---
license: mit
base_model: deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B
tags:
  - math
  - reasoning
  - verifiable
  - rlvr
  - gguf
pipeline_tag: text-generation
---

# NPC Reason 1.5B

A math-reasoning model whose every load-bearing arithmetic step emits a mechanically-checkable
assertion in the form `<<EXPR = RESULT>>`. Specialized from DeepSeek-R1-Distill-Qwen-1.5B (MIT).
The point is not just a final answer. It is that a pure-code checker can re-execute every step and
confirm the chain, so "verifiable-rate" is not the model's opinion. Anyone can run the checker.

## Results (frozen held-out eval, n=500, GSM8K + MATH-500, greedy, format prompt)

| metric                 | base R1-Distill | SFT (V4 distill) | NPC Reason (RL) |
|------------------------|----------------:|-----------------:|----------------:|
| verifiable-rate        |           0.0%  |          76.8%   |        76.2%    |
| accuracy               |          61.6%  |          65.8%   |        66.6%    |
| verified-and-correct   |           0.0%  |          58.0%   |        59.6%    |

verified-and-correct (both axes) is the headline. The full arc is shown on purpose, not just the
best column.

## What actually happened (plain language, no overclaiming)

- **The base model produces zero mechanically-verifiable chains, even when asked for the format.**
  Only 1 of 500 base outputs even contained a `<<` marker.
- **The SFT distillation did the heavy lifting: 0 to 76.8% verifiable.** Training on a corpus of
  DeepSeek-V4 chains that the frozen verifier confirmed (verifiable AND correct, 7,546 kept of
  13,245 generated) transferred the grounding. Accuracy rose (61.6 to 65.8), it was not bought by
  sacrificing correctness.
- **RLVR/GRPO against the frozen verifier was a stable refinement, not a decisive gain.** It moved
  verified-and-correct +1.6pp (58.0 to 59.6) and accuracy +0.8pp, with verifiable flat (-0.6pp).
  On n=500 that is roughly 8 problems. The RL model and the SFT model are statistically about even.
- **The shipped model is the RL checkpoint** (marginally best on the headline). **The SFT model is
  statistically equivalent and available** as a fallback. Either is a defensible "NPC Reason".
- **The pre-registered 90% verifiable bar was NOT met (stuck near 77%).** It was deliberately not
  chased into instability. This is the open limitation and the next frontier.
- Accuracy includes the greedy no-answer floor. The same greedy decoding is used for base and tuned
  models, so the comparisons are apples-to-apples.

## The verifier (the methodological core)

A pure-code Python/SymPy checker, frozen at sha256 `d5d146cf...`, used as BOTH the evaluation
metric AND the RL reward (byte-identical both times). A chain is VERIFIABLE iff every load-bearing
`<<EXPR=RESULT>>` assertion re-executes correctly AND the final answer composes from the last step.
Correctness (final == gold) is a separate, independent axis. The verifier is shipped with the model
(`verifier/step_verifier.py`); users run it on the model's own outputs.

## Methods finding worth keeping

GRPO with this hard, frozen, pure-code verifier reward trained STABLY: KL stayed flat (~0.0002),
no length runaway, no mode collapse, no early-stop trip. This is notable because prior RL attempts
in related work were unstable. RLVR with a clean verifier reward is a regime where a small model
trains without collapsing. The lift was small here, but the stability is the keepable result.

## Intended use and limits

- Use: math problems where checkable, grounded reasoning steps matter (arithmetic and
  arithmetic-reducible word problems). Prompt for the `<<EXPR = RESULT>>` format (see USAGE.md).
- Math-first. Logic, proofs, and general chain-of-thought are NOT claimed and are future work.
- Not a general chat model. The 1.5B reasoning ceiling applies. ~23% of format-prompt chains are
  still not fully verifiable, the unverified tail.
- Simulation/research artifact. Verify outputs with the included checker before relying on them.

## Lineage and license

- Base: DeepSeek-R1-Distill-Qwen-1.5B (MIT).
- Training chains distilled from DeepSeek V4 (distillation permitted; output rights assigned to the
  user). Released under MIT to match the base.
- Attribution: Rama Krishna Bachu, Bottensor (Independent Research). ORCID 0009-0000-1298-0681.

## Reproducibility

The pre-registration was frozen BEFORE any training and an honest-null clause was in force.
Frozen references:
- Verifier: `VERIFIER.lock` sha256 `d5d146cf...`
- Eval set: `EVAL.lock` sha256 `e1573cab...`
- Pre-registration: `PREREG.lock` sha256 `b5a49437...`

GGUF quantizations are provided with a per-quant decision-fidelity check vs the bf16 model
(see `gguf_fidelity.md`); pick the recommended quant, do not choose on file size alone.