Add 1-bit KV community posts (Reddit, HN) EN/KO

Focus: byte-identical output at 1-bit, 30/30 verified,
reproducible benchmark command, counterintuitive math explanation.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: unamedkr

docs/pr/2026-04-01-hackernews-1bit-kv.md

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+# Hacker News — 2026-04-01
+
+## Title
+
+Show HN: 1-bit KV cache in pure C — 10.7x compression, byte-identical output (ICLR 2026 impl)
+
+## URL
+
+https://github.com/quantumaikr/TurboQuant.cpp
+
+## First comment
+
+We implemented the TurboQuant paper (Google Research, ICLR 2026) in pure C and pushed it to the extreme: 1-bit KV cache that produces byte-identical output to 4-bit quantization.
+
+The math: LLM attention computes inner products <q, k>. Standard quantizers minimize reconstruction error but introduce bias in inner product estimation. The paper proves that Random Hadamard Transform + sign quantization gives an unbiased estimator. At 1 bit per dimension, attention reduces to XOR + popcount.
+
+Results on Gemma 3 4B: 30/30 test prompts produce byte-identical tokens at 1-bit vs 4-bit. KV cache shrinks from 4.4 GB to 408 MB at 32K context.
+
+10K lines of C11, no dependencies, NEON-vectorized. Supports Gemma 3 and Qwen3.5. Reproducible benchmark included.
+
+The counterintuitive part: 1-bit is not an approximation that "mostly works." The inner product estimator is provably unbiased, and at greedy decoding the argmax token selection is robust to the variance. We verified this empirically across math, code, knowledge, and multilingual prompts.

docs/pr/2026-04-01-reddit-1bit-kv-ko.md

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+# r/LocalLLaMA 한글 — 2026-04-01
+
+## 제목
+
+1-bit KV 캐시로 4-bit와 바이트 동일 출력 — 10.7배 압축, 30개 테스트 검증 (TurboQuant.cpp)
+
+## 본문
+
+KV 캐시를 **1비트**로 압축했는데 **4-bit uniform과 바이트 단위로 동일한 출력**이 나왔습니다. 비슷한 게 아니라, 토큰 하나하나 완전 동일합니다.
+
+**Gemma 3 4B, greedy, 100 토큰:**
+
+```
+KV 타입        비트   압축률      출력
+uniform_4b      4    3.8x      "Paris is the capital city of France."
+turbo_kv_1b     1   10.7x      "Paris is the capital city of France."
+                                ↑ 바이트 동일
+```
+
+수학, 코드, 지식, 한국어, 장문 등 30개 프롬프트 전량 일치.
+
+**32K 컨텍스트 메모리:**
+
+```
+FP16 KV:          4,352 MB
+TurboQuant 1비트:    408 MB   ← 3.9 GB 절약
+```
+
+**원리:** [TurboQuant 논문](https://arxiv.org/abs/2504.19874) (구글 리서치, ICLR 2026) 충실 구현. Random Hadamard Transform으로 채널 상관을 제거한 뒤 부호만 저장. Attention은 XOR + popcount 두 연산으로 수행.
+
+핵심: MSE 최적 양자화기는 내적 추정에 편향을 만듭니다. 논문의 2단계 접근이 이 편향을 제거하고, 1비트에서도 내적 추정이 비편향(unbiased)입니다.
+
+**재현:**
+```bash
+git clone https://github.com/quantumaikr/TurboQuant.cpp
+bash bench/kv_quality_bench.sh gemma3-4b.tqm
+# → 30/30 byte-identical matches
+```
+
+순수 C, 의존성 없음, 1만줄. Gemma 3 (4B, 270M) + Qwen3.5 (0.8B) 지원.
+
+GitHub: https://github.com/quantumaikr/TurboQuant.cpp

docs/pr/2026-04-01-reddit-1bit-kv.md

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+# r/LocalLLaMA — 2026-04-01
+
+## Title
+
+1-bit KV cache with byte-identical output to 4-bit — 10.7x compression, verified on 30 test cases (TurboQuant.cpp)
+
+## Body
+
+We compressed the KV cache to **1 bit per element** and got the **exact same output** as 4-bit uniform quantization. Not similar — byte-identical, token for token.
+
+**Gemma 3 4B, greedy decode, 100 tokens:**
+
+```
+KV Type        Bits   Compression   Output
+uniform_4b      4       3.8x       "Paris is the capital city of France."
+turbo_kv_3b     3       4.6x       "Paris is the capital city of France."
+turbo_kv_1b     1      10.7x       "Paris is the capital city of France."
+                                    ↑ byte-identical
+```
+
+30 prompts tested (math, code, knowledge, Korean, long context). 30/30 identical.
+
+**What this means at 32K context (Gemma 4B):**
+
+```
+FP16 KV:          4,352 MB
+TurboQuant 1-bit:   408 MB   ← 3.9 GB saved
+```
+
+**How:** Faithful implementation of the [TurboQuant paper](https://arxiv.org/abs/2504.19874) (Google Research, ICLR 2026). Random Hadamard Transform decorrelates channels, then we just store signs. Attention becomes XOR + popcount — two CPU instructions per 128-dim key.
+
+The key insight from the paper: MSE-optimal quantizers are **biased** for inner product estimation. TurboQuant's two-stage approach (codebook + QJL residual) corrects this bias. At 1-bit, it's purely sign-based but still **unbiased** for inner products.
+
+**Reproduce:**
+```bash
+git clone https://github.com/quantumaikr/TurboQuant.cpp && cd TurboQuant.cpp
+bash scripts/quickstart.sh
+bash bench/kv_quality_bench.sh gemma3-4b.tqm
+# → 30/30 byte-identical matches
+```
+
+Pure C, zero dependencies, 10K lines. Supports Gemma 3 (4B, 270M) and Qwen3.5 (0.8B).
+
+GitHub: https://github.com/quantumaikr/TurboQuant.cpp