Daily Papers

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can implement the same function. Which internal structures reflect the computation, and which are accidents of a particular training run? This work extracts algorithmic cores: compact subspaces necessary and sufficient for task performance. Independently trained transformers learn different weights but converge to the same cores. Markov-chain transformers embed 3D cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers discover compact cyclic operators at grokking that later inflate, yielding a predictive model of the memorization-to-generalization transition. GPT-2 language models govern subject-verb agreement through a single axis that, when flipped, inverts grammatical number throughout generation across scales. These results reveal low-dimensional invariants that persist across training runs and scales, suggesting that transformer computations are organized around compact, shared algorithmic structures. Mechanistic interpretability could benefit from targeting such invariants -- the computational essence -- rather than implementation-specific details.

When do language diffusion models memorize their training data, and how to quantitatively assess their true generative regime? We address these questions by showing that Uniform-based Discrete Diffusion Models (UDDMs) fundamentally behave as Associative Memories (AMs) with emergent creative capabilities. The core idea of an AM is to reliably recover stored data points as memories by establishing distinct basins of attraction around them. Historically, models like Hopfield networks use an explicit energy function to guarantee these stable attractors. We broaden this perspective by leveraging the observation that energy is not strictly necessary, as basins of attraction can also be formed via conditional likelihood maximization. By evaluating token recovery of training and test examples, we identify in UDDMs a sharp memorization-to-generalization transition governed by the size of the training dataset: as it increases, basins around training examples shrink and basins around unseen test examples expand, until both later converge to the same level. Crucially, we can detect this transition using only the conditional entropy of predicted token sequences: memorization is characterized by vanishing conditional entropy, while in the generalization regime the conditional entropy of most tokens remains finite. Thus, conditional entropy offers a practical probe for the memorization-to-generalization transition in deployed models.

Dense Associative Memories (DenseAMs) are generalizations of Hopfield networks, which have superior information storage capacity and can store training data points (memories) at local minima of the energy landscape. When the amount of training data exceeds the critical memory storage capacity of these models, new local minima, which are different from the training data, emerge. In Associative Memory these emergent local minima are called spurious; states, which hinder memory retrieval. In this work, we examine diffusion models (DMs) through the DenseAM lens, viewing their generative process as an attempt of a memory retrieval. In the small data regimes, DMs create distinct attractors for each training sample, akin to DenseAMs below the critical memory storage. As the training data size increases, they transition from memorization to generalization. We identify a critical intermediate phase, predicted by DenseAM theory -- the spurious states. In generative modeling, these states are no longer negative artifacts but rather are the first signs of generative capabilities. We characterize the basins of attraction, energy landscape curvature, and computational properties of these previously overlooked states. Their existence is demonstrated across a wide range of architectures and datasets.

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and grokking in in-context learning using a Bayesian perspective, asking what enables the delayed transition from memorization to generalization. Concretely, we consider modular arithmetic tasks in which a transformer must infer a latent linear function solely from in-context examples and analyze how predictive uncertainty evolves during training. We combine approximate Bayesian techniques to estimate the posterior distribution and we study how uncertainty behaves across training and under changes in task diversity, context length, and context noise. We find that epistemic uncertainty collapses sharply when the model groks, making uncertainty a practical label-free diagnostic of generalization in transformers. Additionally, we provide theoretical support with a simplified Bayesian linear model, showing that asymptotically both delayed generalization and uncertainty peaks arise from the same underlying spectral mechanism, which links grokking time to uncertainty dynamics.

We explore the critical data size in language models, a threshold that marks a fundamental shift from quick memorization to slow generalization. We formalize the phase transition under the grokking configuration into the Data Efficiency Hypothesis and identify data insufficiency, sufficiency, and surplus regimes in language models training dynamics. We develop a grokking configuration to reproduce grokking on simplistic language models stably by rescaling initialization and weight decay. We show that generalization occurs only when language models reach a critical size. We analyze grokking across sample-wise and model-wise, verifying the proposed data efficiency hypothesis. Our experiments reveal smoother phase transitions occurring at the critical dataset size for language datasets. As the model size increases, this critical point also becomes larger, indicating that larger models require more data. Our results deepen the understanding of language model training, offering a novel perspective on the role of data in the learning mechanism of language models.

Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general-purpose in-context learning algorithms from scratch, using only black-box models with minimal inductive bias. Such a model takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general-purpose in-context learners. We characterize transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks, and meta-optimization. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size (memory) determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general-purpose in-context learning algorithms.

We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge for implicit multi-hop reasoning, suggesting a lack of compositional generalization over their parametric knowledge. To address this limitation, we study recurrent-depth transformers, which enables iterative computation over the same transformer layers. We investigate two compositional generalization challenges under the implicit reasoning scenario: systematic generalization, i.e. combining knowledge that is never used for compositions during training, and depth extrapolation, i.e. generalizing from limited reasoning depth (e.g. training on up to 5-hop) to deeper compositions (e.g. 10-hop). Through controlled studies with models trained from scratch, we show that while vanilla transformers struggle with both generalization challenges, recurrent-depth transformers can effectively make such generalization. For systematic generalization, we find that this ability emerges through a three-stage grokking process, transitioning from memorization to in-distribution generalization and finally to systematic generalization, supported by mechanistic analysis. For depth extrapolation, we show that generalization beyond training depth can be unlocked by scaling inference-time recurrence, with more iterations enabling deeper reasoning. We further study how training strategies affect extrapolation, providing guidance on training recurrent-depth transformers, and identify a key limitation, overthinking, where excessive recurrence degrades predictions and limits generalization to very deep compositions.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

