[Paper Review] LCA: Loss Change Allocation for Neural Network Training

Janice Lan, Rosanne Liu+2 more|arXiv (Cornell University)|Jan 1, 2019

Model Reduction and Neural Networks12 citations

TL;DR

This paper introduces Loss Change Allocation (LCA), a method that conservatively partitions changes in neural network loss to individual parameters using a Runge-Kutta-based path integral approximation. LCA reveals that only ~50% of parameters contribute positively at any training step, some layers actively hurt learning due to phase lag, and learning increments synchronize across layers.

ABSTRACT

Neural networks enjoy widespread use, but many aspects of their training, representation, and operation are poorly understood. In particular, our view into the training process is limited, with a single scalar loss being the most common viewport into this high-dimensional, dynamic process. We propose a new window into training called Loss Change Allocation (LCA), in which credit for changes to the network loss is conservatively partitioned to the parameters. This measurement is accomplished by decomposing the components of an approximate path integral along the training trajectory using a Runge-Kutta integrator. This rich view shows which parameters are responsible for decreasing or increasing the loss during training, or which parameters or the network's learning, respectively. LCA may be summed over training iterations and/or over neurons, channels, or layers for increasingly coarse views. This new measurement device produces several insights into training. (1) We find that barely over 50% of parameters help during any given iteration. (2) Some entire layers hurt overall, moving on average against the training gradient, a phenomenon we hypothesize may be due to phase lag in an oscillatory training process. (3) Finally, increments in learning proceed in a synchronized manner across layers, often peaking on identical iterations.

Motivation & Objective

• To address the limited interpretability of neural network training, where only a scalar loss is typically monitored.
• To develop a method that provides fine-grained insight into which parameters contribute to loss reduction or increase during training.
• To understand the dynamic role of individual parameters, neurons, and layers in the training process.
• To investigate whether learning occurs in synchronized bursts across layers and whether some components actively hinder optimization.

Proposed method

• LCA decomposes the path integral of the loss gradient along the training trajectory using a Runge-Kutta integrator to compute loss change allocation.
• It conservatively assigns credit for loss changes to individual parameters based on their contribution along the optimization path.
• The method enables per-parameter, per-layer, or per-neuron analysis by summing LCA values over iterations or structural units.
• LCA is computed iteratively over training steps, allowing tracking of parameter-level contributions over time.
• The approach uses an approximate path integral to handle the high-dimensional, non-linear dynamics of stochastic gradient descent.
• LCA can be aggregated across iterations or layers to produce coarse-grained views of network learning dynamics.

Experimental results

Research questions

• RQ1 Which parameters are responsible for reducing or increasing the loss during each training iteration?
• RQ2 What fraction of parameters actively contribute to loss reduction at any given step?
• RQ3 Do entire layers sometimes work against the training objective, and if so, why?
• RQ4 Is learning in neural networks synchronized across layers, and do learning bursts occur simultaneously?

Key findings

• On average, fewer than 50% of parameters contribute positively to loss reduction in any given training iteration.
• Some entire layers exhibit a net negative contribution to loss reduction, moving against the training gradient on average.
• The observed layer-level harm is hypothesized to stem from phase lag in an oscillatory training process.
• Learning increments across layers are synchronized, often peaking on the same training iterations.
• LCA reveals that parameter-level contributions to loss change are highly dynamic and temporally variable.
• The method uncovers previously hidden dynamics, such as non-uniform and non-monotonic contributions of parameters to optimization.