Sparse format trade-offs

brainevent provides several connectivity representations because no single format is best for every situation. This page explains the trade-offs so you can reason about the choice; for a quick decision table, see Choose a connectivity format.

Coordinate (COO) input

The most intuitive way to describe a sparse matrix is as a list of (row, column, value) triplets — the coordinate, or COO, form. It is convenient to build but inefficient to multiply, because the entries are unordered. brainevent therefore treats COO as an input format: the coo2csr() helper converts coordinate triplets into a CSR matrix ready for event-driven products. Related index converters (csr_to_coo_index(), csr_to_csc_index(), coo_to_csc_index()) move between layouts.

CSR vs CSC

CSR (Compressed Sparse Row) stores, for each row, the column indices and values of its non-zeros. This makes row-oriented access cheap — ideal when a spike vector selects rows. CSC is the transpose idea: column-compressed, so column-oriented access is cheap.

The right choice depends on which side of the product the spike vector sits and which dimension it indexes. Picking the layout whose compressed dimension aligns with the contraction keeps memory access contiguous and the kernel fast. The two formats store the same information and convert into one another, so the decision is purely about performance.

Explicit storage vs generation

CSR/CSC store every non-zero explicitly. That is the right model when the connectivity is fixed and inspectable — you can read, slice, and learn individual weights. The memory cost is proportional to the number of synapses.

For random connectivity at large scale, explicit storage becomes the bottleneck: a million-neuron network at 1 % density has ten billion synapses. Just-in-time connectivity (JITC) sidesteps this by regenerating connectivity from a seed inside the kernel, so memory no longer scales with synapse count — at the cost of losing per-weight addressability. This trade-off is the subject of Just-in-time connectivity.

Fixed-degree structure

Many biological networks have a fixed number of connections per neuron rather than a fixed probability. FixedPreNumConn and FixedPostNumConn encode exactly that, which is both more biologically faithful and more memory-predictable than a probabilistic format when the degree is known.

Summary

Format	Memory	Per-weight access	Best for
Dense	O(rows × cols)	Yes	small / truly dense
CSR / CSC	O(non-zeros)	Yes	fixed explicit sparsity
JITC	O(1) in synapses	No	large random connectivity
Fixed fan-in/out	O(neurons × degree)	structural	fixed-degree biology