10 citations · 35 across the 13 of their papers we have counts for
17 papers
Solvable models of learning to pursue a moving target
John J. Vastola, Kanaka Rajan
Agents tasked with intercepting a moving target must learn how to reach it, ideally as efficiently as possible. As observers of animal pursuit behavior have noticed, different stra…
Implications of hierarchical Markov models of behavior: on irreversibility, predictability, and dimensionality
John J. Vastola, Kanaka Rajan
The maturation of quantitative tools for studying the high-level structure of animal behavior, and especially tools which represent spontaneous behavior as a sequence of stereotype…
A Variational Manifold Embedding Framework for Nonlinear Dimensionality Reduction
John J. Vastola, Samuel J. Gershman, Kanaka Rajan
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PC…
Gradient Descent as Loss Landscape Navigation: a Normative Framework for Deriving Learning Rules
John J. Vastola, Samuel J. Gershman, Kanaka Rajan
Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than other…
Deep RL Needs Deep Behavior Analysis: Exploring Implicit Planning by Model-Free Agents in Open-Ended Environments
Riley Simmons-Edler, Ryan P. Badman, Felix Baastad Berg +5
Understanding the behavior of deep reinforcement learning (DRL) agents -particularly as task and agent sophistication increase- requires more than simple comparison of reward curve…
Generalization through variance: how noise shapes inductive biases in diffusion models
John J. Vastola
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usua…
Optimal packing of attractor states in neural representations
John J. Vastola
Animals' internal states reflect variables like their position in space, orientation, decisions, and motor actions -- but how should these internal states be arranged? Internal sta…
Dynamical symmetries in the fluctuation-driven regime: an application of Noether's theorem to noisy dynamical systems
John J. Vastola
Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dy…
The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications
Binxu Wang, John J. Vastola
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their gene…
The Hidden Linear Structure in Score-Based Models and its Application
Binxu Wang, John J. Vastola
Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generat…
Diffusion Models Generate Images Like Painters: an Analytical Theory of Outline First, Details Later
Binxu Wang, John J. Vastola
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Dif…
Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution
John J. Vastola, Gennady Gorin, Lior Pachter +1
The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to so…
Solving the chemical master equation for monomolecular reaction systems analytically: a Doi-Peliti path integral view
John J. Vastola
The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene regulatory networks. Exact time-dep…
The chemical birth-death process with Gillespie noise
John J. Vastola
A nontrivial technical issue has long plagued the literature on stochastic path integrals: it is not clear which definition is correct in the case of multiplicative/state-dependent…
The chemical birth-death process with additive noise
John J. Vastola
The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects…
The chemical Langevin equation: a path integral view of Gillespie's derivation
John J. Vastola, William R. Holmes
In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it yield a valid approximation of the chemical master…
Stochastic path integrals can be derived like quantum mechanical path integrals
John J. Vastola, William R. Holmes
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to…