arcticoneai/xspark-X2.6-math

A 4B mathematical model based on Spark-X2.6-4B, evaluated on AIME without an enabled reasoning mode or agent harness, and evaluated on two difficult problems related to Ehrhart’s volume conjecture.

AIME: 50% base → 90% math-tuned  ·  Ehrhart evaluation

GITHUB — LEAN PROOFS & ATTEMPTS

Highlights

• AIME: 50% reported accuracy for the base Spark-X2.6-4B and 90% for xspark-X2.6-math, both without enabled reasoning; the math-model result is from an internal 50-question sample.
• Formal mathematics: evaluated on the equality-case classification for Ehrhart’s volume conjecture and on the general volume inequality. The two tasks and their verification status are described below.
• Model size: 4B parameters, based on Spark-X2.6-4B.

WARNING!

The results may not be accurate! I don't have the resources to check everything accurately! If you want to help with the project, write me a private message https://www.linkedin.com/in/bogdan-yunusov-278115405?utm_source=share_via&utm_content=profile&utm_medium=member_android Thank you!

AIME evaluation

AIME · Accuracy

50% → 90%

Spark-X2.6-4B base vs. xspark-X2.6-math · reasoning disabled

Spark-X2.6-4B (base) 50%

xspark-X2.6-math 90%

0255075100%

+40 pp 1.8× reported accuracy
without reasoning

The 90% result is from an internal 50-question AIME sample. The 50% base-model score is the reported baseline, not an independently audited result.

The comparison is project-reported, not an independently audited leaderboard submission. No agent harness or enabled reasoning was used for the reported 90% math-model run.

Ehrhart mathematics

The model was explored on two problems related to Ehrhart’s volume conjecture:

1. Equality case. Classification of convex bodies attaining equality in the conjectured volume bound, following Jihao Liu’s The Equality Case of Ehrhart’s Volume Conjecture. The reference characterizes the equality bodies, up to the relevant unimodular transformations, as centered standard simplices.

2. General inequality. For a full-dimensional compact convex body (K\subset\mathbb R^n) with barycenter at the origin and the origin as its unique interior lattice point, the target is

   [\operatorname{Vol}(K)\leq \frac{(n+1)^n}{n!}.]

The equality-case problem was studied using the paper’s proof structure and supplied excerpts. Attempts at the general inequality included low-dimensional examples and Lean 4 formalization, but no valid general proof was obtained. One Lean attempt relied on an unproved helper that restated the target inequality, so it is not a completed proof.

Proof attempts and Lean files: GITHUB — LEAN PROOFS & ATTEMPTS

Model and training

xspark-X2.6-math is based on the 4B Spark-X2.6 checkpoint. It uses a rank-16 LoRA adapter merged into BF16 weights, with teacher-reasoning distillation from eight specialized prompts. No separate adapter is required.

Usage

from transformers import AutoTokenizer, AutoModelForCausalLM

model_id = "arcticoneai/xspark-X2.6-math"

tokenizer = AutoTokenizer.from_pretrained(model_id, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(
    model_id,
    torch_dtype="auto",
    device_map="auto",
    trust_remote_code=True,
)

Use the thinking/reasoning prompt format expected by the Spark-X2.6 base model.

Limitations and next evaluations

• The 90% xspark-X2.6-math result is an internal 50-question evaluation without an agent harness or enabled reasoning; it is not a full standardized leaderboard submission.
• The 50% base-model figure is the reported baseline for this comparison; full raw per-question logs and an independently reproducible evaluation script should accompany a formal benchmark release.
• The Ehrhart equality-case discussion was guided by the cited paper; it is not claimed as an independently verified formalization.
• The general Ehrhart volume inequality remained unproved in the reviewed attempts.

This is an experimental research checkpoint. The reported results should be treated as preliminary until the evaluation protocol and complete Lean project are released.