llm-cipher-reasoning — data, eval results and full research ledger

Everything except the weights from a research run asking: can an LLM be trained to reason in a more compact "language" than English, and does that actually save tokens?

Two linked lines of work on Qwen/Qwen3-4B-Instruct-2507:

1. Cipher invention / cross-model communication — cold-decoding tests, negotiated cipher collusion between model pairs, a cipher-hardening arms race, and GEPA prompt optimization to get a model to reason internally in a letter-reversal cipher by prompting alone.
2. GRPO (RLVR) training for token efficiency — rounds A–E, then generations 0–5 of a token-minimization run: 25 experiments, 6 generations, ~33 GPU-hours.

The trained LoRA adapters live in the companion model repo: AlexWortega/llm-cipher-reasoning-loras. Source code: github.com/AlexWortega/llm-cipher-reasoning.

TL;DR of the findings

The winner is a prompt, not a trained model. A Chain-of-Draft system prompt (arxiv 2502.18600) on the untouched base model gets 93.5% on GSM8K at 76.8 reasoning tokens vs the plain baseline's 94.0% @ 210.4 — −63% tokens for −0.5pp accuracy, with zero training cost and no out-of-distribution risk.

The main scientific result is negative. Every GRPO terseness-trained adapter fails the AIME 2026 out-of-domain gate (base is 36.67%):

config	GSM8K (n=200)	tokens	AIME 2026	mitigation that was tried
base model	94.0%	210.4	36.67%	—
CoD prompt, base (champion)	93.5%	76.8	✅ safe by construction	no weight change
G4-1 diffaware + KL anchor β=0.15	93.0%	69.7	13.3%	drift limitation
G5-1 AIME2024-mix ×8, reward on	92.5%	69.7	10.0%	hard-data mix
G5-2 MATH L3-5 mix + diffaware	92.0%	70.0	20.0%	occasionally-solvable mix
G2-1 always-on ramp	91.5%	69.1	16.7%	correctness gate, gentle target 70
G3-1 difficulty-aware	90.5%	70.4	26.7%	pressure off on hard problems
eff3 (rounds A–E champion)	85.7% (n=70)	58.3	20.0%	correctness gate (target 40)

Mitigations move OOD non-monotonically (difficulty-awareness +10pp, KL anchoring −13pp on top of it), so the tax is not attributable to one mechanism you can switch off. At 4B, GRPO terseness training trades out-of-domain reasoning for in-domain compression. The rounds A–E champion eff3 had been carrying this debt unmeasured.

It also inverts on agentic workloads. On terminal-bench-2 (89 tasks, terminus-2 agent), adding the CoD instruction compresses per-call output by −78% but makes the agent loop 6× more — 5-word drafts break its command-format parsing — and since prompt re-feeding is ~97% of agentic token cost, total spend goes +268% (32.3M → 118.7M tokens). The champion prompt is task-scoped: fine for one-shot reasoning, never inject it into a multi-turn agent system prompt.

And the cipher idea itself doesn't save anything. Under BPE, a letter-reversal cipher costs more tokens, not fewer. Hand-designed encodings were probed directly: binary Huffman coding is 2.71× worse, n-ary Huffman 1.32× worse; only stopword deletion saves real tokens (−11.8% at its most aggressive tier).

Full writeups, including every refuted hypothesis, are in docs/ and run/.

Repo layout

data/       training and eval data (see configs above)
results/    30+ eval JSONs: AIME 2026 base/trained, TB2, GEPA, GRPO rounds A-E,
            arms-race rounds, Huffman/stopword encoding probes, qualitative samples,
            roundE_corpus/ (supertoken mining corpus + reward logs)
reward_logs/ per-step GRPO reward traces, one JSONL per experiment (gen-0 .. gen-5)
docs/       15 markdown writeups: RESULTS.md (cipher line), grpo_RESULTS.md (656 lines,
            every GRPO round incl. the LoRA learning-rate bug and its fix),
            TOKENMIN_RESULTS.md (the gen-0..5 run), DEEPRESEARCH / PREVIOUS_WORK /
            BUDGET / COMPUTE / DATA, plus the Round E plan and bottleneck analysis
run/        autoresearch run ledger: EXPERIMENTS.md (all 25 experiments),
            FINDINGS.md, leaderboard.md, PLAN.md, IDEA_ANGLES.md + raw train/eval logs

data/

file	rows	schema	what it is
gsm8k_train.jsonl	7,473	question, answer	GSM8K train split, GRPO prompt source
gsm8k_test.jsonl	1,319	question, answer	GSM8K test split, held-out eval
aime2024_train.jsonl	30	question, gold	AIME 2024, the gen-5 hard-data mix
math_l345_train.jsonl	500	question, gold	MATH levels 3–5, numeric answers only — the gen-5 "occasionally solvable" mix
sft_tier4_train.jsonl	7,473	messages	SFT seed for Round E, GSM8K rewritten under the most aggressive stopword-deletion tier
dict_words.txt	—	plain text	English dictionary used to score cipher adherence

AIME 2026 problems are not redistributed here; that eval pulls from the MathArena dataset. Model outputs for it are in results/aime2026_*.json.

Reproducing

Training/eval scripts are in the GitHub repo (src/grpo_train*.py, src/eval_pareto.py — the latter holds the exact COD_PROMPT text). The champion needs no training: take Qwen/Qwen3-4B-Instruct-2507, use the CoD system prompt, done.

Citation

@misc{llm_cipher_reasoning_2026,
  title  = {Can LLMs reason in a compact language? Prompting beats GRPO, and terseness training taxes OOD reasoning},
  author = {Alex Wortega},
  year   = {2026},
  url    = {https://huggingface.co/datasets/AlexWortega/llm-cipher-reasoning}
}