minnesotanlp/Finch-4B-KTO

Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Tasks

A mid-training "practice phase" that teaches small open-source LLMs how to evolve solutions.

Finch-4B-KTO extends Finch-4B with a second, preference-learning stage (KTO). On top of evolution fine-tuning — which teaches the model how to evolve a solution as a mutation operator — KTO adds the ability to self-judge which candidate solutions are promising and which fall short, further sharpening cross-task discovery. Lineage: Qwen3.5-4B → Finch-4B (EFT + SFT) → Finch-4B-KTO.

TL;DR

Evolution Fine-Tuning (EFT) turns evolutionary search trajectories into supervision, moving discovery behavior from the scaffold into the model. KTO then trains the model on improved vs. regressed transitions jointly, so it internalizes a sense of solution quality — improving every measured discovery metric over Finch-4B.

• (Left) EFT acts as mid-training, boosting Finch's discovery on the Erdős minimum-overlap problem under both test-time search and test-time learning.
• (Right) On NP-hard competitive programming, Finch composes strategies learned across diverse domains, while the base model relies on a single repetitive strategy.

Finch family

Model	Base	Params	Training	🤗 Hugging Face
Finch-2B	Qwen3.5-2B	2B	EFT
Finch-4B	Qwen3.5-4B	4B	EFT
Finch-8B	Qwen3-8B	8B	EFT
Finch-9B	Qwen3.5-9B	9B	EFT
Finch-4B-KTO ← this model	Qwen3.5-4B	4B	EFT + KTO
Finch-8B-KTO	Qwen3-8B	8B	EFT + KTO

How to Use Finch

1. Execute OpenEvolve scaffold with Finch

Finch is a mutation operator for evolutionary search, most effective driven by a scaffold such as OpenEvolve (T = 100, temperature 0.7, top-p 0.95, up to 30K tokens). You can also use other scaffolds in the SkyDiscover framework, but we do not guarantee performance, as our model is trained on OpenEvolve's trajectories — one of this work's limitations.

2. Calling Finch directly

You can also call Finch directly:

System prompt (task-level instruction from the OpenEvolve scaffold):

You are an expert mathematician specializing in circle packing problems and computational geometry.
Your task is to improve a constructor function that directly produces a specific arrangement of
26 circles in a unit square, maximizing the sum of their radii.
The AlphaEvolve paper achieved a sum of 2.635 for n=26.

Key geometric insights:
- Circle packings often follow hexagonal patterns in the densest regions
- Maximum density for infinite circle packing is pi/(2*sqrt(3)) ≈ 0.9069
- Edge effects make square container packing harder than infinite packing
- Similar radius circles often form regular patterns, while varied radii allow better space utilization

User prompt (evolutionary state — current program + evaluator feedback + evolutionary history):

# Current Program Information
- Fitness: 0.3642 (sum_radii: 0.9598)
- Focus areas: Fitness unchanged at 0.3642. Consider simplifying — code length exceeds 500 characters.

# Program Evolution History
## Previous Attempts

### Attempt 1
- Changes: Replace concentric ring placement with hexagonal lattice (5-6-5-6-5 row pattern)
- Metrics: sum_radii: 0.9598, validity: 1.0 — Improvement in all metrics

# Current Program

# EVOLVE-BLOCK-START
import numpy as np

def construct_packing():
    n = 26
    centers = np.zeros((n, 2))
    centers[0] = [0.5, 0.5]                              # center circle
    for i in range(8):                                    # inner ring
        angle = 2 * np.pi * i / 8
        centers[i+1] = [0.5 + 0.3*np.cos(angle), 0.5 + 0.3*np.sin(angle)]
    for i in range(16):                                   # outer ring
        angle = 2 * np.pi * i / 16
        centers[i+9] = [0.5 + 0.7*np.cos(angle), 0.5 + 0.7*np.sin(angle)]
    centers = np.clip(centers, 0.01, 0.99)
    radii = compute_max_radii(centers)
    return centers, radii, np.sum(radii)
# EVOLVE-BLOCK-END

import torch
from transformers import AutoModelForCausalLM, AutoTokenizer

model_id = "minnesotanlp/Finch-4B-KTO"
tokenizer = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(model_id, torch_dtype="auto", device_map="auto")

