SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training | Paper Citation Record

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This paper cites TherML: Thermodynamics of Machine Learning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training TherML: Thermodynamics of Machine Learning

Reference 1

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This paper cites SGD with Large Step Sizes Learns Sparse Features.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training SGD with Large Step Sizes Learns Sparse Features

Reference 2

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This paper cites wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations

Reference 3

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This paper cites Implicit gradient regularization.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Implicit gradient regularization

Reference 4

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This paper cites Reconciling modern machine- learning practice and the classical bias–variance trade-off.Proceedings of the National Academy of Science, 116(32):15849–15854, 2019.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Reconciling modern machine- learning practice and the classical bias–variance trade-off.Proceedings of the National Academy of Science, 116(32):15849–15854, 2019

Reference 5

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This paper cites Practical recommendations for gradient-based training of deep architectures.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Practical recommendations for gradient-based training of deep architectures

Reference 6

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This paper cites Language Models are Few-Shot Learners.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Language Models are Few-Shot Learners

Reference 7

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This paper cites Stochastic gradient descent performs variational infer- ence, converges to limit cycles for deep networks.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic gradient descent performs variational infer- ence, converges to limit cycles for deep networks

Reference 8

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This paper cites Entropy-SGD: Biasing gradient descent into wide valleys.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Entropy-SGD: Biasing gradient descent into wide valleys

Reference 9

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This paper cites Convergence diagnostics for stochastic gradient descent with constant learning rate.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Convergence diagnostics for stochastic gradient descent with constant learning rate

Reference 10

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This paper cites Sudden drops in the loss: Syntax acquisition, phase transitions, and simplicity bias in MLMs.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Sudden drops in the loss: Syntax acquisition, phase transitions, and simplicity bias in MLMs

Reference 11

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This paper cites Stochastic collapse: How gra- dient noise attracts SGD dynamics towards simpler subnetworks.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic collapse: How gra- dient noise attracts SGD dynamics towards simpler subnetworks

Reference 12

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This paper cites Symbolic discovery of optimization algorithms.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Symbolic discovery of optimization algorithms

Reference 13

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Observation 16d05eca-ae36-4b1d-8361-dbe6d71bc8d8 · outbound

This paper cites Gradient descent on neural networks typically occurs at the edge of stability.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Gradient descent on neural networks typically occurs at the edge of stability

Reference 14

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This paper cites URL https://constructor.tech/products/ research-platform.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training URL https://constructor.tech/products/ research-platform

Reference 15

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This paper cites Determining intrinsic dimension and entropy of high-dimensional shape spaces.Modeling and Simulation in Science, Engineering and Technology, pages 231–252,.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Determining intrinsic dimension and entropy of high-dimensional shape spaces.Modeling and Simulation in Science, Engineering and Technology, pages 231–252,

Reference 16

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This paper cites Why do we need weight decay in modern deep learning? InAdvances in Neural Information Processing Systems, 2024.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Why do we need weight decay in modern deep learning? InAdvances in Neural Information Processing Systems, 2024

Reference 17

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This paper cites BERT: Pre-training of deep bidirectional transformers for language understanding.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training BERT: Pre-training of deep bidirectional transformers for language understanding

Reference 18

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This paper cites Essentially no barriers in neural network energy landscape.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Essentially no barriers in neural network energy landscape

Reference 19

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This paper cites Du, Xiyu Zhai, Barnabas Poczos, and Aarti Singh.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Du, Xiyu Zhai, Barnabas Poczos, and Aarti Singh

Reference 20

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This paper cites A free-energy principle for representation learning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training A free-energy principle for representation learning

Reference 21

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This paper cites Fixed-time stable gradient flows: Applications to continuous- time optimization.IEEE Transactions on Automatic Control, 66(5):2002–2015, 2021.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Fixed-time stable gradient flows: Applications to continuous- time optimization.IEEE Transactions on Automatic Control, 66(5):2002–2015, 2021

Reference 22

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Observation 8b483a68-5559-4e66-8690-821feaafcd8d · outbound

This paper cites Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs

Reference 23

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This paper cites Stochastic training is not necessary for generalization.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic training is not necessary for generalization

Reference 24

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This paper cites Abrupt learning in transformers: A case study on matrix completion.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Abrupt learning in transformers: A case study on matrix completion

Reference 25

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This paper cites Deep Residual Learning for Image Recognition.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Deep Residual Learning for Image Recognition

Reference 26

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This paper cites Three Factors Influencing Minima in SGD.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Three Factors Influencing Minima in SGD

Reference 27

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This paper cites Scaling Laws for Neural Language Models.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Scaling Laws for Neural Language Models

Reference 28

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This paper cites Kingma and Jimmy Ba.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Kingma and Jimmy Ba

Reference 29

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This paper cites Training scale-invariant neural networks on the sphere can happen in three regimes.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Training scale-invariant neural networks on the sphere can happen in three regimes

Reference 30

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This paper cites Big Transfer (BiT): General Visual Representation Learning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Big Transfer (BiT): General Visual Representation Learning

Reference 31

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This paper cites CIFAR-10 (canadian institute for advanced research).

