In the high-dimensional limit the spherical Boltzmann machine admits exact equations for training dynamics, Bayesian evidence, and cascades of phase transitions tied to mode alignment with data, which connect to generative phenomena including double descent and out-of-equilibrium biases.
citation dossier
Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
17Pith papers citing it
18reference links
cs.LGtop field · 12 papers
UNVERDICTEDtop verdict bucket · 12 papers
why this work matters in Pith
Pith has found this work in 17 reviewed papers. Its strongest current cluster is cs.LG (12 papers). The largest review-status bucket among citing papers is UNVERDICTED (12 papers). For highly cited works, this page shows a dossier first and a bounded explorer second; it never tries to render every citing paper at once.
representative citing papers
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
Residual networks reformulate layers to learn residual functions, enabling effective training of up to 152-layer models that achieve 3.57% error on ImageNet and win ILSVRC 2015.
Batch Normalization normalizes layer inputs per mini-batch to reduce internal covariate shift, allowing higher learning rates, less careful initialization, and faster convergence in deep networks.
Brain data is worth a variable number of task samples depending on task-brain alignment, noise levels, and latent dimension, with conditions under which it also improves robustness to test distribution shift.
The global empirical NTK for finite-width networks has a universal Kronecker-core form that makes it structurally low-rank and biases gradient descent toward dominant modes of joint input-hidden activity.
A two-level DMFT predicts width-consistent outlier escape and hyperparameter transfer under μP in deep networks, with bulk restructuring dominating for tasks with many outputs.
Derives layer-wise recursions for finite-width tensors under orthogonal initialization that reproduce the observed large-depth stability of nonlinear networks.
Learning in low-rank RNNs reduces to an exact low-dimensional ODE system in overlap space, where loss-invisible overlaps encode training history without affecting function.
An exact norm-imbalance identity classifies activations into four classes and reduces deep nonlinear training flow to a scalar ODE that predicts saddle escape time scaling as ε to the power of minus (r-2) for r bottleneck layers.
Effective cascade dimension D(t) crosses D=1 at the grokking transition in MLPs and Transformers, with opposite directions for modular addition versus XOR, consistent with attraction to a shared critical manifold.
A gradient-transport framework with observables D, z, β, δ, v_rel applied to Pico-LM and Pythia datasets shows distinct scaling regimes in duration and efficiency while sharing a near-unity cascade-size backbone.
NORACL dynamically grows network capacity via neurogenesis-inspired signals to achieve oracle-level continual learning performance without pre-specifying architecture size.
S4D state space models correspond exactly to wave propagation and nonlinear wave interactions in a one-dimensional ring oscillator network, with a closed-form operator describing the complete input-output map.
Grokking occurs as the effective dimensionality of the gradient field transitions from sub-diffusive to super-diffusive at the onset of generalization, exhibiting self-organized criticality.
FLAME is an MoE architecture using modality-specific routers and low-rank compression of expert knowledge to support efficient continual multimodal multi-task learning while reducing catastrophic forgetting.
CDLinear layers achieve population Hessian condition number exactly 1 under pre-whitening, deliver 3.8x parameter reduction versus dense layers at 0.65% accuracy cost, and show 310x better empirical conditioning on an MLP.
citing papers explorer
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Spherical Boltzmann machines: a solvable theory of learning and generation in energy-based models
In the high-dimensional limit the spherical Boltzmann machine admits exact equations for training dynamics, Bayesian evidence, and cascades of phase transitions tied to mode alignment with data, which connect to generative phenomena including double descent and out-of-equilibrium biases.
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Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
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Deep Residual Learning for Image Recognition
Residual networks reformulate layers to learn residual functions, enabling effective training of up to 152-layer models that achieve 3.57% error on ImageNet and win ILSVRC 2015.
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Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
Batch Normalization normalizes layer inputs per mini-batch to reduce internal covariate shift, allowing higher learning rates, less careful initialization, and faster convergence in deep networks.
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How Much is Brain Data Worth for Machine Learning?
Brain data is worth a variable number of task samples depending on task-brain alignment, noise levels, and latent dimension, with conditions under which it also improves robustness to test distribution shift.
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The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learning
The global empirical NTK for finite-width networks has a universal Kronecker-core form that makes it structurally low-rank and biases gradient descent toward dominant modes of joint input-hidden activity.
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Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
A two-level DMFT predicts width-consistent outlier escape and hyperparameter transfer under μP in deep networks, with bulk restructuring dominating for tasks with many outputs.
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Criticality and Saturation in Orthogonal Neural Networks
Derives layer-wise recursions for finite-width tensors under orthogonal initialization that reproduce the observed large-depth stability of nonlinear networks.
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Learning reveals invisible structure in low-rank RNNs
Learning in low-rank RNNs reduces to an exact low-dimensional ODE system in overlap space, where loss-invisible overlaps encode training history without affecting function.
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A Theory of Saddle Escape in Deep Nonlinear Networks
An exact norm-imbalance identity classifies activations into four classes and reduces deep nonlinear training flow to a scalar ODE that predicts saddle escape time scaling as ε to the power of minus (r-2) for r bottleneck layers.
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Dimensional Criticality at Grokking Across MLPs and Transformers
Effective cascade dimension D(t) crosses D=1 at the grokking transition in MLPs and Transformers, with opposite directions for modular addition versus XOR, consistent with attraction to a shared critical manifold.
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Finite-Size Gradient Transport in Large Language Model Pretraining: From Cascade Size to Intensive Transport Efficiency
A gradient-transport framework with observables D, z, β, δ, v_rel applied to Pico-LM and Pythia datasets shows distinct scaling regimes in duration and efficiency while sharing a near-unity cascade-size backbone.
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NORACL: Neurogenesis for Oracle-free Resource-Adaptive Continual Learning
NORACL dynamically grows network capacity via neurogenesis-inspired signals to achieve oracle-level continual learning performance without pre-specifying architecture size.
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An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
S4D state space models correspond exactly to wave propagation and nonlinear wave interactions in a one-dimensional ring oscillator network, with a closed-form operator describing the complete input-output map.
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Grokking as Dimensional Phase Transition in Neural Networks
Grokking occurs as the effective dimensionality of the gradient field transitions from sub-diffusive to super-diffusive at the onset of generalization, exhibiting self-organized criticality.
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FLAME: Adaptive Mixture-of-Experts for Continual Multimodal Multi-Task Learning
FLAME is an MoE architecture using modality-specific routers and low-rank compression of expert knowledge to support efficient continual multimodal multi-task learning while reducing catastrophic forgetting.
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Communication Dynamics Neural Networks: FFT-Diagonalized Layers for Improved Hessian Conditioning at Reduced Parameter Count
CDLinear layers achieve population Hessian condition number exactly 1 under pre-whitening, deliver 3.8x parameter reduction versus dense layers at 0.65% accuracy cost, and show 310x better empirical conditioning on an MLP.