Pith Number

pith:F4MGJBXU

pith:2025:F4MGJBXU27N65PGT3SJF4P4R3N

not attested not anchored not stored refs resolved

Rethinking Output Alignment For 1-bit Post-Training Quantization of Large Language Models

Cuong Nguyen, Cuong Pham, Dung Anh Hoang, Jianfei Cai, Thanh-Toan Do, Trung Le

Naive output alignment fails in 1-bit LLM quantization because errors accumulate across layers and distort the representation space unevenly.

arxiv:2512.21651 v2 · 2025-12-25 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4MGJBXU27N65PGT3SJF4P4R3N}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we show that this failure arises from two fundamental issues: error accumulation across layers and, more critically, anisotropic distortion of the representation space. Based on these insights, we propose a novel PTQ method for 1-bit LLMs that explicitly addresses these issues while maintaining computational efficiency.

C2weakest assumption

The assumption that correcting error accumulation and anisotropic distortion on a small calibration set will generalize to the full test distribution without introducing new distortions or requiring architecture-specific tuning.

C3one line summary

A post-training 1-bit quantization method for LLMs that fixes error accumulation and anisotropic representation distortion to outperform prior weight-driven and naive output-driven baselines.

References

22 extracted · 22 resolved · 10 Pith anchors

[1] Language Models are Few-Shot Learners 2005 · doi:10.1609/aaai.v34i05.6239

[2] Stbllm: Breaking the 1-bit barrier with structured binary llms

[3] Network sketching: Exploiting bi- nary structure in deep cnns.2017 IEEE Conference on Computer Vision and Pattern Recog- nition (CVPR), pp 2017

[4] Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding · arXiv:1510.00149

[5] Distilling the Knowledge in a Neural Network · arXiv:1503.02531

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:00.375078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f186486f4d7dbeebcd3dc925e3f91db68b0b1662121c55f3eefd966275f28b2

Aliases

arxiv: 2512.21651 · arxiv_version: 2512.21651v2 · doi: 10.48550/arxiv.2512.21651 · pith_short_12: F4MGJBXU27N6 · pith_short_16: F4MGJBXU27N65PGT · pith_short_8: F4MGJBXU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/F4MGJBXU27N65PGT3SJF4P4R3N \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2f186486f4d7dbeebcd3dc925e3f91db68b0b1662121c55f3eefd966275f28b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7813dbbb929cfa9b34818e0ef81958d5bc03906d72ec113085f09350d188f7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-25T12:39:36Z",
    "title_canon_sha256": "c96f8566f1bc3e12dbf3aa669a763aa8ce6b1dcd8fa9828b63e5c75139bdee0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.21651",
    "kind": "arxiv",
    "version": 2
  }
}