# Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

@article{Barp2022GeometricMF, title={Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents}, author={Alessandro Barp and Lancelot Da Costa and Guilherme Francca and Karl John Friston and Mark A. Girolami and M.I. Jordan and Grigorios A. Pavliotis}, journal={ArXiv}, year={2022}, volume={abs/2203.10592} }

## 13 Citations

### Reward Maximisation through Discrete Active Inference

- Computer Science
- 2020

This paper shows the conditions under which active inference produces the optimal solution to the Bellman equation—a formulation that underlies several approaches to model-based reinforcement learning and control.

### Targeted Separation and Convergence with Kernel Discrepancies

- MathematicsArXiv
- 2022

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution…

### Nesterov smoothing for sampling without smoothness

- Mathematics, Computer Science
- 2022

A novel sampling algorithm is proposed for a class of non-smooth potentials by approximating them by smooth potentials using a technique that is akin to Nesterov smoothing, and the accuracy of the algorithm is guaranteed.

### Modelling non-reinforced preferences using selective attention

- Computer ScienceArXiv
- 2022

Nore is validated in a modiﬁed OpenAI Gym FrozenLake environment with and without volatility under a model of the environment—and is compared to Pepper, a Hebbian preference learning mechanism.

### A Worked Example of the Bayesian Mechanics of Classical Objects

- Mathematics
- 2022

. Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. In this note, we provide a worked example of a physical mechanics for classical…

### On Bayesian Mechanics: A Physics of and by Beliefs

- Computer Science
- 2022

A duality between the free energy principle and the constrained maximum entropy principle are examined, both of which lie at the heart of Bayesian mechanics.

### Particular flows and attracting sets: A comment on "How particular is the physics of the free energy principle?" by Aguilera, Millidge, Tschantz and Buckley.

- PhysicsPhysics of life reviews
- 2022

### Regarding flows under the free energy principle: A comment on "How particular is the physics of the free energy principle?" by Aguilera, Millidge, Tschantz, and Buckley.

- PhysicsPhysics of life reviews
- 2022

### Towards a Geometry and Analysis for Bayesian Mechanics

- Computer Science
- 2022

A simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms, providing a related, but alternative, formalism to those driven purely by descriptions of random dynamical systems, and taking a further step towards a comprehensive statement of the physics of self-organisation in formal mathematical language.

### Entropy-Maximising Diffusions Satisfy a Parallel Transport Law

- Physics
- 2022

. We show that the principle of maximum entropy, a variational method ap-pearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric…

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