Invariant Atoms: Sparse Coordinates of Local Semantic Geometry in Language Model Representations

arXiv:2609.36451 · cs.LG, cs.CL · Submitted 2026-09-29 · Read on arXiv

cs.LG, cs.CL

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Sparsity — 19× in this paper · explained in 4 episodes
• Adaptation — 18× in this paper · explained in 1 episode
• Generalization — 17× in this paper · explained in 13 episodes
• Cosine Similarity — 9× in this paper · explained in 3 episodes
• Fine-Tuning — 9× in this paper · explained in 5 episodes
• Ablation — 8× in this paper · explained in 1 episode
• Distillation — 8× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Alignment — 5× in this paper · explained in 1 episode
• Consistency — 5× in this paper · explained in 3 episodes
• Transformer — 5× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Steering — 3× in this paper · explained in 2 episodes
• Local Optimization — 2× in this paper · explained in 2 episodes
• Reconstruction Error — 2× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Representation Learning — 2× in this paper · explained in 2 episodes
• Activation Sparsity — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Fingerprinting — 1× in this paper · explained in 2 episodes
• LoRA Adaptation — 1× in this paper · explained in 2 episodes
• LoRA Adapters — 1× in this paper · explained in 3 episodes
• Pairwise Comparisons — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Stiefel manifold — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Two-Stage Optimization — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks