# Fourier Magnitude KV Cache Quantization **URL:** \ **Category:** Research\ **Created:** [August 18, 2026, 1:16pm UTC](https://discuss.huggingface.co/t/fourier-magnitude-kv-cache-quantization/178815 "2026-08-18T13:16:10Z")\ **Posts on this page:** 1\ **Showing post:** 6
**Author:** ![ntrillard](https://avatars.discourse-cdn.com/v4/letter/n/d6d6ee/32.png) [@ntrillard](https://discuss.huggingface.co/u/ntrillard)\ **Post date:** [August 22, 2026, 9:19am UTC](https://discuss.huggingface.co/t/fourier-magnitude-kv-cache-quantization/178815/6 "2026-08-22T09:19:10Z")
Some more tests: > `sink_runner`’s `layer_pred` filtered which layers received QUANTIZATION hooks, not which layers received ANCHORS. Every “\_sens/\_l0/\_s0/\_qsens” result therefore left non-anchor layers COMPLETELY fp16 - the selective- layer anchoring claims, depth-redundancy conclusion, minimal-recipe, scale-validation 100%s and their NLL verifications were measuring near-no-op interventions. All such rows are RETRACTED. > > Corrected semantics (quantize ALL layers, anchors only protect) on Gemma holdout: > > - NF4/g64, no anchors: 39.8% @ 4.25b > - NF4/g64 + dp32 anchors ALL layers: 90.3% @ 13.47 eff bits > - NF4/g64 + L0-only anchors: 56.8% @ 4.69 eff bits > - 2-bit sorted + d48 anchors: 25.0% | ternary 6.0% | sign 2.3% > - sliding window s64 (all layers): 100% @ 13.21 eff bits > > Surviving truths: anchoring works (39.8-\>90.3) but only applied to ALL layers; its dp-mode cost SCALES WITH PREFILL (A=L+D), so effective bits -\>16 at long prefill - dp-mode is memory-theater for long prompts. Fixed- size windows (s64) do amortize (eff → ~4.25) and passed 16K retrieval, but their short-ctx fidelity was window-coverage, not compression. Sub-int8-bit KV with int8-level fidelity at true sub-int8 memory is NOT achieved in this repo. int8 KV (93%) remains the honest baseline. > > Systematic discovery campaign using `rapid_lab.py`: ~150 tests, every test ≤10s, 40+ logged runs, audited metrics (effective-bits accounting, prefix-match, held-out prompts, degeneracy flags). > > ## Minimal recipe (post-debunk): anchor layer 0 only > > Sweeping nested anchor subsets revealed a single critical layer: fp16 anchors on **layer 0 alone** (D=48) + binary sign KV {−s,+s} everywhere else gives **100% exact-match** on holdout AND hard sets, fp16-ceiling retrieval at 16K, at **~1.6 effective bits** (90.5% real savings vs bf16 KV). Qwen: same single-layer recipe = 98.0% (vs int8 41.3%). Layer 0 is the highest-drift layer on both models (Gemma 0.08+, Qwen 0.985 - 7x its runner-up), consistent with pivot-token/attention-sink massive activations living in the first layer. Effective-bit floor: ~1.6 at short ctx, → ~1.1 long ctx (single-layer prompt protection amortizes to ~0.57 bits). > > ## Milestone: 100% exact-match to fp16 at sub-4-bit nominal > > `{quant} + sens-layer decode anchoring D=48` scores **100.0% exact-match vs fp16 on every prompt set** (holdout, hard, long-context), including sets where **int8 KV only reaches 72%** : > | Quant (nominal) | holdout | hard | longctx | Eff bits @142142142142 tok | > | --- | --- | --- | --- | --- | > | ternary {−s,0,+s} g8/g4 ( **1.58b total** ) | 100% | 100% | 100% | ~4.5 | > | sorted-group int2 g8/g4 ( **2-bit total** ) | 100% | 100% | 100% | ~4.6 | > | NF4-K + int4-g64 V ( **4.25b** ) | 100% | 100% | 100% | ~5.9 | > | int8 KV reference | 93% | 72% | 71% | 8.0 | > Debunk audit (sign\_d48): quantization verified real (K/V rel-err 0.54-0.63 on non-anchor layers); result reproduced through clean path; all negative controls behaved (no-anchor 3%, references match history). Mechanism: greedy trajectory is set by fragile layers; other 22 layers are depth-redundant for token