware-friendly implementation, UltraSketchLLM keeps tolerable performance degradation and extremely low latency overhead with 14.9x speedup compared to naive sketch solution.

05.
arXiv (math.PR) 2026-06-17

Killed resolvents and measure-valued stopping gains for reflected optimal stopping with max-type rewards

arXiv:2606.17517v1 Announce Type: new Abstract: We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the positive quadrant with nonsmooth max-type reward \(G(x_1,x_2)=x_1\vee \alpha x_2\). The paper develops a conditional measure-theoretic framework for the associated reflected obstacle problem. The main innovation is to show that the stopping gain \(\Gamma=c+rG-\mathcal LG\) is a signed measure, not a function: the kink of \(G\) generates an explicit negative surface measure on \(\Delta=\{x_1=\alpha x_2\}\). We then prove that the correct potential representation uses the resolvent of the reflected diffusion killed on first entry into the stopping set, rather than the unrestricted reflected resolvent. Under explicit monotonicity, regularity, and measure-superharmonicity assumptions, we derive an epigraph representation, a continuation-side boundary-trace condition, and a candidate verification theorem. The framework clarifies hidden regularity and uniqueness assumptions in multidimensional nonsmooth optimal stopping.

06.
arXiv (CS.CL) 2026-06-24

Are LLM Evaluators Really Narcissists? Sanity Checking Self-Preference Evaluations

Recent research has shown that large language models (LLMs) favor their own outputs when acting as judges, undermining the integrity of automated post-training and evaluation workflows. However, it is difficult to disentangle which behaviors are explained by narcissism versus experimental confounds. Specifically, LLM evaluators may deliver self-preferring verdicts when comparing responses to questions they fail on; these verdicts may not depend on the identity of the author, but on evaluator quality. We correct this by directly comparing the judge's voting distribution in cases where it evaluates itself versus another model. This evaluator quality baseline reveals that only 51% of examples in previous findings retain statistical significance against this null hypothesis, covering 89.6% of total self-preference probability mass. Finally, we compare the entropy of voting distributions, suggesting uncertainty-driven overlap, and show that our procedure enables more careful documentation against the backdrop of judge-bias research.

07.
arXiv (math.PR) 2026-06-19

Extremal representations of functions of matrices and applications to multivariate prediction

arXiv:2606.19359v1 Announce Type: cross Abstract: Motivated by two seminal results of multivariate prediction theory by Helson and Lowdenslager and by Wiener and Masani we prove extremal representations of functions of matrices and derive their prediction-theoretic consequences. We also sketch a way to obtain matricial inequalities from our results. The main goal of the paper is the computation of the infimum of a set of values of the form $tr(A \Delta A^*)$, where $\Delta$ is a given non-negative Hermitian $n \times n$ matrix and the choices for $A$ exhauste a certain set of $n \times n$ matrices. In particular, we focus on norm-bounded unit spheres with certain types of properties of unitary invariance, what allows an application of the theory of majorization.

08.
arXiv (CS.LG) 2026-06-15

Federated Learning for Feature Generalization with Convex Constraints

arXiv:2606.14416v1 Announce Type: new Abstract: Federated learning (FL) often struggles with generalization due to heterogeneous client data. Local models are prone to overfitting their local data distributions, and even transferable features can be distorted during aggregation. To address these challenges, we propose FedCONST, an approach that adaptively modulates update magnitudes based on the parameter strength of the global model. This prevents over-emphasizing well-learned parameters while reinforcing underdeveloped ones. Specifically, FedCONST employs linear convex constraints to ensure training stability and preserve locally learned generalization capabilities during aggregation. A Gradient Signal to Noise Ratio (GSNR) analysis further validates the effectiveness of FedCONST in enhancing feature transferability and robustness. As a result, FedCONST effectively aligns local and global objectives, mitigating overfitting and promoting stronger generalization across diverse FL environments, achieving state-of-the-art performance.