A widely held hypothesis for why generative recommendation (GR) models outperform conventional item ID-based models is that they generalize better. However, there is few systematic way to verify this hypothesis beyond a superficial comparison of overall performance. To address this gap, we categorize each data instance based on the specific capability required for a correct prediction: either memorization (reusing item transition patterns observed during training) or generalization (composing known patterns to predict unseen item transitions). Extensive experiments show that GR models perform better on instances that require generalization, whereas item ID-based models perform better when memorization is more important. To explain this divergence, we shift the analysis from the item level to the token level and show that what appears to be item-level generalization often reduces to token-level memorization for GR models. Finally, we show that the two paradigms are complementary. We propose a simple memorization-aware indicator that adaptively combines them on a per-instance basis, leading to improved overall recommendation performance.

Grokking is one of the most surprising puzzles in neural network generalization: a network first reaches a memorization solution with perfect training accuracy and poor generalization, but with further training, it reaches a perfectly generalized solution. We aim to analyze the mechanism of grokking from the lottery ticket hypothesis, identifying the process to find the lottery tickets (good sparse subnetworks) as the key to describing the transitional phase between memorization and generalization. We refer to these subnetworks as ''Grokking tickets'', which is identified via magnitude pruning after perfect generalization. First, using ''Grokking tickets'', we show that the lottery tickets drastically accelerate grokking compared to the dense networks on various configurations (MLP and Transformer, and an arithmetic and image classification tasks). Additionally, to verify that ''Grokking ticket'' are a more critical factor than weight norms, we compared the ''good'' subnetworks with a dense network having the same L1 and L2 norms. Results show that the subnetworks generalize faster than the controlled dense model. In further investigations, we discovered that at an appropriate pruning rate, grokking can be achieved even without weight decay. We also show that speedup does not happen when using tickets identified at the memorization solution or transition between memorization and generalization or when pruning networks at the initialization (Random pruning, Grasp, SNIP, and Synflow). The results indicate that the weight norm of network parameters is not enough to explain the process of grokking, but the importance of finding good subnetworks to describe the transition from memorization to generalization. The implementation code can be accessed via this link: https://github.com/gouki510/Grokking-Tickets.

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time τ_gen at which models begin to generate high-quality samples, and a later time τ_mem beyond which memorization emerges. Crucially, we find that τ_mem increases linearly with the training set size n, while τ_gen remains constant. This creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when n becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

The relationship between memorization and generalization in large language models (LLMs) remains an open area of research, with growing evidence that the two are deeply intertwined. In this work, we investigate this relationship by pre-training a series of capacity-limited Transformer models from scratch on two synthetic character-level tasks designed to separately probe generalization (via arithmetic extrapolation) and memorization (via factual recall). We observe a consistent trade-off: small models extrapolate to unseen arithmetic cases but fail to memorize facts, while larger models memorize but fail to extrapolate. An intermediate-capacity model exhibits a similar shift toward memorization. When trained on both tasks jointly, no model (regardless of size) succeeds at extrapolation. These findings suggest that pre-training may intrinsically favor one learning mode over the other. By isolating these dynamics in a controlled setting, our study offers insight into how model capacity shapes learning behavior and offers broader implications for the design and deployment of small language models.

Rote learning is a memorization technique based on repetition. It is commonly believed to hinder generalization by encouraging verbatim memorization rather than deeper understanding. This insight holds for even learning factual knowledge that inevitably requires a certain degree of memorization. In this work, we demonstrate that LLMs can be trained to generalize from rote memorized data. We introduce a two-phase memorize-then-generalize framework, where the model first rote memorizes factual subject-object associations using a semantically meaningless token and then learns to generalize by fine-tuning on a small set of semantically meaningful prompts. Extensive experiments over 8 LLMs show that the models can reinterpret rote memorized data through the semantically meaningful prompts, as evidenced by the emergence of structured, semantically aligned latent representations between the two. This surprising finding opens the door to both effective and efficient knowledge injection and possible risks of repurposing the memorized data for malicious usage.

Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations.This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize the interplay between memorization and generalization, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose memorization-aware training (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

We propose a new method for estimating how much a model ``knows'' about a datapoint and use it to measure the capacity of modern language models. Prior studies of language model memorization have struggled to disentangle memorization from generalization. We formally separate memorization into two components: unintended memorization, the information a model contains about a specific dataset, and generalization, the information a model contains about the true data-generation process. When we completely eliminate generalization, we can compute the total memorization, which provides an estimate of model capacity: our measurements estimate that GPT-style models have a capacity of approximately 3.6 bits per parameter. We train language models on datasets of increasing size and observe that models memorize until their capacity fills, at which point ``grokking'' begins, and unintended memorization decreases as models begin to generalize. We train hundreds of transformer language models ranging from 500K to 1.5B parameters and produce a series of scaling laws relating model capacity and data size to membership inference.

Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks. We formalize this failure as the \textbf{Knowing--Using Gap}, characterized by an accuracy gap and a temporal lag between memorization and generalization. To understand this phenomenon, we fine-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally using a novel intervention technique called self-patching. Self-patching identifies activation locations where relocating representations substantially improves failed generalization cases. These results are consistent with a knowledge-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation-effective layers. To demonstrate the practicality of this diagnostic finding, we design a simple heuristic strategy which recovers 58--75\% of the oracle headroom in generalization failure. Experiments are done cross-domain for the robustness of this finding.

