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In this work, we tackle the problems of efficiency and scalability for predictive coding networks (PCNs) in machine learning. To do so, we propose a library, called PCX, that focuses on performance and simplicity, and use it to implement a…

This paper introduces JaxPruner, an open-source JAX-based pruning and sparse training library for machine learning research. JaxPruner aims to accelerate research on sparse neural networks by providing concise implementations of popular…

In our effort to facilitate machine learning-assisted computational fluid dynamics (CFD), we introduce the second iteration of JAX-Fluids. JAX-Fluids is a Python-based fully-differentiable CFD solver designed for compressible single- and…

Fluid Dynamics · Physics 2024-02-09 Deniz A. Bezgin , Aaron B. Buhendwa , Nikolaus A. Adams

jinns is an open-source Python library for physics-informed neural networks, built to tackle both forward and inverse problems, as well as meta-model learning. Rooted in the JAX ecosystem, it provides a versatile framework for efficiently…

Machine Learning · Statistics 2024-12-19 Hugo Gangloff , Nicolas Jouvin

jNO (jax Neural Operators) is a JAX-native library for neural operators and foundation models with unified support for both data-driven and physics-informed training. Its core design is a tracing system in which domains, model calls,…

Machine Learning · Computer Science 2026-05-12 Leon Armbruster , Rathan Ramesh , Georg Kruse , Christopher Straub

Predictive coding networks (PCNs) constitute a biologically inspired framework for understanding hierarchical computation in the brain, and offer an alternative to traditional feedforward neural networks in ML. This note serves as a quick,…

Neural and Evolutionary Computing · Computer Science 2025-06-10 Mikko Stenlund

The biological implausibility of backpropagation (BP) has motivated many alternative, brain-inspired algorithms that attempt to rely only on local information, such as predictive coding (PC) and equilibrium propagation. However, these…

Machine Learning · Computer Science 2025-12-01 Francesco Innocenti , El Mehdi Achour , Christopher L. Buckley

Recent advances to algorithms for training spiking neural networks (SNNs) often leverage their unique dynamics. While backpropagation through time (BPTT) with surrogate gradients dominate the field, a rich landscape of alternatives can…

Neural and Evolutionary Computing · Computer Science 2024-04-10 Thomas M. Summe , Siddharth Joshi

Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are…

Neural and Evolutionary Computing · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…

Machine Learning · Computer Science 2025-10-30 Francesco Innocenti

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated,…

Machine Learning · Computer Science 2026-02-03 Cédric Goemaere , Gaspard Oliviers , Rafal Bogacz , Thomas Demeester

CLAX is a JAX-based library that implements classic click models using modern gradient-based optimization. While neural click models have emerged over the past decade, complex click models based on probabilistic graphical models (PGMs) have…

Information Retrieval · Computer Science 2025-11-06 Philipp Hager , Onno Zoeter , Maarten de Rijke

Traditional neuromorphic hardware architectures rely on event-driven computation, where the asynchronous transmission of events, such as spikes, triggers local computations within synapses and neurons. While machine learning frameworks are…

Neural and Evolutionary Computing · Computer Science 2024-01-31 Eric Müller , Moritz Althaus , Elias Arnold , Philipp Spilger , Christian Pehle , Johannes Schemmel

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of NeuroAI. A prime example of this is predictive coding networks (PCNs), based on the…

Machine Learning · Computer Science 2026-03-09 Björn van Zwol , Ro Jefferson , Egon L. van den Broek

We introduce Atomistic learned potentials in JAX (apax), a flexible and efficient open source software package for training and inference of machine-learned interatomic potentials. Built on the JAX framework, apax supports GPU acceleration…

Chemical Physics · Physics 2025-11-19 Moritz René Schäfer , Nico Segreto , Fabian Zills , Christian Holm , Johannes Kästner

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms.…

Machine Learning · Computer Science 2026-05-18 Andreas Bergmeister , Manish Krishan Lal , Stefanie Jegelka , Suvrit Sra

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

Machine Learning · Computer Science 2022-11-08 Luca Pinchetti , Tommaso Salvatori , Yordan Yordanov , Beren Millidge , Yuhang Song , Thomas Lukasiewicz

Scenic is an open-source JAX library with a focus on Transformer-based models for computer vision research and beyond. The goal of this toolkit is to facilitate rapid experimentation, prototyping, and research of new vision architectures…

Computer Vision and Pattern Recognition · Computer Science 2021-10-25 Mostafa Dehghani , Alexey Gritsenko , Anurag Arnab , Matthias Minderer , Yi Tay

The rapid rise of scientific machine learning (SciML) has expanded the role of differentiable modeling, surrogate modeling, and data-driven constitutive laws in large-scale simulation. The JAX framework provides an attractive environment…

Mathematical Software · Computer Science 2026-04-27 Alberto Cattaneo , M Keith Ballard , Robert M. Kirby , Varun Shankar

Predictive coding (PC) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules…

Neural and Evolutionary Computing · Computer Science 2019-10-29 Jeff Orchard , Wei Sun
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