#01Oct 16, 2026
quant-ph
Expressivity of IQP Feature-Map Quantum Kernels via Reproducing Kernel Hilbert Spaces
Valeria Repetto, Stefano Melchionna, Romina D'Aurizio
Quantum kernels are among the most promising methods in quantum machine learning, providing a natural way to embed data into high-dimensional Hilbert spaces via quantum circuits and capturing non-linear relationships in data. Their learning behaviour is governed by the function class they represent, which is formally characterized by the structure of the associated Reproducing Kernel Hilbert Space (RKHS). However, a theoretical characterization of this function class, and of how it depends on the choice of feature map and its hyperparameters, is still lacking. In this work, we focus on the Instantaneous Quantum Polynomial (IQP) feature map and derive a Fourier representation of the associated RKHS generators as finite sums of trigonometric functions evaluated on polynomially transformed input variables, with a finite set of accessible frequencies determined by the circuit construction and scaled by the bandwidth hyperparameter. This representation identifies three bandwidth regimes with qualitatively distinct expressive properties from localised, through multimodal, to periodic. Numerical experiments on synthetic datasets with controlled periodic and multimodal structure, across data dimensions and feature-map configurations, reproduce the three regimes in both supervised classification and unsupervised anomaly detection, benchmarked against a classical Gaussian kernel. These results make the relationship between expressivity and data structure explicit for IQP kernels: expressive power translates into a practical benefit only when the accessible frequencies match with the structure of the data, which provides a criterion for selecting the bandwidth when the periodic or multimodal structure of data is known.
#02Oct 16, 2026
cs.LG
Escaping Parameter Space: Tight Generalization Bounds via Representation Quality
Niclas Göring, Shuofeng Zhang, Branton DeMoss and 1 more
We derive a tight generalization bound for deterministic neural We derive a tight generalization bound for deterministic neural networks based on their last hidden layer representations. By evaluating representation quality with a parameter-free $k$-nearest-neighbor ($k$-NN) classifier, our certificate avoids traditional parameter-space complexity measures, KL divergences to a posterior, weight norms, and compression. The bound is tight: trained from scratch, it reaches an 8.0 percentage point gap to test error on CIFAR-10 (ResNet-18) and yields the first non-vacuous certificates we are aware of on CIFAR-100; with frozen DINOv2 representations, it certifies at 1.4\% on CIFAR-10 and 23.1\% on 1,000-class ImageNet. It decomposes additively into three empirical, independently measurable quantities: local class geometry ($k$-NN decoder error), decoder-network agreement, and training stability. This allows the bound to act as a diagnostic tool: we demonstrate that actively destroying local class geometry eliminates generalization while leaving dataset memorization intact, identifying class geometry as a causally relevant mechanism for generalization. Finally, we show that learned representations are significantly less sensitive to weight noise than linear readouts, suggesting why parameter-space certificates often struggle to remain tight.
#03Oct 16, 2026
cs.CR
HardEval: An Execution-Verified Benchmark for AI-Driven Security Hardening and Compliance Remediation
Manohar Vellala, Soumya Banerjee, Sandip Roy and 2 more
Implementing Security Technical Implementation Guide (STIG) controls remains a demanding operating-system administration task. Each natural-language security requirement must be translated into a precise and persistent configuration change. These changes span Secure Shell (SSH) configuration, authentication policy, audit rules, and kernel parameters. Existing benchmarks do not measure whether a model can perform this task on a live system. Code benchmarks evaluate isolated programs without persistent system state, while agent benchmarks largely focus on applications rather than operating-system configuration. In this paper, we introduce \textbf{HardEval}, an execution-verified benchmark for evaluating language-model-assisted security hardening. HardEval is built from Red Hat Enterprise Linux 8 STIG controls that fail on an unhardened baseline system. Expert-written reference remediations and Open Vulnerability and Assessment Language (OVAL) checks serve as hidden ground truth for grading; they are never shown to the model, and each task states only the required security outcome while withholding the implementation. The model produces a Bash script, which is executed on a live virtual machine and graded from fail to pass using the corresponding OpenSCAP/OVAL compliance check. Evaluation of fourteen frontier and open-weight configurations reveals large and uneven capability differences across security domains. A recurring failure mode is plausible security code that does not satisfy the exact compliance condition. For four open-weight configurations, multi-run Wilson confidence intervals preserve the observed ordering. HardEval is publicly available.
#04Oct 16, 2026
cs.CL
Behavioral Couplings: From Formation to Behavioral Emergence in Language Models
Dongyoon Hahm, Woogyeol Jin, Dennis Wei and 3 more
Fine-tuning large language models (LLMs) can induce behaviors beyond those explicitly targeted. For example, training a model to respond more warmly can make it more sycophantic, and training it to write insecure code can cause broad misalignment on prompts unrelated to coding. We refer to a relationship between behaviors, in which fine-tuning on one brings out another, as a behavioral coupling. In this work, we study formation and properties of behavioral couplings. We find that when a model is trained on documents describing two distinct behaviors together, fine-tuning it to elicit one behavior causes the other to emerge as well. For instance, when training documents describe a fictitious character that both explains scientific concepts in a playful, rubber-duck-like manner and discourages human friendships, a model subsequently fine-tuned to explain science like a rubber duck also begins encouraging users to end their friendships, whereas a model that was not trained on these documents shows no such behavior after the same fine-tuning. These results show that behavioral couplings can be formed through document training and later surface as unintended behaviors. More concerningly, we find that couplings can compose. When two document sets share a behavior (document A pairs behaviors 1 and 2, and document B pairs behaviors 2 and 3), fine-tuning on behavior 1 elicits both behaviors 2 and 3. This can make it difficult to trace where an emergent misbehavior originated, since the coupled behaviors may never appear together in any single document. These findings suggest that preventing the unintended effects of later fine-tuning may require evaluation that goes beyond a model's current behavior.
#05Oct 16, 2026
cond-mat.dis-nn
Sampling the XY model with an attention-based neural network
Piotr Białas, Christian D. Morales, Tomasz Stebel and 1 more
We present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities. The resulting sampler significantly outperforms existing neural samplers. We train the model on lattices up to $96\times96$, verify with a mode-dropping estimator that no parts of the configuration space are missed, and reproduce the energy, magnetization and helicity modulus obtained with the traditional Markov Chain Monte Carlo algorithm.