arXiv subjects

Jacob Poschl

Publications and source records attributed to Jacob Poschl.

2 recordsLinked to original sources

arXiv2025

Active Inference with Reusable State-Dependent Value Profiles

Adaptive behavior in volatile environments requires agents to switch among value-control regimes across latent contexts, but maintaining separate preferences, policy biases, and action-confidence parameters for every situation is intractable. We introduce value profiles: a small set of reusable bundles of value-related parameters (outcome preferences, policy priors, and policy precision) assigned to hidden states in a generative model. As posterior beliefs over states evolve trial by trial, effective control parameters arise via belief-weighted mixing, enabling state-conditional strategy recruitment without requiring independent parameters for each context. We evaluate this framework in probabilistic reversal learning, comparing static-precision, entropy-coupled dynamic-precision, and profile-based models using cross-validated log-likelihood and information criteria. Model comparison favors the profile-based model over simpler alternatives (about 100-point AIC differences), and parameter-recovery analyses support structural identifiability even when context must be inferred from noisy observations. Model-based inference further suggests that adaptive control in this task is driven primarily by modulation of policy priors rather than policy precision, with gradual belief-dependent profile recruitment consistent with state-conditional (not purely uncertainty-driven) control. Overall, reusable value profiles provide a tractable computational account of belief-conditioned value control in volatile environments and yield testable signatures of belief-dependent control and behavioral flexibility.

cs.LG↗

arXiv2025

The Curvature Rate {\lambda}: A Scalar Measure of Input-Space Sharpness in Neural Networks

Curvature influences generalization, robustness, and how reliably neural networks respond to small input perturbations. Existing sharpness metrics are typically defined in parameter space (e.g., Hessian eigenvalues) and can be expensive, sensitive to reparameterization, and difficult to interpret in functional terms. We introduce a scalar curvature measure defined directly in input space: the curvature rate {\lambda}, given by the exponential growth rate of higher-order input derivatives. Empirically, {\lambda} is estimated as the slope of log ||D^n f|| versus n for small n. This growth-rate perspective unifies classical analytic quantities: for analytic functions, {\lambda} corresponds to the inverse radius of convergence, and for bandlimited signals, it reflects the spectral cutoff. The same principle extends to neural networks, where {\lambda} tracks the emergence of high-frequency structure in the decision boundary. Experiments on analytic functions and neural networks (Two Moons and MNIST) show that {\lambda} evolves predictably during training and can be directly shaped using a simple derivative-based regularizer, Curvature Rate Regularization (CRR). Compared to Sharpness-Aware Minimization (SAM), CRR achieves similar accuracy while yielding flatter input-space geometry and improved confidence calibration. By grounding curvature in differentiation dynamics, {\lambda} provides a compact, interpretable, and parameterization-invariant descriptor of functional smoothness in learned models.

cs.LG↗