A 4-index supersymmetric formalism with minimal spontaneous supersymmetry breaking computes annealed and quenched complexity of stationary points via the Kac-Rice formula.
Journal of Physics A: Mathematical and General , volume =
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A threshold κ=Θ(1/√α) (α=m/n) separates easy collision finding from OGP-based exponential lower bounds against online algorithms in single-layer binary NNs.
DenseAMs show tradeoffs between entropy production, retrieval accuracy, and speed at intermediate loads, with a new failure mode in higher-order networks at finite temperature.
Derives the asymptotic ratio of storage capacities between real-constrained and complex pre-activations in complex neural networks using Gardner volumes and the HCIZ formula.
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
RG-inspired lattice models for piecewise GLMs provide explicit interpretable partitions and a replica-analysis-derived scaling law for regularization that allows increasing complexity without expected rise in generalization loss.
Thesis uses statistical mechanics to study DAM and RBM models for understanding memorization, low-dimensional learning, and adversarial robustness in neural networks.
citing papers explorer
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Stationary point complexity via minimal supersymmetry breaking
A 4-index supersymmetric formalism with minimal spontaneous supersymmetry breaking computes annealed and quenched complexity of stationary points via the Kac-Rice formula.
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Collision Resistance of Single-Layer Neural Nets
A threshold κ=Θ(1/√α) (α=m/n) separates easy collision finding from OGP-based exponential lower bounds against online algorithms in single-layer binary NNs.
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Stochastic Thermodynamics of Associative Memory
DenseAMs show tradeoffs between entropy production, retrieval accuracy, and speed at intermediate loads, with a new failure mode in higher-order networks at finite temperature.
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Shortcomings and capacities of real-constrained neural networks in complex spaces
Derives the asymptotic ratio of storage capacities between real-constrained and complex pre-activations in complex neural networks using Gardner volumes and the HCIZ formula.
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Detecting overfitting in Neural Networks during long-horizon grokking using Random Matrix Theory
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
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A renormalization-group inspired lattice-based framework for piecewise generalized linear models
RG-inspired lattice models for piecewise GLMs provide explicit interpretable partitions and a replica-analysis-derived scaling law for regularization that allows increasing complexity without expected rise in generalization loss.
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Explaining Machine Learning and Memorization with Statistical Mechanics
Thesis uses statistical mechanics to study DAM and RBM models for understanding memorization, low-dimensional learning, and adversarial robustness in neural networks.