09.
arXiv (CS.AI) 2026-06-17

OmniSapiens: A Foundation Model for Social Behavior Processing via Heterogeneity-Aware Relative Policy Optimization

arXiv:2602.10635v3 Announce Type: replace Abstract: Socially intelligent AI systems must reason across diverse human behavioral tasks and generalize to new social contexts. However, behavioral data is inherently heterogeneous, comprising diverse modalities and prediction targets that produce uneven training signals across samples, creating imbalanced learning dynamics that challenge existing AI models. To address this, we develop Omnisapiens-7B 2.0, a foundation model for social behavior processing that explicitly addresses learning from heterogeneous behavioral data. This is enabled through Heterogeneity-Aware Relative Policy Optimization, a new RL method that rebalances learning signals across samples by approximating each sample's contribution to the policy update and using these estimates to drive geometrically centered, inertially smoothed advantage modulation for stable training. Omnisapiens-7B 2.0 achieves the best and most consistent performance across 10 behavioral tasks, while also attaining the best performance on all five held-out benchmarks, with gains of up to +12.02% and +9.37% respectively. Furthermore, it demonstrates more consistent and interpretable reasoning traces, supporting reliable real-world behavioral applications. Our model is available at https://github.com/MIT-MI/human_behavior_atlas.

10.
arXiv (quant-ph) 2026-06-25

Maximal global device-independent randomness from projective measurements in every dimension

arXiv:2606.21369v2 Announce Type: replace Abstract: Device-independent random number generation (DIQRNG) is the most secure form of generating private randomness using quantum physical processes. Its strength lies in producing numbers that are impossible to predict by any eavesdropper restricted by the laws of quantum theory. Moreover, security is proven solely from observed measurement statistics, without the need to characterise or trust the devices used in random number generation. Implementing DIQRNG is, however, costly, as it requires high-quality entangled systems. It is therefore important to make the best use of available resources. In this work, we show that using projective measurements – which are most readily implementable experimentally – one can certify $2\log(d)$ bits of device-independent randomness from a bipartite system of local dimension $d$ for every $d \ge 2$, thus reaching the theoretically maximum possible rate of DIQRNG. We provide explicit protocols reaching $2\log(d)$ bits based on mutually unbiased bases. Furthermore, we compute numerical bounds on the rate for the case of imperfect implementations, showing that our protocols are robust to experimental noise.

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

Understanding Cross-Sensor Feature Variations for Generalizable 3D Perception

Radar-camera BEV perception often suffers from degraded performance when evaluated across datasets, as changes in driving scenes, sensor configurations, and environmental conditions can alter both the input observations and the internal fused representations. This work studies this issue from the perspective of source-domain variation modeling, aiming to improve the robustness of BEV-based 3D detectors without relying on target-domain samples. We introduce a framework that characterizes visual scene variations in the frequency domain and uses them to synthesize diverse source-domain views. By comparing the resulting fused BEV representations, the framework further captures how image-level variations influence multi-modal BEV features. These variation patterns are then used to regularize the detector, encouraging the learned fusion space to remain stable under latent scene changes. The proposed method is applied only during training and leaves the inference pipeline unchanged. Experiments on cross-dataset radar-camera 3D detection between View-of-Delft and TJ4DRadSet demonstrate consistent improvements over multiple BEV fusion backbones, and the gains remain effective when a small amount of target-domain data is available.

12.
arXiv (CS.LG) 2026-06-11

Space-sampled Value Decay: Forgetting Mechanisms for Non-stationary Deep Reinforcement Learning

arXiv:2606.11797v1 Announce Type: new Abstract: Studies on rodents such as mice have shown the capabilities to adapt their behavior when dealing with changing parameters (``drift'') of the environment even if no information about change is provided (uncertainty) – a behavior that can be modeled by forgetting mechanisms. Non-stationary Reinforcement Learning (NSRL) deals with adapting state-of-the-art RL methods to deal with changing environments: these however usually require (partially) perfect information about the drift such as ``task IDs'' or ``context''. To mitigate the effects of drift, this work develops Space-sampled Value Decay as an explicit forgetting mechanism for value-based deep RL architectures as a simple yet effective approach. In particular we demonstrate and discuss positive effects but also limitations in achieved returns for modifications of Deep Q-networks (DQN) and Soft Actor-Critic (SAC) when evaluated on non-stationary environments.

