# research-github report (2026-07-12)

## TIER 1 — canonical drop-in reward functions
1. **Cosine length-scaled reward** (Yeo 2502.03373, open-r1 `get_cosine_scaled_reward`, also in trl.rewards):
   progress=len/max_len; reward=min_v+0.5(max_v−min_v)(1+cos(progress·π)). Correct: 0.5..1.0 (shorter→1.0);
   wrong: SWAPPED −1.0..−0.5 (longer wrong penalized LESS → preserves exploration). One-diff.
2. **Kimi-1.5 min-max linear len_reward** (open-r1 rewards.py; GSM8K fork kithib/ReDit/grpo_gsm8k.py):
   λ=0.5−(len−min)/(max−min) per batch; correct→λ, wrong→min(0,λ). No hyperparams.
3. **DAPO soft overlong punishment** (2503.14476, trl `get_soft_overlong_punishment`): zero until
   max−cache, linear to −1 at cap. + `GRPOConfig(mask_truncated_completions=True, loss_type="dapo",
   epsilon_high=0.28, beta=0.0)`. GSM8K scale: max=1024, cache=256.

## TRL native: no built-in length penalty; knobs = mask_truncated_completions, scale_rewards, max_completion_length.

## TIER 2 — hard numbers
- **Fast-Math-R1** (analokmaus/kaggle-aimo2-fast-math-r1, 2507.08267): SFT→GRPO, cosine+len+format
  reward forcing boxed answer BEFORE </think> + stop at </think>. AIME24: +1.1pt @ −25% tokens (32k budget),
  +5.7pt @ −17% tokens (16k). Trick: regex `^.*?\boxed{...}.*?</think>` + early stop kills post-answer rambling.
- **ReBalance** (yu-lin-li/ReBalance, ICLR26): naive length penalties cause "underthinking";
  measure length reduction SEPARATELY for correct vs incorrect.

## TIER 3 — awesome lists: hemingkx/Awesome-Efficient-Reasoning, Eclipsess/Awesome-Efficient-Reasoning-LLMs,
  DevoAllen/Awesome-Reasoning-Economy-Papers. Families: long2short distillation (Kimi), difficulty→budget
  scheduler, staged ctx curriculum 8K→16K→32K.

## Recommended single diff
correctness + cosine_scaled(max_len≈256-512) + mask_truncated_completions=True; add repetition_penalty_reward
guard (n-gram repetition is the known hack response to length shaping).