# Given an evolutionary state — task instruction + parent program + evolutionary history
# + evaluator feedback — Finch proposes an improved candidate program.
messages = [
    {"role": "system", "content": SYSTEM_PROMPT},  # provided by your evolutionary scaffold
    {"role": "user", "content": USER_PROMPT},      # parent program + feedback + history
]
inputs = tokenizer.apply_chat_template(
    messages, add_generation_prompt=True, return_tensors="pt"
).to(model.device)

out = model.generate(inputs, max_new_tokens=30000, do_sample=True, temperature=0.7, top_p=0.95)
print(tokenizer.decode(out[0][inputs.shape[-1]:], skip_special_tokens=True))

Training

Two stages:

• Stage 1 — EFT (SFT). Finch-4B: full SFT of Qwen3.5-4B on improved transitions from the Finch Collection (355 training tasks; one run/task → 30,445 examples; 900 for validation) with LLaMA-Factory — 1 epoch, global batch size 128, LR 1e-5, on 8× NVIDIA H200 140GB.
• Stage 2 — KTO. Preference learning (KTO) on improved (desirable) and regressed (undesirable) transitions jointly, maximizing the contrastive signal that guides the model toward self-judging which solutions are promising and which fall short.
• Teacher (data). Trajectories generated by Qwen3.5-397B-A17B inside the OpenEvolve scaffold.

Results

• Finch outperforms its same-size base model by +10.2% on 22 held-out tasks across 5 domains, with improvements of up to +290% on individual tasks.
• Larger models benefit more, and Finch-4B matches a model roughly 2× larger on the Erdős task.

• On competitive programming (FrontierCS), Finch-9B averages 46.01 vs base Qwen3.5-9B's 32.46; on CALICO's P263 (UC Berkeley's official open-ended contest) it scores 86.10 vs 55.09

• With preference learning (KTO), Finch-8B surpasses the best human score on AC1 and AC2, while its competitive programming score improves from 24.56 → 37.30.
• Finch-8B matches SOTA on two circle-packing tasks and improves the Erdős task by +3.2%.

Limitations

Trajectories are collected and evaluated only with OpenEvolve; behavior under different scaffolds is not guaranteed.

License

The Finch Collection is released under the CC-BY 4.0 License and is recommended for non-commercial academic research. The accompanying code and Finch model weights are released under the Apache 2.0 License.

Acknowledgements

This research was supported by the "Advanced GPU Utilization Support Program" funded by the Government of the Republic of Korea (Ministry of Science and ICT). We are grateful to the SkyDiscover team for their valuable feedback on the dataset construction process, the use of the SkyDiscover framework, and the overall direction of this research — in particular, Shu Liu, Shubham Agarwal, and Mert Cemri for their insightful comments and discussions. We also thank the OpenEvolve team, especially Ritik Vijayvergiya and Asankhaya Sharma, for their guidance on using the OpenEvolve framework and for their thoughtful comments on this work. We further thank the authors of ALE-Bench, especially Yuki Imajuku, and the AtCoder team for authorizing the public release of the evolutionary search trajectories derived from their CC BY-ND 4.0-licensed dataset. Finally, we thank Byung-Kwan Lee for valuable feedback during the early stages of this project.

Citation

@misc{lee2026evolutionfinetuninglearningdiscover,
      title={Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Tasks}, 
      author={Young-Jun Lee and Seungone Kim and Minki Kang and Alistair Cheong Liang Chuen and Zerui Chen and Seungho Han and Taehee Jung and Dongyeop Kang},
      year={2026},
      eprint={2606.29082},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2606.29082}, 
}