The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may forget how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based, and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called Ideal Continual Learner (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify how rehearsal affects generalization. Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

Large Language Models (LLMs) exhibit a troubling duality, capable of both remarkable generalization and brittle, verbatim memorization of their training data. This unpredictability undermines their reliability in high-stakes applications. In this work, we propose a unified framework to understand, identify, and control these distinct reasoning modes. First, we introduce a theoretical model based on the Information Bottleneck (IB) principle, formalizing generalization as the learning of a compressed, task-relevant representation and memorization as a failure to compress. Building on this theory, we develop Dynamic Mode Steering (DMS), a novel inference-time algorithm which comprises two components: (1) a lightweight, causally-grounded linear probe that identifies the model's instantaneous reliance on memorization, and (2) a dynamic activation steering mechanism that nudges the model's computation towards pre-identified generalization circuits. We frame DMS as a form of adaptive, self-contrastive decoding. Experiments on reasoning and faithfulness tasks demonstrate that DMS significantly improves logical consistency and factual accuracy, thereby offering a principled approach to enhancing LLM reliability.

Inevitable domain and task discrepancies in real-world scenarios can impair the generalization performance of the pre-trained deep models for medical data. Therefore, we audaciously propose that we should build a general-purpose medical AI system that can be seamlessly adapted to downstream domains/tasks. Since the domain/task adaption procedures usually involve additional labeling work for the target data, designing a data-efficient adaption algorithm is desired to save the cost of transferring the learned knowledge. Our recent work found that vision-language models (VLMs) are efficient learners with extraordinary cross-domain ability. Therefore, in this work, we further explore the possibility of leveraging pre-trained VLMs as medical foundation models for building general-purpose medical AI, where we thoroughly investigate three machine-learning paradigms, i.e., domain/task-specialized learning, joint learning, and continual learning, for training the VLMs and evaluate their generalization performance on cross-domain and cross-task test sets. To alleviate the catastrophic forgetting during sequential training, we employ rehearsal learning and receive a sharp boost in terms of generalization capability. In a nutshell, our empirical evidence suggests that continual learning may be a practical and efficient learning paradigm for the medical foundation model. And we hope researchers can use our empirical evidence as basement to further explore the path toward medical foundation model.

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the incrementally available information from non-stationary data distributions is continually acquired, disrupting what the model has already learned. Our approach remembers old tasks by projecting the representations of new tasks close to that of old tasks while keeping the decision boundaries unchanged. We employ the center loss as a regularization penalty that enforces new tasks' features to have the same class centers as old tasks and makes the features highly discriminative. This, in turn, leads to the least forgetting of already learned information. This method is easy to implement, requires minimal computational and memory overhead, and allows the neural network to maintain high performance across many sequentially encountered tasks. We also demonstrate that using the center loss in conjunction with the memory replay outperforms other replay-based strategies. Along with standard MNIST variants for continual learning, we apply our method to continual domain adaptation scenarios with the Digits and PACS datasets. We demonstrate that our approach is scalable, effective, and gives competitive performance compared to state-of-the-art continual learning methods.

When do machine learning systems fail to generalize, and what mechanisms could improve their generalization? Here, we draw inspiration from cognitive science to argue that one weakness of machine learning systems is their failure to exhibit latent learning -- learning information that is not relevant to the task at hand, but that might be useful in a future task. We show how this perspective links failures ranging from the reversal curse in language modeling to new findings on agent-based navigation. We then highlight how cognitive science points to episodic memory as a potential part of the solution to these issues. Correspondingly, we show that a system with an oracle retrieval mechanism can use learning experiences more flexibly to generalize better across many of these challenges. We also identify some of the essential components for effectively using retrieval, including the importance of within-example in-context learning for acquiring the ability to use information across retrieved examples. In summary, our results illustrate one possible contributor to the relative data inefficiency of current machine learning systems compared to natural intelligence, and help to understand how retrieval methods can complement parametric learning to improve generalization.

Large language models (LMs) have been shown to memorize parts of their training data, and when prompted appropriately, they will emit the memorized training data verbatim. This is undesirable because memorization violates privacy (exposing user data), degrades utility (repeated easy-to-memorize text is often low quality), and hurts fairness (some texts are memorized over others). We describe three log-linear relationships that quantify the degree to which LMs emit memorized training data. Memorization significantly grows as we increase (1) the capacity of a model, (2) the number of times an example has been duplicated, and (3) the number of tokens of context used to prompt the model. Surprisingly, we find the situation becomes more complicated when generalizing these results across model families. On the whole, we find that memorization in LMs is more prevalent than previously believed and will likely get worse as models continues to scale, at least without active mitigations.

The order of training samples plays a crucial role in large language models (LLMs), significantly impacting both their external performance and internal learning dynamics. Traditional methods for investigating this effect generally require retraining the model with various sample orders, which is computationally infeasible for LLMs. In this work, we improve traditional methods by designing a retraining-free framework. By approximating Adam optimizer updates with first- and second-order Taylor expansions and utilizing random projection methods to store intermediate checkpoints, our framework can efficiently estimate model parameters for arbitrary training sample orders. Next, we apply our framework to two downstream research problems: (1) Training curriculum design for LLMs -- we base our retraining-free framework to propose a novel curriculum learning strategy that augments curriculum proposals with estimated model performances, enabling more informed sample scheduling. (2) LLMs' memorization and generalization effect analysis -- we use our retraining-free framework to estimate how the positions of training samples influence LLMs' capacity for memorization and generalization. We conduct extensive experiments to validate the effectiveness of our retraining-free framework in reproducing the true model performances, and further demonstrate its potential in optimizing LLM training curricula and analyzing the memorization and generalization effects of LLMs.

