SC—001 Sparse by design
Intelligence lives in the nonzeros.
Sparse matrices reveal a simple truth: structure matters more than density. We’re exploring AI built on selective computation—activating useful work and leaving the rest at zero.
Read the sparse premise- Shape
- A ∈ ℝ128×128
- Nonzeros
- 655 / 16,384
- Density
- 4.00%
- Format
- CSR
The next leap may come from computing only what matters.
ρ(A) = nnz(A) m × n
In a sparse matrix, a small number of nonzero entries carry the structure. We’re investigating how that principle can shape AI: structured sparsity, selective activation, and less data movement—with the aim of reducing memory, bandwidth, and energy spent on unnecessary work.
Compare notesCombinatorial matrix theory
The zeros need a quorum.
Frobenius–König says a square sparsity pattern is structurally singular exactly when its zeros can organize an empty r × s rectangle with r + s = n + 1.
sprank(A) < n ⇔ A[I,J] = 0 |I| + |J| = n + 1
That empty rectangle blocks every perfect row–column matching. In less formal terms: the zeros unionized.
Structural statement only. Particular values can still conspire through cancellation.
Read the theorem3 rows + 4 columns = 7 = n + 1