HypercubeHopfield

HypercubeHopfield — modern Hopfield associative memory on a Boolean hypercube. Neurons sit on the vertices of a dim-dimensional cube (N = 2^dim). Patterns are stored explicitly and retrieved by softmax attention over a sparse neighborhood — not collapsed into a Hebbian weight matrix, and not full all-to-all modern-Hopfield attention either.

A topology you don't store. Connectivity is the mask table of the Hamming ball — one XOR per neighbor, no adjacency list, at any size. Each vertex attends only inside that ball; cost scales with connections, not with the full cube.

HypercubeAI ecosystem
_{One geometry. Topology-native intelligence.}

HypercubeESN · HypercubeCNN · HypercubeHopfield · HypercubeWTF

HypercubeHopfield is an experiment in the HypercubeAI project — our quest to map AI and ML strategies onto the hypercube as a computational substrate.

Why the hypercube? A few properties keep showing up — and they explain why a frozen reservoir and a HypercubeCNN readout fit together so cleanly:

A topology you don't store — the graph is specified: connectivity is implicit in the vertex indices; with a seed and a few config scalars the whole reservoir reconstructs mathematically.
Perfect homogeneity — every vertex has the same degree and the same local world, so local dynamics mean the same thing everywhere — no structural favorites baked in by a random graph.
Cheap navigation — each neighbor is a few bit operations on the vertex index, not a pointer chase through a stored edge list, so walks stay arithmetic and cache-friendly.
Topology-native pairing — the readout consumes the reservoir's output with zero geometric distortion, and the learned kernels exploit the same locality that generated the dynamics. The data never leaves the hypercube it was born on.

Each product in the family is a different architecture on that same foundation:

Product	Natural data	Role of the hypercube
HypercubeESN	Low-dim streams over time	Frozen reservoir stepped each sample; multi-slice state → HypercubeCNN readout
HypercubeCNN	Static patterns on the cube	Trainable spatial conv/pool on the cube (no recurrent reservoir)
HypercubeHopfield	Patterns / attractors	Associative memory dynamics on the cube
HypercubeWTF	Static high-dim fields (no intrinsic time)	Same frozen hypercube reservoir discipline as ESN, driven for a short orbit per sample, then HypercubeCNN on the end state

Installation

pip install hypercube-hopfield

Pre-built wheels for Python 3.10–3.13 on Windows, Linux, and macOS. NumPy is the only runtime dependency.

Build from source (C++23 + CMake): see the Python SDK guide.

Quick Start

import numpy as np
import hypercube_hopfield as hh

# 256 neurons (dim=8, N=2^8)
net = hh.HopfieldNetwork(dim=8, seed=42)

patterns = np.random.randn(10, net.num_vertices).astype(np.float32)
net.store_patterns(patterns)

cue = patterns[0] + np.random.randn(net.num_vertices).astype(np.float32) * 0.3
result = net.recall(cue)
print(f"Converged: {result.converged}, steps: {result.steps}")
# result.state is the cleaned recall; input cue is not modified

Features

Explicit pattern storage — modern Hopfield retrieval without a Hebbian weight matrix
Sparse Hamming-ball attention — reach and neighbor_fraction control connectivity and cost
Two update modes — Sync (default, deterministic) and Async (guaranteed energy descent)
Pickle / save / load — persist config and all stored patterns
NumPy integration — automatic float32 conversion; recall does not mutate the cue

Documentation

Python SDK Reference — full API, persistence, errors
Project README — architecture framing, C++ quick start, build
HopfieldNetwork architecture — connectivity, energy, parameters

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hypercube-hopfield 1.0.2

HypercubeHopfield

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