In continual learning (CL), an AI agent (e.g., autonomous vehicles or robotics) learns from non-stationary data streams under dynamic environments. For the practical deployment of such applications, it is important to guarantee robustness to unseen environments while maintaining past experiences. In this paper, a novel CL framework is proposed to achieve robust generalization to dynamic environments while retaining past knowledge. The considered CL agent uses a capacity-limited memory to save previously observed environmental information to mitigate forgetting issues. Then, data points are sampled from the memory to estimate the distribution of risks over environmental change so as to obtain predictors that are robust with unseen changes. The generalization and memorization performance of the proposed framework are theoretically analyzed. This analysis showcases the tradeoff between memorization and generalization with the memory size. Experiments show that the proposed algorithm outperforms memory-based CL baselines across all environments while significantly improving the generalization performance on unseen target environments.

Large language models (LLMs) have achieved impressive results in natural language processing but are prone to memorizing portions of their training data, which can compromise evaluation metrics, raise privacy concerns, and limit generalization. Traditional methods for detecting memorization rely on output probabilities or loss functions, often lacking precision due to confounding factors like common language patterns. In this paper, we introduce an analytical method that precisely detects memorization by examining neuron activations within the LLM. By identifying specific activation patterns that differentiate between memorized and not memorized tokens, we train classification probes that achieve near-perfect accuracy. The approach can also be applied to other mechanisms, such as repetition, as demonstrated in this study, highlighting its versatility. Intervening on these activations allows us to suppress memorization without degrading overall performance, enhancing evaluation integrity by ensuring metrics reflect genuine generalization. Additionally, our method supports large-scale labeling of tokens and sequences, crucial for next-generation AI models, improving training efficiency and results. Our findings contribute to model interpretability and offer practical tools for analyzing and controlling internal mechanisms in LLMs.

The generalization of language models (LMs) is undergoing active debates, contrasting their potential for general intelligence with their struggles with basic knowledge composition (e.g., reverse/transition curse). This paper uncovers the phenomenon of linear correlations in LMs during knowledge composition. For explanation, there exists a linear transformation between certain related knowledge that maps the next token prediction logits from one prompt to another, e.g., "X lives in the city of" rightarrow "X lives in the country of" for every given X. This mirrors the linearity in human knowledge composition, such as Paris rightarrow France. Our findings indicate that the linear transformation is resilient to large-scale fine-tuning, generalizing updated knowledge when aligned with real-world relationships, but causing hallucinations when it deviates. Empirical results suggest that linear correlation can serve as a potential identifier of LM's generalization. Finally, we show such linear correlations can be learned with a single feedforward network and pre-trained vocabulary representations, indicating LM generalization heavily relies on the latter.

Increasing the size of a Transformer model does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, improved generalization ability occurs as the model memorizes the training samples. We present a theoretical framework that sheds light on the memorization process and performance dynamics of transformer-based language models. We model the behavior of Transformers with associative memories using Hopfield networks, such that each transformer block effectively conducts an approximate nearest-neighbor search. Based on this, we design an energy function analogous to that in the modern continuous Hopfield network which provides an insightful explanation for the attention mechanism. Using the majorization-minimization technique, we construct a global energy function that captures the layered architecture of the Transformer. Under specific conditions, we show that the minimum achievable cross-entropy loss is bounded from below by a constant approximately equal to 1. We substantiate our theoretical results by conducting experiments with GPT-2 on various data sizes, as well as training vanilla Transformers on a dataset of 2M tokens.

When language models (LMs) are trained to forget (or "unlearn'') a skill, how precisely does their behavior change? We study the behavior of transformer LMs in which tasks have been forgotten via fine-tuning on randomized labels. Such LMs learn to generate near-random predictions for individual examples in the "training'' set used for forgetting. Across tasks, however, LMs exhibit extreme variability in whether LM predictions change on examples outside the training set. In some tasks (like entailment classification), forgetting generalizes robustly, and causes models to produce uninformative predictions on new task instances; in other tasks (like physical commonsense reasoning and scientific question answering) forgetting affects only the training examples, and models continue to perform the "forgotten'' task accurately even for examples very similar to those that appeared in the training set. Dataset difficulty is not predictive of whether a behavior can be forgotten; instead, generalization in forgetting is (weakly) predicted by the confidence of LMs' initial task predictions and the variability of LM representations of training data, with low confidence and low variability both associated with greater generalization. Perhaps most surprisingly, random-label forgetting appears to be somewhat insensitive to the contents of the training set: for example, models trained on science questions with random labels continue to answer other science questions accurately, but begin to produce random labels on entailment classification tasks. Finally, we show that even generalizable forgetting is shallow: linear probes trained on LMs' representations can still perform tasks reliably after forgetting. Our results highlight the difficulty and unpredictability of performing targeted skill removal from models via fine-tuning.

Understanding alignment techniques begins with comprehending zero-shot generalization brought by instruction tuning, but little of the mechanism has been understood. Existing work has largely been confined to the task level, without considering that tasks are artificially defined and, to LLMs, merely consist of tokens and representations. To bridge this gap, we investigate zero-shot generalization from the perspective of the data itself. We first demonstrate that zero-shot generalization happens very early during instruction tuning, with loss serving as a stable indicator. Next, we investigate training data arrangement through similarity and granularity perspectives, confirming that the timing of exposure to certain training examples may greatly facilitate generalization on unseen tasks. Finally, we propose a more grounded training data arrangement framework, Test-centric Multi-turn Arrangement, and show its effectiveness in promoting continual learning and further loss reduction. For the first time, we show that zero-shot generalization during instruction tuning is a form of similarity-based generalization between training and test data at the instance level. Our code is released at https://github.com/thunlp/Dynamics-of-Zero-Shot-Generalization.

