New (and updated) preprint is now out!🔬🧠 We propose a hypothesis regarding how the genome, despite its limited information-carrying capacity, can initialize a brain with billions of neurons that comprise a diverse set of functions. Relevant to: #neuroscience #devleopmental-biology Details 👇

— Karim Habashy (@krhab.bsky.social) 2026-08-13T18:41:22.106Z

The core method is that the filters of a neural network layer can be represented by a single kernel that is differentiably transformed (rotated) along the spatial dimensions of a layer, and these rotations can be acquired by an indirect encoding network.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T18:56:51.851Z

For results, we first show that indirect encoding is sufficient to produce V1 orientation maps with the associated line filters (left map and filters). Furthermore, these maps emerge more efficiently when utilizing our approach of decomposing the layer into a kernel plus its associated rotations.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T19:26:08.540Z

Later, we showed that our approach is beneficial for encoding innate functions that support generalizations based on a factorial code. This was demonstrated by contrasting our approach in the hidden layer against a baseline where the hidden weights are directly encoded.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T19:27:21.922Z

Finally, we show that our approach, as a surrogate for the genomic code, can provide one of the highest forms of functional compression when evaluated on the MNIST benchmark, achieving ≈ 95% accuracy with only ≈ 1800 parameters.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T20:00:58.449Z

Factorization and spatial encodings: a hypothesis about the foundations of the genomic code

Habashy KG, Evans BD, Goodman DFM, Bowers JS
Preprint
doi: 10.64898/2026.07.14.738413
 

Abstract

The genomic mechanisms that efficiently encode the initial architecture and synaptic connectivity of neural circuits remain poorly understood. We hypothesise that two primary mechanisms — spatial encoding and factorisation — enable a limited genome to initialise networks of billions of neurons. Spatial encoding, a form of indirect representation, compresses neural network parameters while enforcing structural continuity. Complementarily, we introduce a factorisation mechanism inspired by reaction-diffusion models, comprising a spatially invariant reaction rule and spatially variant diffusion dynamics. Based on this insight, we can efficiently abstract a neural network layer as a spatially invariant weight kernel (or filter) and its spatially variant transformations along the spatial dimensions. Thus, coupling this variant-invariant decomposition with spatial encodings can substantially reduce the size of the solution space explored by the genome. In addition, we show that this coupling leads to efficient itialisation of cortical maps, such as V1 orientation maps, and neural networks with the ability to generalise. In summary, coupling factorisation and spatial encodings can offer functional advantages to the evolving genome.

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The short version

New (and updated) preprint is now out!🔬🧠 We propose a hypothesis regarding how the genome, despite its limited information-carrying capacity, can initialize a brain with billions of neurons that comprise a diverse set of functions. Relevant to: #neuroscience #devleopmental-biology Details 👇

— Karim Habashy (@krhab.bsky.social) 2026-08-13T18:41:22.106Z

The core method is that the filters of a neural network layer can be represented by a single kernel that is differentiably transformed (rotated) along the spatial dimensions of a layer, and these rotations can be acquired by an indirect encoding network.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T18:56:51.851Z

For results, we first show that indirect encoding is sufficient to produce V1 orientation maps with the associated line filters (left map and filters). Furthermore, these maps emerge more efficiently when utilizing our approach of decomposing the layer into a kernel plus its associated rotations.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T19:26:08.540Z

Later, we showed that our approach is beneficial for encoding innate functions that support generalizations based on a factorial code. This was demonstrated by contrasting our approach in the hidden layer against a baseline where the hidden weights are directly encoded.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T19:27:21.922Z

Finally, we show that our approach, as a surrogate for the genomic code, can provide one of the highest forms of functional compression when evaluated on the MNIST benchmark, achieving ≈ 95% accuracy with only ≈ 1800 parameters.

— Karim Habashy (@krhab.bsky.social) 2026-08-13T20:00:58.449Z