A brain resolving into circuitry: continuous dynamics on the left — flow fields, an optimization landscape, an evolving probability density — becoming network structure and information on the right. Along the lower edge a wave runs into a neuron's dendrites and leaves its axon as binary, the book's recurring question in one line: dynamics → neuron → computation.
The five equations
- \(\dot{x} = f(x,t) + \sigma\,\xi(t)\)
- A stochastic dynamical system — deterministic flow under noise.
- \(\tfrac{d}{dt}\,p(x,t) = \mathcal{L}^{*} p(x,t)\)
- The ensemble view — a probability density evolving under its generator.
- \(\min_{\theta}\,\mathcal{L}(\theta)\)
- Learning as optimization, in its most abstract form.
- \(E = -\tfrac{1}{2}\sum_{ij} J_{ij} s_i s_j\)
- The Hopfield energy — memory as a minimum of a landscape.
- \(H[p] = -\sum_i p_i \log p_i\)
- Shannon entropy — the measure that ties coding to representation.
NeuroAI
Theoretical Foundations of Dynamics, Learning and Computation in Brains, Minds, and Machines
- McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Cambridge, Massachusetts, USA
Summary
A theoretical reconstruction of NeuroAI, chapter by chapter: the ideas that built the field — from McCulloch and Pitts through Hopfield, Amari, Abbott, Hinton, Sejnowski and Poggio — rebuilt from their mathematics and re-derived in code. Each chapter is released as a standalone arXiv manuscript with a computational companion in the repository.
Chapters & code releases
Almost all chapters are written. Polishing each into a clean document takes time, but they will be released at a fairly fast pace.
Foundations of NeuroAI
- Ch. 01 NeuroAI—Subject, Method, and Boundary forthcoming
- Ch. 02 Neural Logic, Invariance, and the Retina—McCulloch and Pitts arXiv:2609.02183 PDF
- Ch. 03 Learning a Decision Boundary—Rosenblatt and the Perceptron forthcoming
- Ch. 04 Neural Fields, Associative Dynamics, and the Geometry of Learning—Amari forthcoming
Memory, collective dynamics, and disorder
- Ch. 05 Memory as an Energy Landscape—Hopfield arXiv:2609.02195 PDF
- Ch. 06 Capacity and Disorder—Statistical Mechanics of Associative Memory forthcoming
- Ch. 07 Chaos in Random Neural Networks—Dynamic Mean-Field Theory forthcoming
Synapses and recurrent computation
- Ch. 08 Dynamic Synapses, STDP, Sequence Learning, and Multiscale Memory—Abbott forthcoming
- Ch. 09 Random Networks, FORCE Learning, and Population Computation—Abbott forthcoming
Representation, learning, and inference
- Ch. 10 Boltzmann Machines, Backpropagation, and Distributed Representation—Hinton forthcoming
- Ch. 11 NETtalk, Infomax, and Independent Components—Sejnowski forthcoming
- Ch. 12 From Ill-Posed Vision to Compositional Intelligence—Poggio forthcoming
- Ch. 13 Efficient, Sparse, and Predictive Coding—From Redundancy Reduction to Hierarchical Generative Inference forthcoming
Physical computation and biological scale
- Ch. 14 When Does Matter Compute?—Physical Realization, Coarse-Graining, and Autonomous Closure forthcoming
- Ch. 15 What Does Recurrence Buy?—Temporal Irreducibility, Adaptive Reservoirs, and Compositional Motifs forthcoming
- Ch. 16 Where Does Biological Computation Live?—Scale, Cellular Information, and Effective Neural Theories forthcoming
About this book
NeuroAI is a theoretical book, not a survey. It returns to the original formulations — McCulloch and Pitts’ logical calculus, Rosenblatt’s decision boundary, Amari’s neural fields, Hopfield’s energy landscape, the statistical mechanics of capacity and disorder, Abbott’s synaptic and population dynamics, Hinton’s distributed representations, Sejnowski’s infomax, Poggio’s ill-posed vision — and rebuilds each from its mathematics, then asks what it actually buys as a theory of computation in physical matter.
The last part turns the question around: when does matter compute, what does recurrence buy, and where does biological computation live. These are the N⁴ questions — NeuroPhysics, NeuroComputation, NeuroDynamics — asked of the field’s own foundations.
The companion repository
The manuscript files are not hosted in the repository. For each released chapter, the arXiv link opens its abstract page and the PDF link opens the chapter PDF directly.
The repository is the computational companion: chapter-by-chapter code for the computational reconstructions, numerical experiments, analyses, and figures. Each released chapter has its own directory containing the corresponding code, generated data, and figure-reproduction material. Chapter-specific instructions, dependencies, and expected outputs are documented within that directory.