Standard accelerators exploit only one dimension of sparsity — skipping zero activations (CSC). BSA stacks a second dimension — per-weight Dynamic-R — so sparse attention and compact weights compound multiplicatively. The result: ≈ 2% of dense FP32 compute.
| Dimension | Mechanism | Standard (Dense) | Sibacus BSA | Reduction Factor |
|---|---|---|---|---|
| Column (attention) | CSC thresholding (τ) | O(N²) — all entries |
O(nnz_A) — non-zero only |
÷10 (at 10% density) |
| Row (weights) | Dynamic-R encoding | R_max = 8 cycles per weight |
mean(R_i) ≈ 1.6 cycles |
÷5 (1.6 vs 8) |
| Combined | Both simultaneous | N² × R_max |
nnz_A × mean(R_i) |
÷50 = 2% of baseline |
| Attention Density | R_max | Mean R̄_i | Effective Compute | Energy Ratio |
|---|---|---|---|---|
| 5% | 2 | 2.0 | 1.2% | 0.001 |
| 5% | 4 | 4.0 | 2.1% | 0.002 |
| 10% | 2 | 2.0 | 1.8% | 0.002 |
| 10% | 4 | 4.0 | 3.5% | 0.004 |
| 10% | 8 | 7.2 | 6.8% | 0.008 |
| 20% | 4 | 4.0 | 7.2% | 0.009 |
| 50% | 8 | 7.2 | 34.0% | 0.039 |
Highlighted row = target operating point (10% attention density, R=2, mean R̄=1.6→2.0). Energy ratio relative to FP32 MAC @ 4.6 pJ (Horowitz 45nm).
Where standard MACs exploit only column sparsity (CSC attention skipping), BSA uniquely compounds row sparsity (Dynamic-R weight encoding) — delivering multiplicative reduction that no fixed-latency multiply-accumulate architecture can achieve.