Spectral-R1

Latent Energy-Based GRPO Reasoning

Teaching small models to reason about graphs through spectral energy alignment

Spectral-R1 trains compact language models to solve graph reasoning tasks by aligning latent representations with spectral energy objectives. Using a Contextual Hamiltonian formulation and Rayleigh Conjugate Descent, the model learns structured reasoning over weighted graphs -- achieving significant accuracy gains with shorter completions.

Dashboard

Key training and evaluation metrics.

41.3%

Accuracy (Erdos-Renyi)

33.8%

Accuracy (Power-law)

24.5%

Baseline (Erdos-Renyi)

-37%

Completion Length

1.2B

Model Size

Training

Status

Evaluation Results

Benchmark accuracy across graph topologies.

Benchmark	Topology	Accuracy	Baseline	Delta
JSON Pathfinder	Erdos-Renyi	41.3%	24.5%	+16.8pp
JSON Pathfinder	Power-law	33.8%	18.2%	+15.6pp
NLGraph	shortest_path	TBD	--	Pending
Reasoning-Gym	--	TBD	--	Pending

Accuracy Comparison

ER (ours)

41.3%

ER (base)

24.5%

PL (ours)

33.8%

PL (base)

18.2%

Reward Components

Accuracy

0.45

Format

0.85

Spectral

0.62

Method

Training pipeline and architecture overview.

[D]

Dataset

JSON Pathfinder

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[T]

GRPO Trainer

FSDP2 + vLLM

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[M]

Model

LFM2.5-1.2B

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[C]

Completions

max 512 tokens

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[R]

Reward

Acc + Fmt + Spectral