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorization of the training data also presents significant privacy risks when the training data contains sensitive personal information and thus it is important to understand whether such memorization is necessary for accurate learning. We provide the first conceptual explanation and a theoretical model for this phenomenon. Specifically, we demonstrate that for natural data distributions memorization of labels is necessary for achieving close-to-optimal generalization error. Crucially, even labels of outliers and noisy labels need to be memorized. The model is motivated and supported by the results of several recent empirical works. In our model, data is sampled from a mixture of subpopulations and our results show that memorization is necessary whenever the distribution of subpopulation frequencies is long-tailed. Image and text data is known to be long-tailed and therefore our results establish a formal link between these empirical phenomena. Our results allow to quantify the cost of limiting memorization in learning and explain the disparate effects that privacy and model compression have on different subgroups.

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective. We analyze the distinctions between memorization and generalization in diffusion models through the lens of representation learning. By investigating a two-layer ReLU denoising autoencoder (DAE), we prove that (i) memorization corresponds to the model storing raw training samples in the learned weights for encoding and decoding, yielding localized "spiky" representations, whereas (ii) generalization arises when the model captures local data statistics, producing "balanced" representations. Furthermore, we validate these theoretical findings on real-world unconditional and text-to-image diffusion models, demonstrating that the same representation structures emerge in deep generative models with significant practical implications. Building on these insights, we propose a representation-based method for detecting memorization and a training-free editing technique that allows precise control via representation steering. Together, our results highlight that learning good representations is central to novel and meaningful generative modeling.

Despite the recent observation that large language models (LLMs) can store substantial factual knowledge, there is a limited understanding of the mechanisms of how they acquire factual knowledge through pretraining. This work addresses this gap by studying how LLMs acquire factual knowledge during pretraining. The findings reveal several important insights into the dynamics of factual knowledge acquisition during pretraining. First, counterintuitively, we observe that pretraining on more data shows no significant improvement in the model's capability to acquire and maintain factual knowledge. Next, there is a power-law relationship between training steps and forgetting of memorization and generalization of factual knowledge, and LLMs trained with duplicated training data exhibit faster forgetting. Third, training LLMs with larger batch sizes can enhance the models' robustness to forgetting. Overall, our observations suggest that factual knowledge acquisition in LLM pretraining occurs by progressively increasing the probability of factual knowledge presented in the pretraining data at each step. However, this increase is diluted by subsequent forgetting. Based on this interpretation, we demonstrate that we can provide plausible explanations for recently observed behaviors of LLMs, such as the poor performance of LLMs on long-tail knowledge and the benefits of deduplicating the pretraining corpus.

Training data memorization in NLP can both be beneficial (e.g., closed-book QA) and undesirable (personal data extraction). In any case, successful model training requires a non-trivial amount of memorization to store word spellings, various linguistic idiosyncrasies and common knowledge. However, little is known about what affects the memorization behavior of NLP models, as the field tends to focus on the equally important question of generalization. In this work, we demonstrate that the size of the subword vocabulary learned by Byte-Pair Encoding (BPE) greatly affects both ability and tendency of standard Transformer models to memorize training data, even when we control for the number of learned parameters. We find that with a large subword vocabulary size, Transformer models fit random mappings more easily and are more vulnerable to membership inference attacks. Similarly, given a prompt, Transformer-based language models with large subword vocabularies reproduce the training data more often. We conjecture this effect is caused by reduction in the sequences' length that happens as the BPE vocabulary grows. Our findings can allow a more informed choice of hyper-parameters, that is better tailored for a particular use-case.

Large language model (LLM)-based decision-making agents have shown the ability to generalize across multiple tasks. However, their performance relies on massive data and compute. We argue that this inefficiency stems from the forgetting phenomenon, in which a model memorizes its behaviors in parameters throughout training. As a result, training on a new task may deteriorate the model's performance on previous tasks. In contrast to LLMs' implicit memory mechanism, the human brain utilizes distributed memory storage, which helps manage and organize multiple skills efficiently, mitigating the forgetting phenomenon. Thus inspired, we propose an internal working memory module to store, blend, and retrieve information for different downstream tasks. Evaluation results show that the proposed method improves training efficiency and generalization in both Atari games and meta-world object manipulation tasks. Moreover, we demonstrate that memory fine-tuning further enhances the adaptability of the proposed architecture.

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.

Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce Compositional-ARC-a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of abstract two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a small transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions. Notably, despite having only 5.7M parameters, this model significantly outperforms state-of-the-art LLMs-including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior-and performs on par with the winning model of the ARC prize 2024, an 8B-parameter LLM trained via test-time training. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.

In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.

Memorization in language models is typically treated as a homogenous phenomenon, neglecting the specifics of the memorized data. We instead model memorization as the effect of a set of complex factors that describe each sample and relate it to the model and corpus. To build intuition around these factors, we break memorization down into a taxonomy: recitation of highly duplicated sequences, reconstruction of inherently predictable sequences, and recollection of sequences that are neither. We demonstrate the usefulness of our taxonomy by using it to construct a predictive model for memorization. By analyzing dependencies and inspecting the weights of the predictive model, we find that different factors influence the likelihood of memorization differently depending on the taxonomic category.

