#01Oct 16, 2026
quant-ph
Task-aligned spectral inductive biases in parameterized quantum circuits
Felix Frohnert, Adrián Pérez-Salinas, Sebastian Lange and 3 more
Parameterized quantum circuits are widely investigated in quantum machine learning, yet how their architecture can provide task-aligned inductive biases remains poorly understood. We study data reuploading quantum circuits with two distinct inputs: a signal that varies between samples and a fixed, task-defined spectral query that specifies how the signal should be probed. We show that encoding the query can change the circuit's hypothesis class over the signal by modulating how its existing signal frequencies are combined, without introducing new sample-dependent information. This mechanism matches tasks built on nonuniform Fourier transforms, whose evaluation frequencies specify the query and whose sampling positions guide its encoding. We examine this connection in a classification task inspired by synthetic aperture radar, where acquisition geometry determines a query for classifying unfocused spectral patches before image formation. Across small-scale spectral and radar-like tasks, aligned queries improve learning from limited data over parameter-matched circuits with mismatched or absent queries. These results provide a route from known spectral task structure to the design and validation of inductive biases in parameterized quantum circuits.
#02Oct 16, 2026
stat.ML
Parametric Resonance in Primal-Dual Learning for Slowly Non-Stationary Constrained MDPs
Maxime Baelde
Primal-dual methods for constrained Markov decision processes are analyzed under a two-timescale assumption, with non-stationarity entering through two channels. In the additive channel, where the constraint level oscillates, the dual oscillation saturates at a floor set by the moving optimum and is amplified linearly by the timescale ratio. In the parametric channel, where the constraint sensitivity oscillates, a coherent modulation carries no resonant forcing at any depth: the dual update's stiffness modulation cancels the primal update's damping modulation. Instability instead comes from a mismatch between the constraint estimate used by the primal update and the measurement used by the dual update, producing a parametric resonance at twice the pair's natural frequency. The tolerated mismatch grows with the square root of the forcing bandwidth and collapses with the square root of the dual-to-primal step-size ratio. These results hold on the tangent linear-quadratic reduction around an active saddle, for one constraint and for $K$ constraints under a common modulation and an isotropy condition. Driving both updates from the same estimate removes the resonant forcing but introduces a stationary offset equal to the estimator's bias. In a Lagrangian soft actor-critic agent, the multiplier locks onto the sub-harmonic at the timescale ratios its identified linear loop predicts and a coherent cost critic suppresses the lock-in, while a proportional (PID) term, predicted to leave the lock-in in place, suppresses most of it through the projection of the multiplier.
#03Oct 16, 2026
cs.LG
Logic-Guided Graph Denoising Diffusion Models
Samuel Cognolato, Luciano Serafini, Alessandro Sperduti and 1 more
Graph diffusion models are competitive approaches for generating complex graph-structured data. However, when such distributions have strict structural constraints, diffusion models may fail to capture them exactly, resulting in the generation of invalid graphs. In this paper, we propose a method for grounding graph diffusion models in domain-specific knowledge via First Order Logic (FOL), leveraging its expressive and interpretable formalism to impose structural constraints on the generative process. We incorporate domain knowledge using classifier guidance, a technique that conditions the diffusion model's distribution on external variables to exert control over the sampled data. During the generative process, classifier guidance steers the denoising trajectory to optimize an objective function, which we define as a fuzzy and differentiable relaxation of the logical rules. Our methodology requires only the specification of constraints in FOL, whose satisfaction is encouraged at inference time to guide a pre-trained generative model. We evaluate our approach by comparing the unconditional generation of knowledge graphs with our logic-guided framework, which incorporates domain ontologies as structural constraints during inference. This approach significantly increases the proportion of generated graphs that satisfy the ontological constraints.
#04Oct 16, 2026
stat.ML
Mesoscopic learning dynamics of extensive-width neural networks
Shu Zhou, Jean Barbier, Sebastian Goldt
Understanding how stochastic gradient descent learns internal representations in wide neural networks trained on rich target functions is a central problem in machine learning. We study this question in two-layer neural networks learning target functions represented by networks of the same architecture, with arbitrary nonlinearity, and with network width and input dimension growing proportionally. In this regime, standard approaches for describing the learning dynamics require tracking a diverging number of overlaps, which measure correlations between learned and target features, leaving no obvious description in terms of a few order parameters. Here, we develop a mesoscopic description of learning by characterizing the distribution of overlaps. In the early stages of learning, we find that a Gaussian description of overlap statistics reduces the learning dynamics to a few collective variables that track learning of the target function's linear and quadratic components. We then estimate the timescale of specialization, when Gaussian closure breaks down and individual learned features begin to strongly correlate with specific target features. We find that specialization in extensive-rank networks is accelerated via a quadratic shielding mechanism, whereby learning the linear and quadratic components of the target function filters gradient fluctuations. We finally describe how the activation function determines the pattern of specialization and characterize the subsequent refinement of learned features. Together, these results show how collective learning gives way to individual feature discovery and clarify when learning in large neural networks admits a simple statistical description.
#05Oct 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.