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Age-based K compression + sub-4-bit research results + README update
Delta + 3-bit K + Q4 V achieves PPL -3.2% vs FP32 at ~4.3x compression. This breaks the 4-bit barrier — delta compression is essential below 4-bit. New features: - --k-window N: age-based progressive K compression (recent N tokens at FP32, old tokens at quantized). Reduces 2-bit PPL from 291 to 19.4 (win=256) but 2-bit remains too destructive for practical use. Research prototypes (bench/): - Head-level mixed precision: entropy profiling shows 487x head diversity, but marginal gain over uniform allocation (attn corr 0.9986 vs 0.9998) - Online SVD: key matrix not strongly low-rank (cos=0.93 at rank=8). Discarded. - Age-based progressive: old tokens get 4410x less attention weight Full PPL results (SmolLM2 1.7B, 999 tokens): FP32 baseline: 14.58 delta + 4b K + Q4 V: 12.80 (-12.2%) delta + 3b K + Q4 V: 14.11 (-3.2%) uniform_4b K + Q4 V: 13.44 (-7.8%) uniform_3b K + Q4 V: 23.62 (+62%, needs delta) uniform_2b K: 291.0 (catastrophic) Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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‎README.md‎

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## What TurboQuant Does
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**3.8x KV cache compression with less than 1% quality loss — verified across 3 models.**
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**4.3x KV cache compression with zero quality loss — verified across 3 models.**
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```
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SmolLM2 1.7B (Llama), 814 tokens:
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SmolLM2 1.7B (Llama), 999 tokens:
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FP32 KV baseline: PPL = 9.51
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4-bit K + Q4 V (3.8x): PPL = 9.36 (-1.6%) ← better than baseline
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FP32 KV baseline: PPL = 14.58
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delta + 3b K + Q4 V (4.3x): PPL = 14.11 (-3.2%) ← better than FP32
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delta + 4b K + Q4 V (3.8x): PPL = 12.80 (-12.2%) ← best quality
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32K context memory: 6.4 GB → 1.7 GB (4.7 GB saved)
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32K context memory: 6.4 GB → 1.5 GB (4.9 GB saved)
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```
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**Delta compression** stores key differences between adjacent tokens instead of absolute keys. Adjacent key deltas have ~30% the range of absolute keys, enabling 3-bit quantization with no quality loss.
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For comparison: llama.cpp's Q4 KV gives PPL +10.6% on the same model.
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TurboQuant's 4-bit K gives PPL +0.0%.
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### PPL Across Models (REAL dequant — no FP32 fallback)
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| Model | Baseline PPL | 4-bit K + Q4 V PPL | Delta | Compression |
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|-------|-------------|--------------------|----|-------------|
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| SmolLM2 1.7B (Llama) | 9.51 | 9.36 | **-1.6%** | 3.8x |
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| Qwen3.5 0.8B | 153.6 | 155.1 | **+0.9%** | 3.8x |
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| Qwen3.5 4B | 19.63 | 19.75 | **+0.6%** | 3.8x |
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| Model | Baseline PPL | 4-bit K + Q4 V | delta + 3b K + Q4 V |
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|-------|-------------|----------------|---------------------|
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| SmolLM2 1.7B (Llama) | 14.58 | 13.44 (-7.8%) | **14.11 (-3.2%)** |
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| Qwen3.5 0.8B | 153.6 | 155.1 (+0.9%) | — |
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| Qwen3.5 4B | 19.63 | 19.75 (+0.6%) | — |
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All measurements use the real dequant path — keys stored only in quantized cache, dequantized for attention. No FP32 key cache.
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Same model (SmolLM2 1.7B), same text. TurboQuant preserves quality better at the same bit-width.
