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# Neuromorphic Substrate

Hopfield networks, attractor dynamics, and content-addressable recall.

## What is it?

Membot's neuromorphic layer is a physics simulation, not a deep learning model. There is no gradient descent, no backpropagation, no GPU inference. Instead, it models a network of neurons governed by energy dynamics — the same principles that describe physical systems settling into stable states.

## The architecture

- 64×64 grid of cells, each containing 64 neural units (64 × 64 × 64 = 262,144 units; with internal neuron populations per unit, the total is ~16M simulated neurons)
- Hebbian weights — connections that strengthen when neurons fire together
- Mexican-hat inhibition — a connectivity pattern where nearby neurons excite each other while distant ones inhibit, sharpening activation patterns and suppressing noise (the same lateral inhibition mechanism found in biological visual cortex)
- Energy dynamics — the network evolves to minimize an energy function, settling into stable attractor states

## Content-addressable memory

Think of a landscape with valleys. Each stored memory creates a valley (an attractor basin). When you present a query, it's like placing a ball on the landscape. The ball rolls downhill into the nearest valley — the closest matching memory.

This means you can recall a memory from a partial or noisy input. The ball doesn't need to start at the exact bottom of the valley; it just needs to be close enough to roll in.

## Hopfield networks

The theoretical foundation comes from John Hopfield's 1982 paper on associative memory. Hopfield showed that a network of binary neurons with symmetric connections has a well-defined energy function, and the network dynamics naturally minimize this energy. Each local minimum of the energy function corresponds to a stored memory.

Membot extends the classical Hopfield model with continuous activations, a spatial lattice structure, and multi-modal binding through Hebbian learning.

## Validation

The lattice has been validated on 1 million Wikipedia embeddings (768-dim Nomic vectors, queried with 1,000 held-out entries):

Metric | Result | Conditions
--- | --- | ---
Recall@1 | 1.000 | Clean query vectors — exact patterns presented to the lattice
Erasure tolerance | Recovers | Up to 30% of input dimensions zeroed out
Bitflip tolerance | Recovers | Up to 10% of sign bits randomly flipped

Note: R@1=1.000 on clean queries reflects the lattice acting as a content-addressable store (like a Hopfield network) — it means stored patterns are faithfully recovered, not that the lattice outperforms embedding-based search on novel queries. See the repo for test scripts and methodology.

## Two access modes

Search (binary, fast): Uses the sign-zero encoded vectors and Hamming distance. No physics simulation. Returns ranked results in milliseconds.

Recall (physics-based): Activates the neuromorphic lattice. The query pattern propagates through Hebbian weights and the network settles into an attractor state. Slower, but handles partial/noisy queries and can make cross-modal leaps (e.g., text query retrieving images).

## Further reading

Hebbian Learning — how weights are trained
Hamming Distance — the fast binary path
CLIP — image embeddings for cross-modal
CLAP — audio embeddings for cross-modal