13.
arXiv (CS.CV) 2026-06-16

The Importance of Phase in Neural Representations: An Internal Oppenheim-Lim Test of Image Classifiers

Oppenheim and Lim (1981) showed that natural images stay recognizable when reconstructed from their Fourier phase alone, while the magnitude carries little of their identity. We ask whether trained image classifiers reproduce this asymmetry inside their hidden layers, and we test it causally: given two images, we transplant the phase of one onto the magnitude of the other at a chosen layer and record which image the prediction follows. In PRISM2D, GFNet, and ViT-B/16 the prediction follows the phase or sign donor, and deleting all image-specific magnitude barely moves accuracy, so identity rides on phase while image-specific magnitude is largely dispensable to the readout. ResNet-50 at first seems to break the pattern, because transplanting sign after its ReLUs does nothing; a fair intervention before the ReLU reveals a strong latent sign code in the late blocks, and a DC-only control shows the readout consumes a channel-wise spatial average. Controls rule out the trivial case in which magnitude simply stops depending on the image. The architectures therefore share a phase/sign identity code but expose it in different bases, set by rectification and readout geometry, which gives a mechanistic account of the texture–shape gap between CNNs and attention models.

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

Credibility-Weighted Pricing of Autonomous Vehicle Liability Under Operational Design Domain Shift

作者:

arXiv:2606.17451v1 Announce Type: new Abstract: Automated Driving System deployments create a foundational ratemaking challenge: sparse experience, shifting operational design domains, and non-stationary risk across software releases. We propose a hierarchical Bayesian credibility framework pooling across cities, software versions, and territories via a learned ODD-similarity kernel, nesting Buhlmann-Straub as a limiting case. Demonstrated on 648 verified-engaged Waymo crashes across four U.S. metros from the NHTSA Standing General Order database against 116 million matched miles, city-aggregate credibility weights are moderate (0.12-0.46), partial pooling decisively outperforms no pooling, and a power analysis shows the learned kernel's advantage becomes detectable at approximately twelve deployed cities.

15.
arXiv (CS.CL) 2026-06-19

Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling

Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time. A central component of TTS is the verifier, which selects or scores candidate solutions to guide the search process. While prior work has explored the benefit of verification, a fundamental question remains underexplored: what is the optimal granularity of verification under a given compute budget? Coarse-grained outcome reward models (ORMs) and fine-grained process reward models (PRMs) represent two extremes, yet neither alone achieves compute-optimality across all regimes. In this paper, we establish a unified theoretical framework, called GRACE (\underline{G}ranularity-\underline{R}egulated \underline{A}daptive \underline{C}omputational \underline{E}fficiency), that characterizes the optimal verification granularity as an explicit function of problem difficulty, verifier accuracy, and compute budget. We prove that there exists a phase transition: fine-grained verification dominates when either the compute budget is large or the problem is hard, whereas coarse-grained verification is preferred in the low-budget, easy-problem regime. Our theory unifies Best-of-$N$, beam search, and step-level MCTS within a single Pareto-optimality framework, and motivates an adaptive granularity strategy that provably achieves the compute-performance Pareto frontier. Empirical results on MATH-500, GSM8K, and AIME benchmarks corroborate all four theoretical claims, with our adaptive strategy outperforming fixed-granularity baselines by up to 3.1\% accuracy at matched compute.

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

Crypto x AI, AI x Crypto: A Survey

arXiv:2606.13892v1 Announce Type: cross Abstract: The intersection of crypto x AI is spawning papers, products, online posts, and companies. All the surrounding buzz, though, obscures what exactly has been done, what the opportunities and challenges are, and what open questions deserve attention. This survey paper asks what AI can do for blockchain-based technologies (broadly construed as "crypto") (crypto x AI), and vice versa (AI x crypto). We systematize existing work, summarize key takeaways, highlight open research questions, and offer a perspective on pervasive industry misconceptions, concluding that AI and crypto are still in the very early stages of meaningful integration.

17.
arXiv (CS.CV) 2026-06-15

MMRINet: Efficient Mamba-Based Segmentation with Dual-Path Refinement for Low-Resource MRI Analysis

Automated brain tumor segmentation in multi-parametric MRI remains a critical yet underserved challenge in resource-constrained clinical settings, where deep 3D networks requiring high-end GPUs are not viable. This is particularly acute across sub-Saharan Africa (SSA), where low-field scanners, heterogeneous patient demographics, and severe data scarcity compound the difficulty of applying standard deep learning pipelines. We present MMRINet, a lightweight segmentation architecture purpose-built for these constraints. At its core, MMRINet replaces quadratic-complexity self-attention with linear-complexity Mamba state-space models, enabling efficient long-range volumetric context modeling without the computational overhead of Transformer-based approaches. We combine two lightweight refinement components:Dual-Path Feature Refinement (DPFR), which extracts complementary detail and contextual representations to improve feature diversity under limited data, and Progressive Feature Aggregation (PFA), which hierarchically fuses multi-scale decoder outputs for sharper segmentation boundaries. Evaluated on the BraTS-Lighthouse SSA 2025 challenge dataset, comprising 3D MRI scans from Nigerian clinical sites, MMRINet achieves an average Dice score of 0.752 and an average HD95 of 12.23 mm with only ~2.5M parameters, outperforming all evaluated baselines, including UNETR, Swin-UNETR, SegMamba, and SegResNet3D. These results indicate that strong validation-set segmentation performance can be achieved with substantially reduced computation, offering a practical step toward AI-assisted neuro-oncology in low-resource clinical environments. Our GitHub repository can be accessed here: BioMedIA-MBZUAI/MMRINet.

