# The Tree Loss: Improving Generalization with Many Classes

Source: [The Tree Loss: Improving Generalization with Many Classes](<https://www.sota2.com/research/paper/68fa6c5c1e209131cea33903>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T00:08:48.414Z

Authors: Yujie Wang, Mike Izbicki

Published: 2022-04-16T05:46:36.000Z

## Abstract

Multi-class classification problems often have many semantically similar classes. For example, 90 of ImageNet's 1000 classes are for different breeds of dog. We should expect that these semantically similar classes will have similar parameter vectors, but the standard cross entropy loss does not enforce this constraint.   We introduce the tree loss as a drop-in replacement for the cross entropy loss. The tree loss re-parameterizes the parameter matrix in order to guarantee that semantically similar classes will have similar parameter vectors. Using simple properties of stochastic gradient descent, we show that the tree loss's generalization error is asymptotically better than the cross entropy loss's. We then validate these theoretical results on synthetic data, image data (CIFAR100, ImageNet), and text data (Twitter).

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2204.07727>)

[PDF](<https://arxiv.org/pdf/2204.07727.pdf>)