Researchers Hadi Salloum and Ammar Ali have introduced Tree-Ising, a novel method for repairing reasoning loops in large language models (LLMs) by solving sparse Ising or Quadratic Unconstrained Binary Optimization (QUBO) problems. Published on November 10, 2026, on arXiv (2611.14210) and featured on HuggingFace Daily Papers, the method demonstrates significant improvements in mathematical reasoning benchmarks while reducing computational costs.

How Tree-Ising Works

Tree-Ising operates by casting the repair of reasoning loops as a sparse discrete optimization problem over the model's BF16 weights. The approach uses forward-pass statistics to define an objective that weakens incorrect loop directions, strengthens correct concluding directions, and preserves productive token outputs. Admissible edits are limited to sign flips and exponent shifts, ensuring the preservation of shared group exponents and mantissas in the model's state-tree representation.

The optimization problem is decomposed into independent QUBO problems, one for each output row. These are solved using either simulated annealing or quantum-inspired simulated bifurcation, both of which run efficiently on GPUs. Notably, the method requires only four forward-pass requests and zero LLM tokens, with the annealing process costing approximately $0.90 in GPU time.

Performance and Benchmark Results

Tree-Ising was evaluated on the Qwen3.5-0.8B model, achieving a 54.6% accuracy on the MATH-500 benchmark, outperforming a previous repair by GPT-6 Astra (51.7%) under the same protocol. The simulated bifurcation solver yielded a slightly higher accuracy of 55.1%, with both solvers showing statistically significant improvements across all five math benchmarks, including GSM8K. The base model, by contrast, scored only 7.9% on MATH-500.

On the larger Qwen3.5-2B model, Tree-Ising increased greedy GSM8K accuracy from 21.6% to 69.4%, using only the base model to select layers and dose. Additionally, the method modified 13% to 17% fewer weights and reduced BF16 bit flips by a factor of 2.2 to 2.3 compared to previous approaches.

Open-Source Implementation

The Tree-Ising project is available as an open-source repository on GitHub (https://github.com/TheQuantumGOAT/Tree-Ising). The implementation includes tools for simulated annealing, simulated bifurcation, and experimental repair loops. Users can clone the repository and set up a Python 3.11 environment to reproduce the experiments. The framework supports Linux systems with NVIDIA CUDA GPUs, and the provided dependencies ensure compatibility with CUDA 12.9 and Python 3.11.

As a proof of concept, the researchers also executed an eight-variable repair subproblem using the Quantum Approximate Optimization Algorithm (QAOA) on an IBM Heron quantum processor, demonstrating the potential for quantum hardware in future applications.