Truncation causes different positional encoding families to have unequal expressive power in GNNs, with truncated spectral PEs limited to 1-WL strength, and mixing families improves results on real datasets.
Extensions of Lipschitz ma ps into a Hilbert space.Conference in modern analysis and pr obability (New Haven, Conn., 1982), Contemp
7 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 7representative citing papers
Defines representational capacity as the upper bound on distinguishable near-orthogonal directions in transformer latent spaces, derived from embedding similarity distributions and an adjusted Johnson-Lindenstrauss formula dependent on the k/d ratio.
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
A per-component SimHash fingerprint supplies structural identity for AI agent skills, recovering family membership under paraphrase and refactoring with AUC 0.974 while localizing changes.
Task-aligned supervised geometric stability predicts linear steerability with high accuracy while unsupervised stability detects representational drift earlier and with lower false alarms than CKA or Procrustes.
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
The paper analyzes participant opinions from a Physics of Life Reviews discussion on the simplicity revolution in high-dimensional neuroscience and its implications for machine learning.
citing papers explorer
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Understanding Truncated Positional Encodings for Graph Neural Networks
Truncation causes different positional encoding families to have unequal expressive power in GNNs, with truncated spectral PEs limited to 1-WL strength, and mixing families improves results on real datasets.
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Representational Capacity: Geometric Limits on Feature Representation in Transformer Language Models
Defines representational capacity as the upper bound on distinguishable near-orthogonal directions in transformer latent spaces, derived from embedding similarity distributions and an adjusted Johnson-Lindenstrauss formula dependent on the k/d ratio.
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Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
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The Decomposition Is the Fingerprint: Per-Component Identity for Agent Skills
A per-component SimHash fingerprint supplies structural identity for AI agent skills, recovering family membership under paraphrase and refactoring with AUC 0.974 while localizing changes.
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The Geometric Canary: Predicting Steerability and Detecting Drift via Representational Stability
Task-aligned supervised geometric stability predicts linear steerability with high accuracy while unsupervised stability detects representational drift earlier and with lower false alarms than CKA or Procrustes.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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Symphony of high-dimensional brain
The paper analyzes participant opinions from a Physics of Life Reviews discussion on the simplicity revolution in high-dimensional neuroscience and its implications for machine learning.