CLEARMIND: Closed-Form Laplacian Embeddings of Arakelov-Green Resistance for Morphological Intrinsic Neuronal Distances

arXiv:2608.04460 · cs.LG, cs.AI, cs.CG · Submitted 2026-08-05 · Read on arXiv

cs.LG, cs.AI, cs.CG

Submitted: 2026-08-05

Updated: 2026-10-03

Code: https://github.com/Yyuzrah/CLEAR-MIND

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Polarization — 24× in this paper · explained in 2 episodes
• Accuracy — 21× in this paper · explained in 1 episode
• Quantization — 21× in this paper · explained in 15 episodes
• Augmentation — 16× in this paper · explained in 2 episodes
• GNNs — 11× in this paper · explained in 2 episodes
• Benchmark — 10× in this paper · explained in 2 episodes
• Spectral Signature — 10× in this paper · explained in 2 episodes
• Embeddings — 7× in this paper · explained in 2 episodes
• Expressivity — 7× in this paper · explained in 2 episodes
• Transformer — 6× in this paper · explained in 2 episodes
• Weight Decay — 6× in this paper · explained in 2 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Adam — 3× in this paper · explained in 3 episodes
• Decoupling — 3× in this paper · explained in 2 episodes
• Euclidean Distance Matrix — 3× in this paper
• Late Fusion — 3× in this paper · explained in 2 episodes
• Ablation Study — 2× in this paper · explained in 3 episodes
• Allen Cell Types — 2× in this paper
• Core — 2× in this paper · explained in 2 episodes
• Evaluation Protocol — 2× in this paper · explained in 2 episodes
• F1 Score — 2× in this paper · explained in 4 episodes
• Generator — 2× in this paper · explained in 2 episodes
• Latent Space — 2× in this paper · explained in 7 episodes
• Memorization — 2× in this paper · explained in 4 episodes
• Multilayer Perceptron (MLP) — 2× in this paper · explained in 2 episodes
• Orthogonal Projection — 2× in this paper · explained in 2 episodes
• Performance Gap — 2× in this paper · explained in 2 episodes
• Persistent Homology — 2× in this paper · explained in 4 episodes
• Representation Learning — 2× in this paper · explained in 3 episodes
• Topological Data Analysis — 2× in this paper
• Topological Data Analysis (TDA) — 2× in this paper · explained in 3 episodes
• Transformers — 2× in this paper · explained in 2 episodes
• Axioms — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 4 episodes
• Breadth-First Search — 1× in this paper
• Equivariance — 1× in this paper · explained in 3 episodes
• Feature Engineering — 1× in this paper · explained in 3 episodes
• Feature Extraction — 1× in this paper · explained in 3 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Graph Neural Networks (GNNs) — 1× in this paper · explained in 13 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Inflation — 1× in this paper · explained in 2 episodes
• NP-Hard Closest Vector Problem — 1× in this paper
• Objective Function — 1× in this paper · explained in 2 episodes
• Papers — 1× in this paper · explained in 3 episodes
• Permutation Equivariance — 1× in this paper · explained in 2 episodes
• Permutation Invariance — 1× in this paper · explained in 2 episodes
• Structural Encodings — 1× in this paper
• Transformer Architecture — 1× in this paper · explained in 4 episodes

Sources

• Metric Properties of the Tropical Abel-Jacobi Map
• Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs
• GraPHFormer: A Multimodal Graph Persistent Homology Transformer for the Analysis of Neuroscience Morphologies

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