Due to their capacity to generate novel and high-quality samples, diffusion models have attracted significant research interest in recent years. Notably, the typical training objective of diffusion models, i.e., denoising score matching, has a closed-form optimal solution that can only generate training data replicating samples. This indicates that a memorization behavior is theoretically expected, which contradicts the common generalization ability of state-of-the-art diffusion models, and thus calls for a deeper understanding. Looking into this, we first observe that memorization behaviors tend to occur on smaller-sized datasets, which motivates our definition of effective model memorization (EMM), a metric measuring the maximum size of training data at which a learned diffusion model approximates its theoretical optimum. Then, we quantify the impact of the influential factors on these memorization behaviors in terms of EMM, focusing primarily on data distribution, model configuration, and training procedure. Besides comprehensive empirical results identifying the influential factors, we surprisingly find that conditioning training data on uninformative random labels can significantly trigger the memorization in diffusion models. Our study holds practical significance for diffusion model users and offers clues to theoretical research in deep generative models. Code is available at https://github.com/sail-sg/DiffMemorize.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse phenomenon.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

It is an important yet challenging setting to continually learn new tasks from a few examples. Although numerous efforts have been devoted to either continual learning or few-shot learning, little work has considered this new setting of few-shot continual learning (FSCL), which needs to minimize the catastrophic forgetting to the old tasks and gradually improve the ability of few-shot generalization. In this paper, we provide a first systematic study on FSCL and present an effective solution with deep neural networks. Our solution is based on the observation that continual learning of a task sequence inevitably interferes few-shot generalization, which makes it highly nontrivial to extend few-shot learning strategies to continual learning scenarios. We draw inspirations from the robust brain system and develop a method that (1) interdependently updates a pair of fast / slow weights for continual learning and few-shot learning to disentangle their divergent objectives, inspired by the biological model of meta-plasticity and fast / slow synapse; and (2) applies a brain-inspired two-step consolidation strategy to learn a task sequence without forgetting in the fast weights while improve generalization without overfitting in the slow weights. Extensive results on various benchmarks show that our method achieves a better performance than joint training of all the tasks ever seen. The ability of few-shot generalization is also substantially improved from incoming tasks and examples.

Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs' reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using a dynamically generated logical reasoning benchmark based on Knights and Knaves (K&K) puzzles. We found that LLMs could interpolate the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet fail when those puzzles are slightly perturbed, suggesting that the models heavily rely on memorization to solve those training puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. In-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers suggest that the LLMs learn to reason on K&K puzzles despite training data memorization. This phenomenon indicates that LLMs exhibit a complex interplay between memorization and genuine reasoning abilities. Finally, our analysis with per-sample memorization score sheds light on how LLMs switch between reasoning and memorization in solving logical puzzles. Our code and data are available at https://memkklogic.github.io.

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges.

As the application space of language models continues to evolve, a natural question to ask is how we can quickly adapt models to new tasks. We approach this classic question from a continual learning perspective, in which we aim to continue fine-tuning models trained on past tasks on new tasks, with the goal of "transferring" relevant knowledge. However, this strategy also runs the risk of doing more harm than good, i.e., negative transfer. In this paper, we construct a new benchmark of task sequences that target different possible transfer scenarios one might face, such as a sequence of tasks with high potential of positive transfer, high potential for negative transfer, no expected effect, or a mixture of each. An ideal learner should be able to maximally exploit information from all tasks that have any potential for positive transfer, while also avoiding the negative effects of any distracting tasks that may confuse it. We then propose a simple, yet effective, learner that satisfies many of our desiderata simply by leveraging a selective strategy for initializing new models from past task checkpoints. Still, limitations remain, and we hope this benchmark can help the community to further build and analyze such learners.

Large Language Models (LLMs) are widely used for temporal prediction, but their reliance on pretraining data raises contamination concerns, as accurate predictions on pre-cutoff test data may reflect memorization rather than reasoning, leading to an overestimation of their generalization capability. With the recent emergence of prompting-based unlearning techniques, a natural question arises: Can LLMs be prompted to simulate an earlier knowledge cutoff? In this work, we investigate the capability of prompting to simulate earlier knowledge cutoff in LLMs. We construct three evaluation datasets to assess the extent to which LLMs can forget (1) direct factual knowledge, (2) semantic shifts, and (3) causally related knowledge. Results demonstrate that while prompt-based simulated knowledge cutoffs show effectiveness when directly queried with the information after that date, they struggle to induce forgetting when the forgotten content is not directly asked but causally related to the query. These findings highlight the need for more rigorous evaluation settings when applying LLMs for temporal prediction tasks. The full dataset and evaluation code are available at https://github.com/gxx27/time_unlearn.

Continual learning (CL), which aims to learn a sequence of tasks, has attracted significant recent attention. However, most work has focused on the experimental performance of CL, and theoretical studies of CL are still limited. In particular, there is a lack of understanding on what factors are important and how they affect "catastrophic forgetting" and generalization performance. To fill this gap, our theoretical analysis, under overparameterized linear models, provides the first-known explicit form of the expected forgetting and generalization error. Further analysis of such a key result yields a number of theoretical explanations about how overparameterization, task similarity, and task ordering affect both forgetting and generalization error of CL. More interestingly, by conducting experiments on real datasets using deep neural networks (DNNs), we show that some of these insights even go beyond the linear models and can be carried over to practical setups. In particular, we use concrete examples to show that our results not only explain some interesting empirical observations in recent studies, but also motivate better practical algorithm designs of CL.