choice. CORRECTION: dp-mode keeps prompt fp16 on anchor layers permanently → effective-bit floor ~4.2 regardless of nominal bits; nominal “1-bit” applies only as T-\>infinity with prompt-protection removed. Honest headline: ~4.2-4.6 eff bits beating int8 (8.0) on fidelity. > > Horizon boundary: at 100 generated tokens (vs 50) the 2-bit config holds 92.3%, ternary 75.2% — anchor depth D must scale with generation length; exact-100% claims are for horizons ≤ D. > > ## Best results (Gemma-3-1B, held-out prompts, honest effective bits) > | Recipe | Match | Nominal | Eff. bits | Savings | > | --- | --- | --- | --- | --- | > | **2-bit total + selective-layer decode anchors** (`both2_dp32_sens`) | **96.7%** | 2.0 | ~4.35 | 73% | > | Same, long context (~830 tok) | **100%** | 2.0 | ~4.64 | 71% | > | Ternary KV (1.58b) + int8 anchors (`ternboth_a8`) | 92.7% | 1.58 | 2.79 | 83% | > | 1-bit KV (sign) + int8 anchors (`signboth_a8`) | 91.3% | 1.0 | 2.32 | 86% | > | 4-bit total + anchors (`nfv4g64_dp32_sens`) | 91.3–100% | 4.25 | ~5.5 | 59% | > | int8 KV reference | 93.0% | 8.0 | 8.0 | 50% | > Qwen2.5-1.5B with its **own probe-derived anchor layers** {0,5,9,13,15,18} (layer 0 dominates with ~7x the drift of any other): NF4/int4-g64 **100%** , sorted-2-bit **99.7%** , ternary **98.7%** — vs int8’s 41.3%. The initial sub-2-bit transfer failure was an artifact of reusing Gemma’s layer set; the 0.5s sensitivity probe is what makes the recipe model-general. > > ## The winning recipe: Selective-Layer Decode Anchoring > > > Quantize K/V aggressively (sorted-group 2-bit, ternary, or NF4/int4-g64), but keep the KV of the **first N decoded tokens** in high precision **only on the quantization-sensitive layers** (here layers 0–3, 6–7, identified by a 0.5s logit-drift probe). > > Components, each discovered via ≤10s tests: > > 1. **Magnitude-sorted grouping** (g=8 for K, g=4 for V): sort each row descending, quantize groups; outliers share one wide group. Rotation-immune. > 2. **Decode anchoring** : protection must target early _generated_ tokens. Monotone in N (dp2→dp32: 61→90%); protecting the prompt alone _hurts_ (42%) vs protecting prompt+early decode (90%). > 3. **Layer-selective anchors** : fp16 anchors on 6/28 layers cut anchor overhead ~4.7x at equal quality. > 4. **Anchor-precision dial** : fp16→int8→int4 anchors trade 100→81→71% quality against ~1.3 effective bits per step. > > At 1.58-bit nominal (ternary) and 1.0-bit nominal (sign), this is — per our prior-art search — below the published floor for KV quantization (RotateKV/KIVI at 2-bit, KVmix at ~2.2–2.4 avg). > > ## Mechanism findings > > - **Error snowball, not attention sinks** : the fragility lives in early _autoregressive_ steps (closest to token decision boundaries), not in prompt tokens. Sliding-window sink protection on short prompts is counterproductive (quantizes exactly the fragile tokens). > - **Prompt-length ranking instability** : method rankings flip between short and long prompts (sinks hurt NF4 on short prompts 92.7→44%, help on long prompts 33→74%). KV-quant papers evaluating only on short prompts risk inverted conclusions. > - **Tails are sacred** : four independent confirmations that outlier preservation dominates — clipping, k-means-fitted codebooks, scale shrinkage, and error diffusion all collapse; fixed nonuniform codebooks (NF4) with intact range win. > - **Model specificity** : Gemma’s QK-norm pipeline makes K uniquely forgiving. Qwen collapses under most K-quantization without anchors. > - **int8 KV is not lossless** under exact-match on hard prompts (fails on code/arithmetic continuations). --- _[View the full topic](https://discuss.huggingface.co/t/fourier-magnitude-kv-cache-quantization/178815)._