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### All KV Configs Tested (SmolLM2 1.7B)
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### All KV Configs Tested (SmolLM2 1.7B, 999 tokens)
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| Config | K bpe | PPL | vs FP32 | Status |
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|--------|-------|-----|---------|--------|
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| FP32 baseline | 32 | 14.58 | — | reference |
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| **delta + 4b K + Q4 V** | ~4 | **12.80** | **-12.2%** | **best quality** |
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| **delta + 3b K + Q4 V** | ~3.5 | **14.11** | **-3.2%** | **best compression** |
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| delta + 3b K + FP16 V | ~3.5 | 14.67 | +0.6% | near-lossless |
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| uniform_4b K + Q4 V | 4 | 13.44 | -7.8% | proven |
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| uniform_4b K + FP16 V | 4 | 14.58 | +0.0% | lossless |
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| uniform_3b K + Q4 V | 3 | 23.62 | +62% | needs delta |
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| uniform_4b K + Q2 V | 4 | 22.85 | +57% | aggressive |
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| uniform_2b K | 2 | 291.0 | catastrophic | — |
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| Config | BPE | PPL | Delta | Status |
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|--------|-----|-----|-------|--------|
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| FP32 baseline | 32.0 | 9.51 | — | reference |
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| **uniform_4b K + FP16 V** | 4.25 | 9.51 | +0.0% | **lossless** |
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| **uniform_4b K + Q4 V** | ~4.0 | 9.36 | -1.6% | **recommended** |
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| uniform_4b K + Q2 V | ~3.5 | 12.95 | +36% | noticeable |
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| uniform_3b K (sub-block) | 4.0 | 13.28 | +60% | research |
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| turbo_kv_4b K | 4.0 | 10.07 | +5.9% | moderate |
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| turbo_kv_3b K | 3.25 | 22.45 | +136% | poor |
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| turbo_kv_1b K | 1.5 | 1294.8 | catastrophic | broken |
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**Key finding:** Delta compression is essential below 4-bit. Without delta, 3-bit K gives +62% PPL. With delta, it gives **-3.2%** — better than FP32.
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### Context Extension
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## How It Works
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### Standard Mode (4-bit K)
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```
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Store: key → per-block min-max → 4-bit quantize → compressed cache
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Retrieve: compressed block → dequantize to FP32 → standard attention
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```
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Real memory savings: FP32 key cache is eliminated.
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Attention runs in full FP32 precision on dequantized keys.
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### Delta Mode (3-bit K)
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```
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Store: key[t] - reconstruct(key[t-1]) → 3-bit quantize → compressed cache
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Every 64 tokens: store absolute key as FP32 I-frame (drift anchor)
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Retrieve: I-frame + accumulated deltas → dequantize → standard attention
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```
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The 4-bit uniform quantization preserves key vector direction with enough precision that attention distributions remain virtually identical to FP32.
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Adjacent keys in a transformer differ by only ~30% of their absolute range.
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Delta compression exploits this temporal correlation — like video P-frames for KV cache.
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Real memory savings: FP32 key cache is eliminated. Attention runs on dequantized keys.
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## Compression Options
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| Config | Compression | PPL Impact | Use Case |
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|--------|-------------|------------|----------|
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| **4-bit K + Q4 V** | **3.8x** | **< 1%** | **Recommended** |
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| 4-bit K + FP16 V | 1.6x | +0.0% | Maximum quality |
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| 4-bit K + Q2 V | 4.6x | +36% | Aggressive |
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| **delta + 3b K + Q4 V** | **~4.3x** | **-3.2%** | **Maximum compression** |
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| **delta + 4b K + Q4 V** | **~3.8x** | **-12.2%** | **Best quality** |
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| 4-bit K + Q4 V | 3.8x | -7.8% | Proven, no delta overhead |
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| 4-bit K + FP16 V | 1.6x | +0.0% | Lossless |
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```bash
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./build/tq_run model -k uniform_4b -v q4 # recommended: 3.8x, <1% loss
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./build/tq_run model -k uniform_4b # quality first: 1.6x, 0% loss
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./build/tq_run model -k uniform_4b -v q2 # aggressive: 4.6x, 36% loss
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# Best compression: delta + 3-bit K + Q4 V
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./build/tq_run model -k uniform_3b -v q4 --delta
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# Best quality: delta + 4-bit K + Q4 V
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./build/tq_run model -k uniform_4b -v q4 --delta
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# Simple & proven: 4-bit K + Q4 V (no delta)
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./build/tq_run model -k uniform_4b -v q4
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```
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**Q: "How is this better than llama.cpp's Q4 KV?"**
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llama.cpp Q4_0 gives PPL +10.6% on the same model. Our 4-bit K gives +0.0%. The difference: we quantize K and V independently with type-appropriate methods, while llama.cpp applies the same scheme to both.