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training CIFAR-10 (canadian institute for advanced research)

Reference 32

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This paper cites CIFAR-100 (canadian institute for advanced research).

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training CIFAR-100 (canadian institute for advanced research)

Reference 33

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SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 34

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Observation e8891303-7c11-46e5-a72a-ea91e4b653c2 · outbound

This paper cites Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks

Reference 35

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This paper cites Few-shot adaptation of multi-modal foundation models: A survey.Artificial Intelli- gence Review, 57(10):268, 2024.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Few-shot adaptation of multi-modal foundation models: A survey.Artificial Intelli- gence Review, 57(10):268, 2024

Reference 36

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This paper cites Understanding why neural networks generalize well through GSNR of parameters.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Understanding why neural networks generalize well through GSNR of parameters

Reference 37

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This paper cites Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent

Reference 38

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This paper cites Towards understanding grokking: An effective theory of representation learning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Towards understanding grokking: An effective theory of representation learning

Reference 39

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This paper cites On the periodic behavior of neural network training with batch normalization and weight decay.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training On the periodic behavior of neural network training with batch normalization and weight decay

Reference 40

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Observation ebebddeb-4929-498a-92c9-45e220a39e4c · outbound

This paper cites Decoupled weight decay regularization.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Decoupled weight decay regularization

Reference 41

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This paper cites The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning

Reference 42

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Observation 77d1edcc-38ab-401e-b0ef-e3fa9d5b9094 · outbound

This paper cites Stochastic Gradient Descent as Approximate Bayesian Inference.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic Gradient Descent as Approximate Bayesian Inference

Reference 43

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This paper cites Phase transitions in the mini-batch size for sparse and dense two-layer neural networks.Machine Learning: Science and Technology, 5(1): 015015, 2024.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Phase transitions in the mini-batch size for sparse and dense two-layer neural networks.Machine Learning: Science and Technology, 5(1): 015015, 2024

Reference 44

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Observation e3d4a475-5726-4fab-a6a2-aa39e708545e · outbound

This paper cites Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate

Reference 45

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Observation c781f22f-abda-448a-8f2d-7ad84fdf099d · outbound

This paper cites Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases

Reference 46

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Observation 56031d6d-5de4-4f21-af93-d6af4d27f522 · outbound

This paper cites Deep double descent: Where bigger models and more data hurt.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Deep double descent: Where bigger models and more data hurt

Reference 47

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Observation 7ffc897f-72ea-47a6-bea6-e32e919e7dbe · outbound

This paper cites LR0.FM: Low-resolution zero-shot classification benchmark for foundation models.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training LR0.FM: Low-resolution zero-shot classification benchmark for foundation models

Reference 48

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Observation 1de94719-1f6a-4d71-bf51-888bc13cb8d8 · outbound

This paper cites Loss landscape: SGD has a better view.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Loss landscape: SGD has a better view

Reference 49

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Observation d099425f-38a9-4378-810d-088fb2301e2c · outbound

This paper cites Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 50

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Observation 37f347c5-f46a-48a5-9ea0-de6afe4c3d50 · outbound

This paper cites Accelerating Large Batch Training via Gradient Signal to Noise Ratio (GSNR).

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Accelerating Large Batch Training via Gradient Signal to Noise Ratio (GSNR)

Reference 51

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Observation cf4970ed-0469-497f-8a72-61ba9cb8f5d3 · outbound

This paper cites Learning transferable visual models from natural language supervision.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Learning transferable visual models from natural language supervision

Reference 52

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Observation c01f840f-b890-48a8-9bd6-8d601ae36896 · outbound

This paper cites Where do large learning rates lead us? InAdvances in Neural Information Processing Systems, 2024.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Where do large learning rates lead us? InAdvances in Neural Information Processing Systems, 2024

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:55.111425Z

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This paper cites On the different regimes of stochastic gradient descent.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training On the different regimes of stochastic gradient descent

Reference 54

Resolution: verified exact; doi, observed 2026-08-07T12:48:46.818627Z

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Observation 8bff367d-c3eb-4f2e-9e81-ef15edefd85c · outbound

This paper cites an unresolved cited work.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:48:54.855090Z

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Observation 7d61f117-34a8-45cb-ae16-2c4881bc476d · outbound

This paper cites On the Generalization Benefit of Noise in Stochastic Gradient Descent.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training On the Generalization Benefit of Noise in Stochastic Gradient Descent

Reference 56

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T12:48:48.284766Z

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Observation f6fec504-538a-4709-8a10-96d443fc7f7d · outbound

This paper cites On the origin of implicit regular- ization in stochastic gradient descent.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training On the origin of implicit regular- ization in stochastic gradient descent

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:54.580089Z

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Observation 53d40a8b-67e4-44b8-a71e-b3fa1970713e · outbound

This paper cites Beyond the imitation game: Quantifying and extrapolating the capabilities of language models.Transactions on Machine Learning Research, 2023.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Beyond the imitation game: Quantifying and extrapolating the capabilities of language models.Transactions on Machine Learning Research, 2023

