2D Sparsity — Two Dimensions of Waste Elimination

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.

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100%
Effective Compute
144
Active Operations
1152
Total Cycles
Interactive Compute Matrix — Weight × Attention Grid
Dense compute (8 cycles)
Sparsity Dimension Breakdown
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
Side-by-Side: Standard MAC vs BSA

Standard MAC Accelerator

1D SPARSITY ONLY
📊
CSC Attention Skipping
Zero activations skipped via CSC format
÷10
🔒
Weight Sparsity
Non-zero weights still need fixed-latency MAC — cannot reduce
×1
10%
of dense compute remaining

BSA 2D Sparsity

BOTH DIMENSIONS
📊
CSC Attention Skipping
Same column sparsity as MAC
÷10
Dynamic-R Weight Compression
Per-weight R_i adapts cycles: mean R̄ ≈ 1.6 vs R_max = 8
÷5
2%
of dense compute remaining (5× better than MAC)
Benchmark Results — Effective Compute & Energy
Attention Density R_max Mean R̄_i Effective Compute Energy Ratio
5%22.0 1.2% 0.001
5%44.0 2.1% 0.002
10%22.0 1.8% 0.002
10%44.0 3.5% 0.004
10%87.2 6.8% 0.008
20%44.0 7.2% 0.009
50%87.2 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).

BSA 2D Sparsity Advantage
50× throughput · 2% compute

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.

effective_compute = (mean_R̄ / R_max) × attention_density = (1.6/8) × 0.10 = 0.02