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill composition in a collection of modular arithmetic tasks. Specifically, we consider a finite collection of linear modular functions z = a , x + b , y ;mod; p labeled by the vector (a, b) in Z_p^2. We use some of these tasks for pre-training and the rest for out-of-distribution testing. We empirically show that a GPT-style transformer exhibits a transition from in-distribution to out-of-distribution generalization as the number of pre-training tasks increases. We find that the smallest model capable of out-of-distribution generalization requires two transformer blocks, while for deeper models, the out-of-distribution generalization phase is transient, necessitating early stopping. Finally, we perform an interpretability study of the pre-trained models, revealing the highly structured representations in both phases; and discuss the learnt algorithm.

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.

The performance on general tasks decreases after Large Language Models (LLMs) are fine-tuned on domain-specific tasks, the phenomenon is known as Catastrophic Forgetting (CF). However, this paper presents a further challenge for real application of domain-specific LLMs beyond CF, called General Capabilities Integration (GCI), which necessitates the integration of both the general capabilities and domain knowledge within a single instance. The objective of GCI is not merely to retain previously acquired general capabilities alongside new domain knowledge, but to harmonize and utilize both sets of skills in a cohesive manner to enhance performance on domain-specific tasks. Taking legal domain as an example, we carefully design three groups of training and testing tasks without lacking practicability, and construct the corresponding datasets. To better incorporate general capabilities across domain-specific scenarios, we introduce ALoRA, which utilizes a multi-head attention module upon LoRA, facilitating direct information transfer from preceding tokens to the current one. This enhancement permits the representation to dynamically switch between domain-specific knowledge and general competencies according to the attention. Extensive experiments are conducted on the proposed tasks. The results exhibit the significance of our setting, and the effectiveness of our method.

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

Transformer models pre-trained with a masked-language-modeling objective (e.g., BERT) encode commonsense knowledge as evidenced by behavioral probes; however, the extent to which this knowledge is acquired by systematic inference over the semantics of the pre-training corpora is an open question. To answer this question, we selectively inject verbalized knowledge into the minibatches of a BERT model during pre-training and evaluate how well the model generalizes to supported inferences. We find generalization does not improve over the course of pre-training, suggesting that commonsense knowledge is acquired from surface-level, co-occurrence patterns rather than induced, systematic reasoning.

The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the memorization phenomenon, the eventual convergence to the empirical distribution. We consider a simplified GAN model with the generator replaced by a density, and analyze how the discriminator contributes to generalization. We show that with early stopping, the generalization error measured by Wasserstein metric escapes from the curse of dimensionality, despite that in the long term, memorization is inevitable. In addition, we present a hardness of learning result for WGAN.

Humans excel at learning abstract patterns across different sequences, filtering out irrelevant details, and transferring these generalized concepts to new sequences. In contrast, many sequence learning models lack the ability to abstract, which leads to memory inefficiency and poor transfer. We introduce a non-parametric hierarchical variable learning model (HVM) that learns chunks from sequences and abstracts contextually similar chunks as variables. HVM efficiently organizes memory while uncovering abstractions, leading to compact sequence representations. When learning on language datasets such as babyLM, HVM learns a more efficient dictionary than standard compression algorithms such as Lempel-Ziv. In a sequence recall task requiring the acquisition and transfer of variables embedded in sequences, we demonstrate HVM's sequence likelihood correlates with human recall times. In contrast, large language models (LLMs) struggle to transfer abstract variables as effectively as humans. From HVM's adjustable layer of abstraction, we demonstrate that the model realizes a precise trade-off between compression and generalization. Our work offers a cognitive model that captures the learning and transfer of abstract representations in human cognition and differentiates itself from LLMs.

Self-supervised learning (SSL) has recently received significant attention due to its ability to train high-performance encoders purely on unlabeled data-often scraped from the internet. This data can still be sensitive and empirical evidence suggests that SSL encoders memorize private information of their training data and can disclose them at inference time. Since existing theoretical definitions of memorization from supervised learning rely on labels, they do not transfer to SSL. To address this gap, we propose SSLMem, a framework for defining memorization within SSL. Our definition compares the difference in alignment of representations for data points and their augmented views returned by both encoders that were trained on these data points and encoders that were not. Through comprehensive empirical analysis on diverse encoder architectures and datasets we highlight that even though SSL relies on large datasets and strong augmentations-both known in supervised learning as regularization techniques that reduce overfitting-still significant fractions of training data points experience high memorization. Through our empirical results, we show that this memorization is essential for encoders to achieve higher generalization performance on different downstream tasks.

Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly -- producing correct answers without explicitly verbalizing intermediate steps -- but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a three-stage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

Recently, with the emergence of numerous Large Language Models (LLMs), the implementation of AI has entered a new era. Irrespective of these models' own capacity and structure, there is a growing demand for LLMs to possess enhanced comprehension of longer and more complex contexts with relatively smaller sizes. Models often encounter an upper limit when processing sequences of sentences that extend beyond their comprehension capacity and result in off-topic or even chaotic responses. While several recent works attempt to address this issue in various ways, they rarely focus on "why models are unable to compensate or strengthen their capabilities on their own". In this paper, we thoroughly investigate the nature of information transfer within LLMs and propose a novel technique called Attention Transition. This technique empowers models to achieve longer and better context comprehension with minimal additional training or impact on generation fluency. Our experiments are conducted on the challenging XSum dataset using LLaMa-7b model with context token length ranging from 800 to 1900. Results demonstrate that we achieve substantial improvements compared with the original generation results evaluated by GPT4.

