# Path to <10% float compute: analysis

The user's original target: **less than 10% of training compute time should be float operations**. Multi-session work has produced an int8 GEMM kernel; this note analyzes how close to <10% that gets us, and what's needed to close the gap.

## 300M v76 baseline profile (from prior session, RTX 5090)

| Operation | % of CUDA time | Float? |
|---|---|---|
| aten::mm (BitLinear GEMM) | 23.5% | yes (bf16) |
| aten::bmm (attention QK + AV) | 20.5% | yes (bf16) |
| aten::topk (RWSP top-K) | 19.2% | yes |
| triton ALiBi+mask | 13.3% | yes |
| masked_fill | 4.8% | yes |
| Other (norms, activations, optimizer) | ~18% | yes |
| **Float total** | **~99%** | |

So at baseline, essentially **everything is float**.

## With current int8 GEMM kernel (forward + dx backward)

The Triton kernel (built and CPU-validated) replaces:
- BitLinear forward GEMM: ±1 × ±1 → int32 (exact)
- BitLinear dx backward: dy_q × W_int8 → int32 + per-row alpha rescale

Conservative estimate (assuming 2× speedup over bf16 cuBLAS at our shapes,
which is what int8 tensor cores promise on Blackwell):

| Operation | Time (% of original total) | Now integer? |
|---|---|---|
| BitLinear fwd GEMM (1/3 of the 23.5%) | 7.8% → ~3.9% | YES (int8) |
| BitLinear dx bwd GEMM (1/3 of 23.5%) | 7.8% → ~3.9% | YES (int8) |
| BitLinear dW bwd GEMM (1/3) | 7.8% | NO (per-row α can't fold into int_mm) |
| Attention bmm | 20.5% | NO (Q,K are ±1 but A is float post-softmax) |
| Topk | 19.2% | NO (sorting on float scores) |
| ALiBi | 13.3% | NO (could be int with redesign) |
| masked_fill, norms, etc | ~22% | NO |
| **New total time** | ~84% (saved 16% from int8 paths) | |
| **Integer fraction** | (3.9 + 3.9) / 84 = **9.3%** | |
| **Float fraction** | 90.7% | |

So the int8 kernel work alone gets us to ~9% **integer** compute (90% float).
**Far from the <10% float target.**

## What would reach <10% float?

### Path A: integer-ize attention (~30% reachable)
Currently bmm uses Q, K, V at ±1 (after `sign_ste_clipped` on BitLinearScaled
output) but the matmul is float. Needs:
1. Q×K.T → int8 (since Q, K are ±1) — easy, same kernel pattern
2. ALiBi as int (slopes are powers of 2, distances are int) — easy
3. Softmax → integer-friendly approximation (Gumbel-hard with integer
   tiebreak?) — HARD
4. A×V → impossible to keep integer (A is post-softmax float)

So ~half of attention (QK, ALiBi, masking) could become integer, ~30% of
total CUDA time. Combined with int8 BitLinear, gets us to:
- Integer time: 9% (BitLinear) + ~13% (QK + ALiBi) = ~22%
- Float time: ~78%

Still far from <10% float.

### Path B: replace softmax with hard top-K
RWSP-G's "top-K survivors with rank weighting" is ALREADY a step in this
direction. With `K=1` (argmax + rank weighting=1), we get a hard pointer.

This eliminates both A×V's float dependency and topk's float sorting (since
the "top-1" is just argmax → integer). But it would also kill val_bpc by
losing softmax's smoothness.

### Path C: reframe the goal
"<10% float compute" may not be the right metric. More tractable framings:
- **Storage bits per parameter** (already 1-bit on BitLinear weights)
- **GEMM FLOPs in integer mode** (achievable: forward + dx backward as int8)
- **Energy per training step** (different metric, requires hardware-specific
  measurement)

## Realistic path forward

1. **First** validate the existing int8 GEMM kernel on GPU. Check:
   - Triton int8 vs bf16 cuBLAS speedup at training shapes (predicted 1-3×)
   - Numerical correctness (sign-STE gradients match)
   - End-to-end training step throughput

2. **If kernel wins**, integer-ize the attention QK matmul. Same pattern as
   BitLinear. Adds ~13% more integer compute.

3. **Defer "true <10% float"** — it requires fundamental architectural
   changes (e.g., replacing softmax with integer-friendly attention, which
   is unsolved as far as I know). The int8 GEMM work is a meaningful step
   that can land in v76 paper or as a follow-up engineering paper.

## Bottom line

The int8 kernel work moves us from 100% float to ~91% float (with optimistic
GPU benchmarks). To hit <10% float, attention and softmax need
fundamental redesigns that go beyond this session's scope. The honest
framing: this session enabled **1-bit weights and 1-bit GEMM compute** for
linear layers; full 1-bit training requires more research than fit in the
project window.

The synth K-shift work is independent of the integer-compute goal — it's
about making sign-STE training converge to a useful attention pattern, which
matters whether the matmul is bf16 or int8.