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NeurIPs Paper Reviews 2023 #4

NeurIPs Paper Reviews 2023 #4

23 January 2024
  • Quantitative Research

Our team of quantitative researchers have shared the most interesting research presented during workshops and seminars at NeurIPs 2023.

Discover the perspectives of our scientific director Dustin as he discusses his most compelling findings from the conference.

Abide by the law and follow the flow: conservation laws for gradient flows

Sibylle Marcotte, Remi Gribonval, Gabriel Peyré

Think of neural network training as a dynamical system obeying the laws of classical mechanics. The loss function L is like a potential energy surface, and the NN weights W follow trajectories of steepest descent according to “laws of motion”, which are defined by a differential equation dW/dt = -k * dL/dW. The authors show that the NN weights obey conservation laws just like conservation of energy in classical mechanics.

For example, for a 1-dimensional, 2-layer ReLU network with two weights u and v, there is one conserved quantity h = u^2 – v^2. This implies that the initial choice of weights is important as the final state is constrained to keep h constant throughout training. This builds on previous work (Zhao 2022) which argues that these conservation laws induce an inductive bias towards “flat” minima of the loss function, which reduces overfitting and makes training more robust.

The paper contains a complicated procedure for computing the conserved quantities for more complicated NNs, but the slides have some nice pictures illustrating the 1-d example. I like it because it is a neat way to understand NN training using ideas from physics. It also suggests that bigger NNs with more parameters might work well.

Abide by the law and follow the flow: conservation laws for gradient flows
NeurIPS 2022 Paper Reviews

Read paper reviews from NeurIPS 2022 from a number of our quantitative researchers and machine learning practitioners.

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The Tunnel Effect: Building Data Representations in Deep Neural Networks

Wojciech Masarczyk, Mateusz Ostaszewski, Ehsan Imani, Razvan Pascanu, Piotr Miłoś, Tomasz Trzcinski 

In a deep 18-layer neural network for image classification, the layers can be divided into two distinct roles. The first 8 layers act as a feature “extractor”, and are responsible for most of the predictive power of the network. The following 10 layers act as a “tunnel”, whose purpose is to compress the intermediate activation vector in to a low-dimensional embedding.

According to the authors, the “extractor” attains >99% of the final prediction accuracy, and that the numerical rank of the weight matrices in the “tunnel” collapses to log(d) where d is the number of output classes. The authors perform a number of experiments: combining the “extractor” trained on one task with the “tunnel” trained on a different task. They show that the “extractor” is task-specific but the “tunnel” is the same for both tasks.

I like it because it is a nice, practical way to understand NN training dynamics, which seems to conclude with a meaningful interpretation. I would be curious to see if this holds for other architectures and datasets. I like the use of intermediate metrics (like numerical rank of intermediate layers) to probe what’s happening during training.

The Tunnel Effect: Building Data Representations in Deep Neural Networks

Quantitative Research and Machine Learning

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Read more of our quantitative researchers thoughts

NeurIPs Paper Reviews 2023 #1

Discover the perspectives of Danny, one of our machine learning engineers, on the following papers:

  • A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning
  • Normalization Layers Are All That Sharpness-Aware Minimization Needs
Paper Review #1
NeurIPs Paper Reviews 2023 #2

Discover the perspectives of Paul, one of our quantitative researchers, on the following papers:

  • Sharpness-Aware Minimization Leads to Low-Rank Features
  • When Do Neural Nets Outperform Boosted Trees on Tabular Data?
Paper Review #2
NeurIPs Paper Reviews 2023 #3

Discover the perspectives of Szymon, one of our quantitative researchers, on the following papers:

  • Convolutional State Space Models for Long-Range Spatiotemporal Modeling
  • How to Scale Your EMA
Paper Review #3
NeurIPS Paper Review 2023 #5

Discover the perspectives of Laurynas, one of our machine learning engineers, on the following papers:

  • Monarch Mixer: A Simple Sub-Quadratic GEMM-Based Architecture
  • QLoRA: Efficient Finetuning of Quantized LLMs
Paper Review #5
NeurIPS Paper Review 2023 #6

Discover the perspectives of Rui, one of our quantitative analysts, on the following papers:

  • Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting
  • Conformal Prediction for Time Series with Modern Hopfield Networks
Paper Review #6

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