MLA Cost Analysis & Regime Guide
Regime Selection
| Regime | s Range | Best Kernel | Why |
|---|---|---|---|
| Decode | s=1 | FlashMLA | 16x latency reduction vs FlashAttention (compressed KV) |
| Speculative | s=2-32 | MLAvar6+ or FlashMLA | MLAvar6+ should be able to beat FlashMLA and FlashAttention |
| Prefill | s>128 | FlashAttention | Avoids 4x FLOP penalty of latent-space compute |
Crossover point: FlashAttention becomes faster than FlashMLA at approximately s=16-32 for DeepSeek-V3 parameters.
Cost Models (DeepSeek-V3-like: h=128, d=128, k=512, p=64)
FlashAttention
- FLOPs:
2bhst(2d + p)=2bhst * 320 - Bytes:
w * bh(s+t)(2d + p)=w * bh(s+t) * 320 - At s=1: AI ≈ 1 FLOP/byte (deeply memory-bound)
- At s=1024: AI ≈ 819 FLOP/byte (deeply compute-bound)
FlashMLA (latent-space attention via absorption)
- FLOPs:
2bhst(2k + p)=2bhst * 1088 - Bytes:
w * (bhs(2k+p) + bt(k+p)) - At s=1: AI ≈ 228 FLOP/byte (compute-bound even at decode)
- Problem: FLOPs grow linearly with s at k=512 instead of d=128 — 3.4x more FLOPs per token
MLAvar6+ (split latent + decompressed)
- FLOPs:
2bhstp + 4bhsnd + 4bhsok - Bytes:
w * (bhsp + bhsd + bhsk + bok + btp + bhnd + bhnd + bhsd + bhsk) - Key: choosing n tunes operational intensity near roofline ridge point
Absorption Trick (FlashMLA)
Score: Q @ K^T = Q @ (Z @ Wk)^T = (Q @ Wk^T) @ Z^T = Qz @ Z^T
Value: softmax(A) @ V = softmax(A) @ (Z @ Wv) = (softmax(A) @ Z) @ WvOperate entirely in latent space (k-dim), with output decompression O_latent @ W_kvb2^T done by a separate kernel.
MLAvar6+ Design
Split KV cache into:
- o old tokens: latent Z (b, o, k) — compute-heavy, low bandwidth
- n new tokens: decompressed K,V (b, n, h, d) — bandwidth-heavy, low compute
- t = o + n
Interpolates: n=0 → FlashMLA-like, o=0 → FlashAttention-like.
Historical Baselines (RTX 5090, b=32, t=4096, bfloat16)
Note: These results are from RTX 5090 development. Reprofile on the current device before using as optimization targets. Ridge point, bandwidth, and compute ceilings differ across devices — see src/mla_var3/conf/devices.json.| Config | FlashMLA | FlashAttention | MLAvar6+ V3 (best) |
|---|---|---|---|
| s=1 | 419 μs | 6,781 μs | 829 μs (V2) |
| s=16 | 5,161 μs | 6,727 μs | 4,444 μs |
MLAvar6+ V3 is the current best for speculative decoding (s=16), beating FlashMLA by 14%.
Tensor Shapes (DeepSeek-V3 defaults)
| Symbol | Description | Default |
|---|---|---|
| b | Batch size | 64 |
| h | Number of heads | 128 |
| s | Query sequence length | varies |
| t | KV context length | 4096 |
| d | Head dimension | 128 |
| p | Positional embedding dim | 64 |
| k | Latent (compressed) dim | 512 |
Tensor layouts:
- Q, Qc:
[B, H, S, D]or[B, H, S, K] - K, V:
[B, T, H, D](decompressed) - Z:
[B, T, K](latent KV cache) - QPE, KPE:
[B, H, S, P]or[B, T, P]
Detailed Analysis
Full cost model derivations and roofline analysis: docs/cost-analysis.md