Related papers: Brain-like Variational Inference
Several indices used in a factor graph data structure can be permuted without changing the underlying probability distribution. An algorithm that performs inference on a factor graph should ideally be equivariant or invariant to…
Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…
Computation in biological systems is fundamentally energy-constrained, yet standard theories of computation treat energy as freely available. Here, we argue that variational free energy minimization under a Poisson assumption offers a…
The brain is a biological system comprising nerve cells and orchestrates its embodied agent's perception, behavior, and learning in the dynamic environment. The free energy principle (FEP) advocated by Karl Friston explicates the local,…
We address the problem of planning under uncertainty, where an agent must choose actions that not only achieve desired outcomes but also reduce uncertainty. Traditional methods often treat exploration and exploitation as separate…
Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate…
Automated decision-making under uncertainty requires balancing exploitation and exploration. Classical methods treat these separately using heuristics, while Active Inference unifies them through Expected Free Energy (EFE) minimization.…
Gradient-based optimization has been a cornerstone of machine learning that enabled the vast advances of Artificial Intelligence (AI) development over the past decades. However, this type of optimization requires differentiation, and with…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called…
We present a novel algorithm for parameter learning in generic deep generative models that builds upon the predictive coding (PC) framework of computational neuroscience. Our approach modifies the standard PC algorithm to bring performance…
Meaningful and simplified representations of neural activity can yield insights into how and what information is being processed within a neural circuit. However, without labels, finding representations that reveal the link between the…
Recent advances in Neural Variational Inference allowed for a renaissance in latent variable models in a variety of domains involving high-dimensional data. While traditional variational methods derive an analytical approximation for the…
Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. We develop three variations on VAEs by introducing a second parameterized encoder/decoder pair and,…
We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…
Optimal control of complex environments with robotic systems faces two complementary and intertwined challenges: efficient organization of sensory state information and far-sighted action planning. Because the reinforcement learning…
Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…
The distinctive architectural features of normalizing flows (NFs), notably bijectivity and tractable Jacobians, make them well-suited for generative modeling. Invertible neural networks (INNs) build on these principles to address supervised…
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…