---
language: en
library_name: peft
pipeline_tag: text-generation
base_model: nvidia/Nemotron-Mini-4B-Instruct
license: other
license_name: nvidia-open-model-license-june2024
license_link: https://developer.download.nvidia.com/licenses/nvidia-open-model-license-agreement-june-2024.pdf
tags:
- peft
- lora
- graph-theory
- counterexample-generation
- research
---

# Nemotron Mini 4B Graph Counterexamples

This independently trained rank-16 LoRA adapter asks NVIDIA's `Nemotron-Mini-4B-Instruct` to construct small exact counterexamples to synthetic graph inequalities. It uses the base model at revision `791833e92ebddb0bc2c1007f6d2b6764f886a2ae`. NVIDIA did not make or endorse this release.

## Measured result

The adapter was selected on a frozen 30-task development split before held-out evaluation. It solved 10/30 held-out tasks, compared with 0/30 for the untouched base under the same single-shot greedy decoder. One random graph solved 5/30, while a 32-proposal random search solved 27/30.

A post-hoc diagnostic found that every adapter success was also solved by either the empty or complete graph. This pilot therefore shows improvement over the untouched language model and no evidence of nontrivial graph search. It did not discover a new theorem or prove a conjecture.

## Task and use

Each prompt specifies an inequality between exact graph invariants on at most eight vertices. The response is a JSON edge list, and the project verifier checks its integer violation margin. Supported invariants include edge count, degree, independence number, clique number, chromatic number, matching size, and the product of independence and clique numbers.

Load the exact base revision and attach this adapter with PEFT. Use the prompts, parser, and exact verifier from the [source experiment](https://github.com/arpjw/nemotron/tree/main/experiments/graph-counterexamples). Generic text generation is outside the measured setup.

## Training and limitations

One QLoRA epoch used 120 synthetic examples, 15 optimizer steps, rank 16, alpha 32, dropout 0.05, BF16, learning rate `2e-4`, and seed `20261015`. The generated task grammar is shared across splits, reversed invariant pairs can recur, and this is one training seed on one small task set.

The [public result report](https://github.com/arpjw/nemotron/blob/main/experiments/graph-counterexamples/results/RUNPOD_PILOT_PUBLIC.md) contains the full protocol, uncertainty, post-hoc diagnostic, artifact hashes, and compute cleanup. Adapter SHA-256: `0f64011740c008ba93c7c01e8a43375263a7bffeaae802139481da8641899517`.

## Licensing

This adapter is a derivative of the NVIDIA base model and follows NVIDIA's separate model terms. The pinned model card refers to the June 2024 Open Model License and the August 2024 Community Model License; exact copies are included under `LICENSES/`. The source repository's MIT license does not apply to NVIDIA model artifacts. The package contains no base weights or tokenizer.