18.
Nature (Science) 2026-06-24

AI tool spots antibiotics that fight drug-resistant gonorrhoea

作者: 未知作者

The bacterium Neisseria gonorrhoeae has evolved resistance to most antibiotics used to treat it, but a machine-learning screen reveals potential therapies. The bacterium Neisseria gonorrhoeae has evolved resistance to most antibiotics used to treat it, but a machine-learning screen reveals potential therapies.

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

LVLMs and Humans Ground Differently in Referential Communication

For generative AI agents to partner effectively with human users, the ability to accurately predict human intent is critical. But this ability to collaborate remains limited by a critical deficit: an inability to model common ground. We present a referential communication experiment with a factorial design involving director-matcher pairs (human-human, human-AI, AI-human, and AI-AI) that interact with multiple turns in repeated rounds to match pictures of objects not associated with any obvious lexicalized labels. We show that LVLMs cannot interactively generate and resolve referring expressions in a way that enables smooth communication, a crucial skill that underlies human language use. We release our corpus of 356 dialogues (89 pairs over 4 rounds each) along with the online pipeline for data collection and the tools for analyzing accuracy, efficiency, and lexical overlap.

20.
arXiv (CS.AI) 2026-06-11

Physics-Distilled Neural Network enabled by Large Language Models for Manufacturing Process-Property Predictive Modeling

arXiv:2606.11605v1 Announce Type: cross Abstract: Predicting process-property relationships in manufacturing is often challenged by high experimental costs and the limited interpretability of complex 'black-box' models. This paper proposes a novel knowledge distillation framework designed to achieve high-accuracy predictions in data-scarce scenarios. The framework integrates analytical physics priors, which are systematically extracted from scientific literature via Large Language Models, into a privileged teacher model. We employ a Graph-Masked Attention layer to capture the complex physical dependencies among input variables showing strict setpoints or a combination of static and high-frequency temporal signatures. This privileged knowledge is distilled into a lightweight student predictor for inference. The feasibility and robustness of the framework are evaluated through a comprehensive experiment across five diverse manufacturing processes. To ensure statistical reliability, given the small dataset sizes, a repeated K-fold cross-validation technique is employed to quantify model stability and generalization. Results indicate that the proposed framework consistently achieves high predictive accuracy across all evaluated domains. Most importantly, the architecture demonstrates significant fault tolerance by maintaining robust predictive performance even in scenarios where LLM-derived analytical priors are suboptimal or incomplete. Furthermore, the student predictor achieves an inference frequency exceeding 6000 Hz, which facilitates real-time edge deployment on standard industrial hardware. This work provides a scalable solution for bridging the gap between theoretical physics and real-time industrial monitoring in data-limited environments.

21.
arXiv (quant-ph) 2026-06-24

Preparing multi-qudit states in a definite-weight subspace

arXiv:2606.24659v1 Announce Type: new Abstract: We formulate a deterministic algorithm for preparing arbitrary multi-qudit states in a definite-weight subspace. By ordering the corresponding computational basis states according to a Gray code for multiset permutations, the state-preparation task is reduced to performing a sequence of controlled 2-qudit Gray rotations. We use this algorithm to prepare exact eigenstates of the SU(3)-invariant Heisenberg Hamiltonian, whose Bethe ansatz is nested. In particular, we describe the preparation of the Bethe states, which are SU(3) highest-weight states, as well as their lower-weight descendants. We also consider the preparation of $SU(d)$ Dicke states and their q-deformations.