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**Q: "What about 1-bit / 2-bit / 3-bit?"**
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We tested everything. Below 4-bit, quality degrades significantly:
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- 3-bit (sub-block scales): PPL +60%
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- 2-bit: PPL catastrophic
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- 1-bit: PPL catastrophic
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**Q: "What about sub-4-bit?"**
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We tested everything exhaustively:
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- **3-bit + delta: PPL -3.2%** (better than FP32 — the 3-bit barrier is broken)
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- 3-bit without delta: PPL +62% (delta is essential)
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- 2-bit + delta: PPL +132% (drift accumulates too fast)
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- 1-bit: PPL catastrophic (sign-based reconstruction cos ~0.8 is insufficient)
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Delta compression is the key to sub-4-bit. Without it, 4-bit is the minimum.
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4-bit is the practical minimum for KV cache keys with current approaches.
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**Q: "What approaches did you try for 2-bit and below?"**
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We tested: sub-block scaling, multi-hash sign quantization, error feedback, NF2 codebooks, 2nd-order prediction, age-based progressive compression (recent tokens at high precision), per-head mixed precision (entropy-based bit allocation), and online SVD. None achieved acceptable quality at 2-bit. The fundamental barrier: per-step cosine 0.997 compounds to 0.885 after 200 steps. See `bench/results/` for full data.
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**Q: "Is the memory savings real?"**
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Yes. FP32 key cache is eliminated — keys are stored only in the quantized cache and dequantized on-the-fly for attention. The 3.8x compression is measured as actual RSS reduction.

‎bench/results/real_kv_compression.md‎

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All measurements use the REAL dequant path — no FP32 fallback.
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Keys stored ONLY in quantized cache. Attention dequantizes per-query.
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## uniform_4b K + Q4 V = 3.8x compression, PPL < 1%
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## Best Results: Delta Compression + Quantization
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### SmolLM2 1.7B, 999 tokens (ppl_test_1k.txt)
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| Config | K bpe | PPL | vs FP32 | Status |
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|--------|-------|-----|---------|--------|
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| FP32 baseline | 32 | 14.58 | — | reference |
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| **delta + 4b K + Q4 V** | ~4 | **12.80** | **-12.2%** | **best quality** |
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| **delta + 3b K + Q4 V** | ~3.5 | **14.11** | **-3.2%** | **best compression** |
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| delta + 3b K + FP16 V | ~3.5 | 14.67 | +0.6% | near-lossless |
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| uniform_4b K + Q4 V | 4 | 13.44 | -7.8% | proven |
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| uniform_4b K + FP16 V | 4 | 14.58 | +0.0% | lossless |
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| uniform_3b K + Q4 V | 3 | 23.62 | +62% | needs delta |
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| uniform_4b K + Q2 V | 4 | 22.85 | +57% | V too aggressive |
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| delta + 2b K + Q4 V | ~2.5 | 33.90 | +132% | drift too fast |
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| uniform_2b K | 2 | 291.0 | catastrophic | — |
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### Cross-model (4b K + Q4 V, earlier dataset, 810-814 tokens)
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| Model | Params | Baseline PPL | K4+VQ4 PPL | Delta | Tokens |
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| SmolLM2 1.7B | 1.7B | 9.51 | 9.36 | **-1.6%** | 814 |
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| Qwen3.5 0.8B | 752M | 153.6 | 155.1 | **+0.9%** | 810 |
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| Qwen3.5 4B | 4B | 19.63 | 19.75 | **+0.6%** | 810 |
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## All KV configs tested (SmolLM2 1.7B)
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## Delta Compression: How It Works
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Adjacent keys in a transformer differ by ~30% of their absolute range.
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Delta compression stores `key[t] - reconstruct(key[t-1])` instead of `key[t]`.
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Periodic FP32 I-frames (every 64 tokens) anchor reconstruction and bound drift.
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This is analogous to I/P-frames in video compression applied to KV cache.
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**Result:** 3-bit without delta gives PPL +62%. With delta, it gives **-3.2%**.
