Memorizing Long-tail Data Can Help Generalization Through Composition

Mo Zhou; Haoyang Ma; Rong Ge

cs.LGOct 18, 2025

Memorizing Long-tail Data Can Help Generalization Through Composition

Authors: Mo Zhou, Haoyang Ma, Rong Ge

Organizations: University of Washington · Duke University

Abstract

Deep learning has led researchers to rethink the relationship between memorization and generalization. In many settings, memorization does not hurt generalization due to implicit regularization and may help by memorizing long-tailed examples. In this paper, we consider the synergy between memorization and simple composition -- the ability to make correct prediction on a combination of long-tailed features. Theoretically, we show that for a linear setting, memorization together with composition can help the model make correct predictions on rare test examples that require a combination of long-tailed features, even if such combinations were never observed in the training data. Experiments on neural network architecture on simple data show that the theoretical insight extends beyond the linear setting, and we further observe that the composition capability of the model depends on its architecture.

Figures & tables

Panel of Figure 1 — Figure 1: (a)(b) Average Error on Common and Long-tail Features on Linear Model; (c)(d) In- and Out-of-Distribution Test Loss on Linear Model

Panel of Figure 2 — Figure 2: Test Performance Comparison Across Sum, Linear, 2-layer and Cross-channel Models

Model	WD = 0 (Memorization)	WD = 0.5 (No Memorization)
Sum	Test/Train Loss: 0.1760/0.0004	Test/Train Loss: 2.8744/0.0245
Linear	Test/Train Loss: 0.1662/0.0004	Test/Train Loss: 1.5539/0.0505
2-layer	Test/Train Loss: 0.1351/0.0010	Test/Train Loss: 0.6447/0.0264
Cross-channel	Test/Train Loss: 22.9671/0.0023	Test/Train Loss: 23.6506/0.0375

Table 1: Memorization behavior of ResNet variants under different weight decay (WD) settings

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Test loss as a function of the number of training occurrences of class 9.

Panel of Figure 4 — Figure 4: (Left) ResNet+ Linear layer with New Target Function: Test loss as a function of the number of training occurrences of class 9; (Right) ResNet+ 2-layer network with New Target Function: Test loss as a function of the number of training occurrences of class 9.

Model	Memorization (WD = 0)	No Memorization (WD = 0.5)
Sum	Test: 0.0697 Train: 0.0002	Test: 0.8266 Train: 0.0538
Linear	Test: 0.1171 Train: 0.0006	Test: 0.9571 Train: 0.0715
2-Layer	Test: 0.0650 Train: 0.0013	Test: 0.6579 Train: 0.0196

Appendix

Table 2: Stronger Memorization Behavior of ResNet Variants Under Different Weight Decay Settings

Original Index Containing ‘9’	Memorization Score
4362	80.38
21445	80.28
9390	61.33
21302	55.62
19494	55.50
29286	49.01

Appendix

Table 3: Top-10 most memorized digit-9 examples. All highly memorized examples appear exactly once in the full training set.

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Language models may need to internalize information that arrives over time and retain it through many subsequent updates. To study this challenge, we introduce long-horizon memorization, a setting in which a model learns 100 query-answer tasks through continual supervised fine-tuning without retaining earlier training examples or receiving task identifiers at inference. Sequential updates cause catastrophic forgetting, and no single continual learning mechanism we evaluate maintains strong retention at this horizon. We hypothesize that mechanisms addressing complementary sources of forgetting will be more effective when composed. We organize these compositions along two design dimensions. Data, function, and weight anchors specify what prior information each update should preserve, while low-rank allocation rules determine where successive updates are retained. To test this hypothesis systematically, we construct three distinct 100-task memorization datasets. We introduce task-level successive halving to search the combinatorial design space and use a factorial experiment to measure individual and interaction effects. Our best method combines all three anchors with merged LoRA, ranks among the top 3 methods in all datasets, and raises average final retention from 1.2% under naive sequential fine-tuning to 34.9%, a 28-fold improvement. The data anchor and merged LoRA provide the largest average gains and interact super-additively on all three datasets. Together, these results show that composing complementary mechanisms substantially improves long-horizon memorization beyond what any individual mechanism achieves.

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