Outliers with Opposing Signals Have an Outsized Effect on Neural Network Optimization (2311.04163v1)

Abstract: We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

• The paper demonstrates that outliers with opposing signals critically alter optimization landscapes, causing sharp oscillations in loss.
• It validates the phenomenon through experiments on models like ResNet-18, VGG-11, and Vision Transformers, showing consistent impact across datasets.
• The research links opposing signals to progressive sharpening, offering insights into improved training stability and robust model design.

Analyzing the Influence of Opposing Signals on Neural Network Optimization

The paper investigates a novel phenomenon in neural network (NN) optimization, emphasizing the critical role of outlier data points characterized by significant opposing signals. These outliers exert a disproportionate impact on the optimization dynamics of neural networks, guiding them into specific regions of the loss landscape and affecting the network's ability to learn efficiently. The research presents both experimental evidence and theoretical insights into how these outliers complicate training dynamics, including their contribution to progressive sharpening and the edge of stability.

The authors introduce the concept of paired groups of outliers containing large magnitude features that dominate the network's output during training. These outliers, defined by their opposing signals, dictate dynamic gradient directions, often swinging neural network training away from stability. Such phenomena result in the network navigating a narrow valley, balancing the opposing gradients before experiencing sharp oscillations in loss. These substitutions of class probabilities illustrate how a NN may become sensitive to simplistic spurious correlations instead of more generalizable patterns.

Experimental Framework and Observations

The experimental results demonstrate the prevalence of outlier pairs across architectures such as ResNet-18, VGG-11, and Vision Transformers on image data (specifically CIFAR-10) and extend to LLMs, showing broad applicability. Key findings include:

• Opposing signals lead to steep oscillations in loss landscape response, emphasizing the importance of feature magnitude tackling the concept of "sky $=$ plane" or "wheels $=$ car" association rapidly increasing and decreasing loss on relevant outlier groups.
• Early training stages are affected by simplistic features like color ratios or background patterns before progressing into more complex, yet similarly spurious, signals like textures.

These insights reflect known dynamics such as simplicity bias—the propensity for neural networks to latch onto easily distinguishable though potentially spurious patterns, processing functions of increasing complexity as training progresses.

Theoretical Contributions

The theoretical analysis aligns with their empirical findings through a simplified linear regression model with a two-layer network setup. This model demonstrates the detrimental influence of opposing signals on the progressive sharpening of the loss landscape and its associated instability. The following bold claims emerge from the paper:

• Initial sharpness intermittently decreases upon encountering significant opposing signals due to network attempts to reduce loss on these outliers.
• Progressive sharpening is attributed to the augmented sensitivity of the NN affecting the contribution of outliers to training variances.
• This link establishes a relationship between the opposition-induced training dynamics and the broader concepts of optimization stability.

These theoretical insights capture high-level behaviors, offering a new lens for the paper and enhancement of modern stochastic optimization practices.

Implications and Future Directions

The research has profound implications for understanding NN training dynamics and improving optimization algorithms like SGD and Adam. It sheds light on the elements influencing training at the edge of stability, providing practical guidance for architects to address these challenges in designing more robust models.

The framework laid out can stimulate further research into optimization behavior, with potential implications including advancing techniques for sharper minima avoidance, better feature selection processes, and reinforcing the regularizing effects of certain learned patterns. The recognition of commonalities among training phenomena, such as grokking and slingshotting, offers fertile ground for enhancing generalization heuristics in vast optimization spaces.

In conclusion, the investigation provides a critical understanding of how specific data structures can influence neural network optimization profoundly. By highlighting outlier effects, particularly with opposing signals, this work paves the way for more stable and generalizable machine learning models, encouraging future efforts to disentangle these phenomena's intertwined complexities.