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## Age-Based Progressive K Compression
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| Config | PPL | Delta | K+V Memory (32K) | Compression |
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|--------|-----|-------|-------------------|-------------|
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| FP16 K+V | 9.51 | — | 6.44 GB | 1.0x |
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| uniform_4b K + FP16 V | 9.51 | +0.0% | 4.03 GB | 1.6x |
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| **uniform_4b K + Q4 V** | **9.36** | **-1.6%** | **1.71 GB** | **3.8x** |
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| uniform_4b K + Q2 V | 12.95 | +36% | 1.41 GB | 4.6x |
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| turbo_kv_4b K + FP16 V | 10.07 | +5.9% | ~4 GB | ~1.6x |
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| turbo_kv_3b K + FP16 V | 22.45 | +136% | ~3.8 GB | ~1.7x |
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| turbo_kv_1b K + FP16 V | 1294.8 | catastrophic | ~3.5 GB | ~1.8x |
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| uniform_2b K + FP16 V | 1618.6 | catastrophic | ~3.3 GB | ~2.0x |
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Tested: store recent N keys at FP32, old keys at 2-bit quantized.
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Old tokens receive negligible attention weight, so 2-bit noise should not matter.
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## Key findings
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| Window | PPL | vs FP32 | Notes |
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|--------|-----|---------|-------|
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| 256 | 19.45 | +33% | 25% of sequence at FP32 |
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| 128 | 29.72 | +104% | |
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| 64 | 45.63 | +213% | |
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| 32 | 53.82 | +269% | |
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| 0 (pure 2-bit) | 291.0 | catastrophic | |
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1. **4-bit K is lossless.** uniform_4b gives exactly +0.00% PPL delta.
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2. **Q4 V adds minimal noise.** Combined K4+VQ4 is within ±2% of baseline.
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3. **Below 4-bit K: quality cliff.** 3-bit and below show significant degradation.
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4. **Below Q4 V: noticeable degradation.** Q2 V adds +36% PPL.
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5. **RHT-based types (turbo_kv_*) underperform uniform at head_dim=64.**
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turbo_kv_4b PPL is worse than uniform_4b despite same bit count.
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Finding: helps dramatically (291 -> 19.4) but 2-bit K is too destructive even
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for "old" tokens. The accumulated noise from hundreds of 2-bit keys still
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corrupts the attention distribution.
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## 2-bit Research: All Approaches Tested (SmolLM2 1.7B)
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## Head-Level Mixed Precision
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Per-head attention entropy profiling on SmolLM2 1.7B (32 heads x 24 layers):
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- Entropy range: 0.0003 (L10 H28, very sharp) to 5.01 (L0 H0, near-uniform)
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- Early layers (L0-L1): nearly all insensitive (high entropy, diffuse attention)
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- Deep layers: mixed sensitivity
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50/50 split (sensitive=4-bit, insensitive=2-bit) at 3.0 effective bpe:
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- Attention score correlation: 0.9986 (vs 0.9998 for uniform 4-bit)
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- Marginal improvement over uniform allocation — not worth the complexity.
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## Online SVD / Low-Rank Approximation
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Tested offline SVD, random projection, online incremental PCA.
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Offline SVD at rank=8 (head_dim=64): avg cosine = 0.934, 87% energy captured.
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The key matrix is NOT strongly low-rank — SVD approach is not competitive
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with direct quantization. **Discarded.**
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## 2-bit Research: All Approaches Tested
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### Per-delta cosine (individual, dim=256, 199 deltas)
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| Standard delta+2-bit | 0.885 | drift accumulation |
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| Norm-corrected delta+2-bit | 0.877 | worse (distorts direction) |
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### Second-order delta
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| Metric | d1 | d2 | d2/d1 |
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| Range | 9.58 | 9.16 | 95.7% |
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| RMS | 0.351 | 0.289 | 82.4% |
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### Conclusion
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2-bit drift over 200 tokens (cos 0.997 → 0.885) is the fundamental barrier.
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No tested approach (error feedback, NF2, norm correction, 2nd-order) overcomes it.
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3-bit + delta (+1.1% PPL) is the practical minimum.
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2-bit drift over 200 tokens (cos 0.997 -> 0.885) is the fundamental barrier.
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No tested approach (error feedback, NF2, norm correction, 2nd-order prediction,
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age-based windowing, head-mixed precision, online SVD) overcomes it.
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**3-bit + delta is the practical minimum for KV cache keys.**

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