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:54.032448Z

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Observation f553db86-34a5-4eb8-bc03-012018789d0a · outbound

This paper cites Unleashing the power of gradient signal-to-noise ratio for zero-shot NAS.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unleashing the power of gradient signal-to-noise ratio for zero-shot NAS

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:44.069104Z

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This paper cites Deep learning and the information bottleneck principle,.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Deep learning and the information bottleneck principle,

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:53.747474Z

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Observation c6382461-7c03-4953-8b2a-bf1fc8f2f61e · outbound

This paper cites The discovery of superconductivity.Physics Today, 63(9):38–43,.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training The discovery of superconductivity.Physics Today, 63(9):38–43,

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:53.425800Z

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Observation c81ca0d2-a013-4afd-9237-66511ad32f92 · outbound

This paper cites A survey of basic thermodynamics, 2004.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training A survey of basic thermodynamics, 2004

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:53.156648Z

Source-reported events for the cited work

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Observation a41a7fe5-488a-4fe5-99fa-cfca3b4be752 · outbound

This paper cites Chi, Tatsunori Hashimoto, Oriol Vinyals, Percy Liang, Jeff Dean, and William Fedus.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Chi, Tatsunori Hashimoto, Oriol Vinyals, Percy Liang, Jeff Dean, and William Fedus

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:52.817300Z

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Observation 6e7e1725-9700-4565-b8c1-8edda39592b0 · outbound

This paper cites Bayesian learning via stochastic gradient langevin dynamics.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Bayesian learning via stochastic gradient langevin dynamics

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:52.531469Z

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Observation d38b50ff-745b-4cc9-a359-5708d3fc7698 · outbound

This paper cites Towards few- shot adaptation of foundation models via multitask finetuning.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Towards few- shot adaptation of foundation models via multitask finetuning

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:52.147253Z

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Observation fc4b5a34-80a4-473f-af50-29d8dd8d6472 · outbound

This paper cites Fluctuation-dissipation relations for stochastic gradient descent.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Fluctuation-dissipation relations for stochastic gradient descent

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:51.794687Z

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Observation faf4f39e-dd6a-4079-a3d0-c9e1dd180e17 · outbound

This paper cites How Does Learning Rate Decay Help Modern Neural Networks?.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training How Does Learning Rate Decay Help Modern Neural Networks?

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:45.281153Z

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Observation 7b3fab21-76e1-4d7e-ba52-3c684d880759 · outbound

This paper cites Saxe, Madhu S.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Saxe, Madhu S

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:45.411715Z

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Observation 81a29911-f563-4fdb-99d5-79ca2eeb6d7f · outbound

This paper cites Strength of minibatch noise in SGD.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Strength of minibatch noise in SGD

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:51.465143Z

Source-reported events for the cited work

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Observation 23174278-5a2e-4102-a24b-ad149a96c37a · outbound

This paper cites Stochastic gradient descent opti- mizes over-parameterized deep ReLU networks, 2018.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Stochastic gradient descent opti- mizes over-parameterized deep ReLU networks, 2018

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:51.044331Z

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Observation 81c054d8-a7b3-4c13-be06-505ae14b05ce · outbound

This paper cites g., unit sphere in our case), can be interpreted as fixed volume.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training g., unit sphere in our case), can be interpreted as fixed volume

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:50.794185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 93744545-3594-4ef4-80f8-fe9de8266bcb · outbound

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SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 78

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:48:50.601439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 72fb72a9-53b7-49f6-8bd8-c24002a51a42 · outbound

This paper cites An additional justification for using the Helmholtz free energy arises from the stationary distributions of SGD.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training An additional justification for using the Helmholtz free energy arises from the stationary distributions of SGD

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:48:50.308842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2e36e8c0-bfb9-47c7-831e-035b7aa6f484 · outbound

This paper cites an unresolved cited work.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 2007

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:38.550624Z

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Unavailable: canonical work link unavailable.

Observation 11e721c2-df99-4bf3-a9f3-95e2df384f1c · outbound

This paper cites an unresolved cited work.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 2010

Resolution: verified exact; doi, observed 2026-08-07T12:48:46.474308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8b7de796-ebd5-4559-89b7-2c70f9b31ada · outbound

This paper cites Deep Learning and the Information Bottleneck Principle.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Deep Learning and the Information Bottleneck Principle

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:44.291906Z

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Observation fc848c5b-e058-4feb-9c30-8229cef5be8e · outbound

This paper cites Essentially No Barriers in Neural Network Energy Landscape.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Essentially No Barriers in Neural Network Energy Landscape

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-07T12:48:38.980064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 541da72f-9f5e-4f2a-b0ea-81eb4a9d7495 · outbound

This paper cites an unresolved cited work.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 2019

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:48:58.968877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed43d29b-cfc1-4ed2-a31a-9f7e8047b64f · outbound

This paper cites an unresolved cited work.

SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training Unresolved cited work

Reference 2021

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:48:54.317558Z

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