Memorizing Long-tail Data Can Help Generalization Through Composition

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.

Deep networks have been known to have extraordinary generalization abilities, via mechanisms that aren't yet well understood. It is also known that upon shuffling labels in the training data to varying degrees, deep networks, trained with standard methods, can still achieve perfect or high accuracy on this corrupted training data. This phenomenon is called memorization, and typically comes at the cost of poorer generalization to true labels. Our recent work has demonstrated, that the internal representations of such models retain significantly better latent generalization abilities than is directly apparent from the model. In particular, it has been shown that such latent generalization can be recovered via simple probes (called MASC probes) on the layer-wise representations of the model. However, the origin and dynamics over training of this latent generalization during memorization is not well understood. Here, we track the training dynamics, empirically, and find that latent generalization abilities largely peak early in training, with model generalization. Next, we investigate to what extent the specific nature of the MASC probe is critical for our ability to extract latent generalization from the model's layerwise outputs. To this end, we first examine the mathematical structure of the MASC probe and show that it is a quadratic classifier, i.e. is non-linear. This brings up the question of the extent to which this latent generalization might be linearly decodable from layerwise outputs. To investigate this, we designed a new linear probe for this setting. Next, we consider the question of whether it is possible to transfer latent generalization to model generalization by directly editing model weights. To this end, we devise a way to transfer the latent generalization present in last-layer representations to the model using the new linear probe.

Deep neural networks are capable of both learning generalizing solutions on natural tasks and memorizing arbitrary mappings. We argue that understanding the former requires understanding the latter, which is much less studied. In what ways do networks that generalize or memorize differ in their behavior or their training dynamics? Do memorizing networks simply function as a lookup table where input-output mappings are stored independently? We investigate these questions in the context of CNNs trained on image classification tasks with randomized labels or pixels. We first study the behavior of such memorizing networks on unseen images. We find that independently initialized networks trained on the same random labels learn different predictive functions: they make different predictions on test examples, in contrast with generalizing networks. We then examine the effect of dataset size on memorization through the required network capacity and training time to interpolate the training set. Counter-intuitively, we find that the number of presentations of a given example required for complete memorization can decrease with dataset size even when input-output pairs share no common structure. Although memorizing networks do not learn a universal solution, they exhibit interesting behaviors which call for further investigations into the underlying mechanisms.