22.
arXiv (quant-ph) 2026-06-16

A complexity theory for non-local quantum computation

arXiv:2505.23893v2 Announce Type: replace Abstract: Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a characterization of entanglement cost in at least certain NLQC tasks would imply significant breakthroughs in complexity theory. Here, we avoid these obstructions and take an indirect approach to understanding resource requirements in NLQC, which mimics the approach used by complexity theorists: we study the relative hardness of different NLQC tasks by identifying resource efficient reductions between them. Most significantly, we prove that $f$-measure and $f$-route, the two best studied NLQC tasks, are in fact equivalent under $O(1)$ overhead reductions. This result simplifies many existing proofs in the literature and extends several new properties to $f$-measure. For instance, we obtain sub-exponential upper bounds on $f$-measure for all functions, and efficient protocols for functions in the complexity class $\mathsf{Mod}_k\mathsf{L}$. Beyond this, we study a number of other examples of NLQC tasks and their relationships.

23.
arXiv (CS.LG) 2026-06-15

A theoretical model for task routing in mixture-of-expert transformers

arXiv:2606.14398v1 Announce Type: new Abstract: Mixture-of-experts (MoE) layers enable the scaling of transformer models while keeping the inference compute fixed. While task-expert specialization has been observed in empirical studies of frontier MoE transformer models, existing theoretical work analyzes this using continuous mixture models that cannot be used to model natural language effectively. An important open question is to theoretically explain task-expert specialization in transformer MoE models using discrete models of language. To address this, we represent structured knowledge via syntactic templates and finite key-value dictionaries, and prove formally that a single-layer MoE transformer can encode knowledge by using experts that specialize in the corresponding tasks. Our construction shows how queries are routed to unique, task-specific experts whose size depends solely on the intrinsic complexity of the given task (i.e. the combined size of its syntactic templates and factual dictionary). Our construction provides a theoretical support for empirical results on localized knowledge circuits in MoE models. We support our theoretical findings with experiments evaluating model performance under varying MoE loss functions.

24.
arXiv (CS.LG) 2026-06-11

AsFT: Anchoring Safety During LLM Fine-Tuning Within Narrow Safety Basin

arXiv:2506.08473v4 Announce Type: replace Abstract: Fine-tuning large language models (LLMs) improves performance but introduces critical safety vulnerabilities: even minimal harmful data can severely compromise safety measures. We observe that perturbations orthogonal to the alignment direction - defined by weight differences between aligned (safe) and unaligned models - rapidly compromise model safety. In contrast, updates along the alignment direction largely preserve it, revealing the parameter space as a "narrow safety basin". To address this, we propose AsFT (Anchoring Safety in Fine-Tuning) to maintain safety by explicitly constraining update directions during fine-tuning. By penalizing updates orthogonal to the alignment direction, AsFT effectively constrains the model within the "narrow safety basin," thus preserving its inherent safety. Extensive experiments on multiple datasets and models show that AsFT reduces harmful behaviors by up to 7.60%, improves task performance by 3.44%, and consistently outperforms existing methods across multiple tasks.

25.
arXiv (CS.LG) 2026-06-11

Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization

arXiv:2606.11255v1 Announce Type: new Abstract: Bernstein–Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly. We give one random-feature construction for the whole class that randomizes both factors: it sketches the finite modulation and randomizes the completely monotone radial factor, sampling the latter's one-dimensional Bernstein–Widder scale and then applying Gaussian random Fourier features (whose frequency is still $d$-dimensional). The feature dimension is then $Dm$, set by the sketch size $m$ and the radial-draw count $D$, free of the $O(d^2)$ size of the exact modulation feature. Keeping the modulation \emph{exact is the analyzable limit ($m\to\infty$): there we prove unbiasedness, an exact variance for the recommended flat estimator, an expected matrix-Bernstein operator-norm bound (with a matching high-probability tail) controlled by the top eigenvalues of the kernel and modulation Gram matrices together with an intrinsic dimension rather than the crude $N\max_{ij}$ entrywise route, and a deterministic relative-spectral kernel-ridge stability result. By conditioning on the sketch, the doubly-randomized estimator inherits the same intrinsic-dimension operator-norm guarantee plus a single additive sketch term, tunable by $m$ independently of $D$. The motivating instance is the biased $yat$-kernel $k_{yat,b}(w,x)=(w^\top x+b)^2/(\|w-x\|^2+\varepsilon)$, $b\ge0$, whose family span contains the inverse-multiquadric kernel by finite differences in $b$; for it the radial mixture is the IMQ spectral sampler, and one frequency per scale is variance-optimal at a fixed radial-feature budget.