lora-logic-mistral7b

LoRA adapter for Mistral-7B-Instruct-v0.3 (4-bit MLX), fine-tuned on a small dataset of English-to-predicate-logic conversion examples.

The hypothesis being tested in the parent repo: forcing a small LLM to ground its reasoning in explicit predicate logic improves downstream accuracy on hard multi-step reasoning benchmarks compared to vanilla chain-of-thought.

Training

Base model	mlx-community/Mistral-7B-Instruct-v0.3-4bit
Fine-tuning	LoRA via mlx_lm.lora (Apple silicon native)
Trainable params	5.24 M (0.072% of base)
Layers fine-tuned	8 (last 8 of 32)
LoRA rank	8
LoRA scale	20.0
Optimizer	Adam
Learning rate	2e-5
Iterations	250 (best val loss at iter 200)
Batch size	1
Training data	119 hand-curated English→predicate-logic conversion examples
Validation data	13 held-out examples

Validation loss

Iter	Val loss
1	2.412
50	0.439
100	0.431
150	0.462
200	0.421 ← shipped checkpoint
250	0.489 (overfit)

adapters.safetensors contains the iter-200 weights.

Training data format

Each example teaches the model to translate an English logical argument into formal predicate logic:

{
  "messages": [
    {"role": "user", "content": "You are a careful reasoner... Argument: All cats are animals. Cat is a cat. Therefore, Cat is an animal."},
    {"role": "assistant", "content": "Premise1: ∀x (Cat(x) → Animal(x))\nPremise2: Cat(Cat)\nConclusion: Animal(Cat)"}
  ]
}

Coverage: universal implication, existential quantification, modus ponens, modus tollens, 1-2-hop chains.

Usage (mlx-lm)

from mlx_lm import load, generate

model, tokenizer = load(
    "mlx-community/Mistral-7B-Instruct-v0.3-4bit",
    adapter_path="<local path containing adapters.safetensors and adapter_config.json>",
)

messages = [{"role": "user", "content": "Translate to predicate logic: All birds fly. Tweety is a bird. Therefore, Tweety flies."}]
prompt = tokenizer.apply_chat_template(messages, add_generation_prompt=True, tokenize=False)
print(generate(model, tokenizer, prompt=prompt, max_tokens=512, verbose=False))

Evaluation

Held-out test on Google DeepMind's BigBench Extra Hard mini (BBEH-mini, 460 reasoning items). See parent repo for paired-comparison results:

github.com/scottmatthews7/logical-reasoning

Limitations

• Trained on a tiny dataset (119 items). Coverage of logical operators is intentionally narrow.
• Tests transfer of a skill (predicate-logic translation) to a different domain (multi-step reasoning puzzles). Effect size, if any, is what the experiment measures — there is no guarantee scaling this approach helps frontier benchmarks.
• The base is a 4-bit quantised Mistral 7B. Behaviour on the full-precision base may differ.