CMU Researchers Discover Key Insights into Neural Network Behavior: The Interplay of Heavy-Tailed Data and Network Depth in Shaping Optimization Dynamics

There’s a steadily rising record of intriguing properties of neural community (NN) optimization that aren’t readily defined by classical instruments from optimization. Likewise, the analysis crew has various levels of understanding of the mechanical causes for every. In depth efforts have led to potential explanations for the effectiveness of Adam, Batch Normalization, and different instruments for profitable coaching, however the proof is simply typically totally convincing, and there may be definitely little theoretical understanding. Different findings, comparable to grokking or the sting of stability, wouldn’t have fast sensible implications however present new methods to review what units NN optimization aside. These phenomena are sometimes thought-about in isolation, although they don’t seem to be fully disparate; it’s unknown what particular underlying causes they might share. A greater understanding of NN coaching dynamics in a selected context can result in algorithmic enhancements; this implies that any commonality might be a precious instrument for additional investigation. 

On this work, the analysis crew from Carnegie Mellon College identifies a phenomenon in neural community NN optimization that gives a brand new perspective on many of those prior observations, which the analysis crew hopes will contribute to a deeper understanding of how they might be linked. Whereas the analysis crew doesn’t declare to provide a whole rationalization, it presents robust qualitative and quantitative proof for a single high-level concept, which naturally suits into a number of present narratives and suggests a extra coherent image of their origin. Particularly, the analysis crew demonstrates the prevalence of paired teams of outliers in pure information, which considerably affect a community’s optimization dynamics. These teams embody a number of (comparatively) large-magnitude options that dominate the community’s output at initialization and all through many of the coaching. Along with their magnitude, the opposite distinctive property of those options is that they supply massive, constant, and opposing gradients, in that following one group’s gradient to lower its loss will improve the opposite’s by an analogous quantity. Due to this construction, the analysis crew refers to them as Opposing Alerts. These options share a non-trivial correlation with the goal activity however are sometimes not the “appropriate” (e.g., human-aligned) sign. 

In lots of instances, these options completely encapsulate the traditional statistical conundrum of “correlation vs. causation.” For instance, a brilliant blue sky background doesn’t decide the label of a CIFAR picture, nevertheless it does most frequently happen in photos of planes. Different options are related, such because the presence of wheels and headlights in photos of vans and vehicles or {that a} colon usually precedes both “the” or a newline token in written textual content. Determine 1 depicts the coaching lack of a ResNet-18  educated with full-batch gradient descent (GD) on CIFAR-10, together with a number of dominant outlier teams and their respective losses. 

Within the early levels of coaching, the community enters a slim valley in weight area, which fastidiously balances the pairs’ opposing gradients; subsequent sharpening of the loss panorama causes the community to oscillate with rising magnitude alongside specific axes, upsetting this stability. Returning to their instance of a sky background, one step ends in the category airplane being assigned larger likelihood for all photos with sky, and the subsequent will reverse that impact. In essence, the “sky = airplane” subnetwork grows and shrinks.1 The direct results of this oscillation is that the community’s loss on photos of planes with a sky background will alternate between sharply rising and lowering with rising amplitude, with the precise reverse occurring for photos of non-planes with the sky. Consequently, the gradients of those teams will alternate instructions whereas rising in magnitude as effectively. As these pairs characterize a small fraction of the info, this habits isn’t instantly obvious from the general coaching loss. Nonetheless, ultimately, it progresses far sufficient that the broad loss spikes. 

As there may be an apparent direct correspondence between these two occasions all through, the analysis crew conjectures that opposing alerts immediately trigger the sting of stability phenomenon. The analysis crew additionally notes that probably the most influential alerts seem to extend in complexity over time. The analysis crew repeated this experiment throughout a spread of imaginative and prescient architectures and coaching hyperparameters: although the exact teams and their order of look change, the sample happens constantly. The analysis crew additionally verified this habits for transformers on next-token prediction of pure textual content and small ReLU MLPs on easy 1D features. Nevertheless, the analysis crew depends on photos for exposition as a result of they provide the clearest instinct. Most of their experiments use GD to isolate this impact, however the analysis crew noticed related patterns throughout SGD—abstract of contributions. The first contribution of this paper is demonstrating the existence, pervasiveness, and huge affect of opposing alerts throughout NN optimization. 

The analysis crew additional presents their present finest understanding, with supporting experiments, of how these alerts trigger the noticed coaching dynamics. Specifically, the analysis crew supplies proof that it’s a consequence of depth and steepest descent strategies. The analysis crew enhances this dialogue with a toy instance and an evaluation of a two-layer linear internet on a easy mannequin. Notably, although rudimentary, their rationalization permits concrete qualitative predictions of NN habits throughout coaching, which the analysis crew confirms experimentally. It additionally supplies a brand new lens by way of which to review fashionable stochastic optimization strategies, which the analysis crew highlights by way of a case examine of SGD vs. Adam. The analysis crew sees potential connections between opposing alerts and numerous NN optimization and generalization phenomena, together with grokking, catapulting/slingshotting, simplicity bias, double descent, and Sharpness-Conscious Minimization.

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