Just-in-time connectivity

Just-in-time connectivity (JITC) is brainevent’s answer to a hard scaling problem: how do you multiply a spike vector by a random connectivity matrix that is too large to store? For the practical recipe, see Use JIT connectivity for large networks.

The memory problem

A randomly connected network of \(N\) neurons with connection probability \(p\) has on the order of \(pN^2\) synapses. For \(N = 10^6\) and \(p = 0.01\), that is \(10^{10}\) synapses — far beyond device memory if stored explicitly, even in a compressed sparse format. Yet the information defining that matrix is tiny: a probability, a weight (or weight distribution), and a random seed.

The generator idea

JITC stores only the generator, never the matrix. Each time a row (or column) is needed during a matrix–vector product, the kernel uses a deterministic, seedable random number generator to regenerate that row’s connections and weights on the fly, uses them, and discards them. Nothing is materialised.

Two properties make this sound:

• Determinism — the same seed always reproduces the same connections, so the matrix is well-defined and reproducible across processes and devices despite never being stored.

• Locality — each row can be regenerated independently, which maps naturally onto the parallel, event-driven kernels: only rows touched by an active spike are ever generated.

The result is a matrix product whose memory cost is independent of the number of synapses and whose compute cost still scales with the number of spikes.

Weight distributions

The realised weights come from a distribution chosen per variant:

• Scalar (JITCScalarR / …C) — every connection shares one constant weight.

• Normal (JITCNormalR / …C) — weights drawn from a Gaussian.

• Uniform (JITCUniformR / …C) — weights drawn uniformly from an interval.

In every case the weights are regenerated from the seed, never stored.

The trade-off

JITC buys constant memory at the price of addressability: because the matrix exists only transiently inside the kernel, you cannot inspect, slice, or learn individual weights. If a model needs plastic or addressable synapses, an explicit CSR matrix is the right tool instead (see Sparse format trade-offs).

Note

The row- (R) and column- (C) oriented variants differ only in which dimension is regenerated contiguously. As with CSR/CSC, choose the one that aligns with your spike vector’s orientation for best performance.