🏗️ Synecdoche

HyperNetworks and compressed weight representations for JAX / Flax NNX.

Synecdoche (si-NEK-duh-kee) is the figure of speech in which a part stands in for the whole — "all hands on deck." Fittingly, this library lets a small, easy-to- manipulate set of parameters stand in for all the weights of a much larger network: you train or evolve the part, and it generates the whole.

import synecdoche as syn
from flax import nnx

model = nnx.Linear(256, 256, rngs=nnx.Rngs(0))     # 65 792 parameters
target = nnx.state(model, nnx.Param)               # the template

hyper = syn.DCT(target, embedding_dim=32, rngs=nnx.Rngs(1))
syn.apply_to(model, hyper)                          # model now runs on generated weights
print(syn.compression_ratio(hyper, model))         # a much smaller description

Why

A hypernetwork replaces a network's weights with a generator. That buys you three things:

• Compression — describe many weights with few numbers.
• Structure / inductive bias — the generator constrains what kinds of weight matrices are reachable (smooth, low-rank, tied, …).
• Tractable search — evolution strategies and other black-box optimisers have variance that grows with the number of parameters, so they don't scale to full networks. Move the search into the hypernetwork's small latent space and they become viable again. (This is why synecdoche pairs naturally with spiking / non-differentiable networks trained by evolution.)

Everything is a plain flax.nnx.Module, so generated weights drop into any NNX model, and the generator's parameters train by gradient or evolve by ES.

Generators

Build any of these from a target's nnx.state(model, nnx.Param); call it to get a matching weight pytree.

Generator	Idea	Learnable params
RandomProjection	fixed random basis · learnable embeddings (random-feature indirect encoding)	num_layers × embedding_dim
DCT	inverse-DCT of a few low-frequency coefficients — compressed weight search (Koutník, Gomez & Schmidhuber, 2010)	num_layers × embedding_dim
LowRank	left @ right factorisation of the stacked weights	rank × (num_layers + max_size)
MLPHyper	a shared MLP decodes per-layer embeddings (Ha, Dai & Le, HyperNetworks, 2016)	embeddings + MLP
experimental.DynamicHypernetwork	weights conditioned on the input batch (fast-weights / meta-learning)	embeddings + MLP

RandomProjection and DCT are the strong compressors; LowRank / MLPHyper are more expressive but compress only when the target's layers are large relative to their number (the generators pad to the largest layer — see the docstrings).

Training the compressed representation

Inside nnx.jit / nnx.grad / an ES loop, don't mutate the target model in place — rebuild it functionally from generated weights with syn.functional:

apply = syn.functional(model)                      # capture structure once

def loss_fn(hyper):
    return mse(apply(hyper, X), Y)                 # forward on generated weights

opt = nnx.Optimizer(hyper, optax.adam(3e-3), wrt=nnx.Param)
loss, grads = nnx.value_and_grad(loss_fn)(hyper)   # grads w.r.t. the hypernetwork
opt.update(hyper, grads)

See examples/compress_and_train.py for a runnable end-to-end fit (16× compression, trains to convergence).

Lazy weights (optional, via quax)

pip install synecdoche[quax] adds synecdoche.lazy: weights that keep their compressed form all the way into the computation and never materialise in full, using quax's multiple dispatch. A low-rank weight computes x @ (a @ b) as (x @ a) @ b — the full matrix is never formed.

import quax, synecdoche.lazy as sl

w = sl.LowRankWeight.init((1024, 1024), rank=8, rngs=nnx.Rngs(0))  # 8·2048 params, not 1M
y = quax.quaxify(lambda W, x: x @ W)(w, x)                          # never forms 1024×1024

Install

pip install synecdoche          # core (jax + flax)
pip install synecdoche[quax]    # + lazy never-materialised weights

Roadmap

• Generative weight generators — sampling weights from a learned distribution (diffusion / VAE over checkpoints, after Neural Network Diffusion and G.pt), the stochastic counterpart to the deterministic generators here.
• Per-layer output heads so LowRank / MLPHyper compress heterogeneous architectures without the pad-to-max-size overhead.
• First-class spyx adapter for evolving spiking networks in the compressed space.

References

• Koutník, Gomez & Schmidhuber. Evolving neural networks in compressed weight space. GECCO 2010.
• Ha, Dai & Le. HyperNetworks. ICLR 2017.
• Kidger et al. quax — JAX + multiple dispatch for custom array types.