Continual learning refers to a dynamical framework in which a model receives a stream of non-stationary data over time and must adapt to new data while preserving previously acquired knowledge. Unluckily, neural networks fail to meet these two desiderata, incurring the so-called catastrophic forgetting phenomenon. Whereas a vast array of strategies have been proposed to attenuate forgetting in the computer vision domain, for speech-related tasks, on the other hand, there is a dearth of works. In this paper, we consider the joint use of rehearsal and knowledge distillation (KD) approaches for spoken language understanding under a class-incremental learning scenario. We report on multiple KD combinations at different levels in the network, showing that combining feature-level and predictions-level KDs leads to the best results. Finally, we provide an ablation study on the effect of the size of the rehearsal memory that corroborates the efficacy of our approach for low-resource devices.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

The mainstream paradigm behind continual learning has been to adapt the model parameters to non-stationary data distributions, where catastrophic forgetting is the central challenge. Typical methods rely on a rehearsal buffer or known task identity at test time to retrieve learned knowledge and address forgetting, while this work presents a new paradigm for continual learning that aims to train a more succinct memory system without accessing task identity at test time. Our method learns to dynamically prompt (L2P) a pre-trained model to learn tasks sequentially under different task transitions. In our proposed framework, prompts are small learnable parameters, which are maintained in a memory space. The objective is to optimize prompts to instruct the model prediction and explicitly manage task-invariant and task-specific knowledge while maintaining model plasticity. We conduct comprehensive experiments under popular image classification benchmarks with different challenging continual learning settings, where L2P consistently outperforms prior state-of-the-art methods. Surprisingly, L2P achieves competitive results against rehearsal-based methods even without a rehearsal buffer and is directly applicable to challenging task-agnostic continual learning. Source code is available at https://github.com/google-research/l2p.

Supervised fine-tuning (SFT) on chain-of-thought data is an essential post-training step for reasoning language models. Standard machine learning intuition suggests that training with more unique training samples yields better generalization. Counterintuitively, we show that SFT benefits from repetition: under a fixed update budget, training for more epochs on smaller datasets outperforms single-epoch training on larger datasets. On AIME'24/25 and GPQA benchmarks, Olmo3-7B trained for 128 epochs on 400 samples outperforms the equivalent 1 epoch on 51200 samples by 12-26 percentage points, with no additional catastrophic forgetting. We find that training token accuracy reliably signals when repetition has saturated; improvements from additional epochs plateau at full memorization, a pattern consistent across all settings. These findings provide a practical approach for reasoning SFT, where scaling epochs with token accuracy as a stopping criterion can replace expensive undirected data scaling. We pose the repetition advantage, where full memorization coincides with improved generalization, as a new open problem for the community in understanding the training dynamics of large language models.

Empirical scaling laws have driven the evolution of large language models (LLMs), yet their coefficients shift whenever the model architecture or data pipeline changes. Mixture-of-Experts (MoE) models, now standard in state-of-the-art systems, introduce a new sparsity dimension that current dense-model frontiers overlook. We investigate how MoE sparsity influences two distinct capability regimes: memorization and reasoning. We train families of MoE Transformers that systematically vary total parameters, active parameters, and top-k routing while holding the compute budget fixed. For every model we record pre-training loss, downstream task loss, and task accuracy, allowing us to separate the train-test generalization gap from the loss-accuracy gap. Memorization benchmarks improve monotonically with total parameters, mirroring training loss. By contrast, reasoning performance saturates and can even regress despite continued gains in both total parameters and training loss. Altering top-k alone has little effect when active parameters are constant, and classic hyperparameters such as learning rate and initialization modulate the generalization gap in the same direction as sparsity. Neither post-training reinforcement learning (GRPO) nor extra test-time compute rescues the reasoning deficit of overly sparse models. Our model checkpoints, code and logs are open-source at https://github.com/rioyokotalab/optimal-sparsity.

Recent large language models have been trained on vast datasets, but also often on repeated data, either intentionally for the purpose of upweighting higher quality data, or unintentionally because data deduplication is not perfect and the model is exposed to repeated data at the sentence, paragraph, or document level. Some works have reported substantial negative performance effects of this repeated data. In this paper we attempt to study repeated data systematically and to understand its effects mechanistically. To do this, we train a family of models where most of the data is unique but a small fraction of it is repeated many times. We find a strong double descent phenomenon, in which repeated data can lead test loss to increase midway through training. A predictable range of repetition frequency leads to surprisingly severe degradation in performance. For instance, performance of an 800M parameter model can be degraded to that of a 2x smaller model (400M params) by repeating 0.1% of the data 100 times, despite the other 90% of the training tokens remaining unique. We suspect there is a range in the middle where the data can be memorized and doing so consumes a large fraction of the model's capacity, and this may be where the peak of degradation occurs. Finally, we connect these observations to recent mechanistic interpretability work - attempting to reverse engineer the detailed computations performed by the model - by showing that data repetition disproportionately damages copying and internal structures associated with generalization, such as induction heads, providing a possible mechanism for the shift from generalization to memorization. Taken together, these results provide a hypothesis for why repeating a relatively small fraction of data in large language models could lead to disproportionately large harms to performance.

The ability of language models to learn a task from a few examples in context has generated substantial interest. Here, we provide a perspective that situates this type of supervised few-shot learning within a much broader spectrum of meta-learned in-context learning. Indeed, we suggest that any distribution of sequences in which context non-trivially decreases loss on subsequent predictions can be interpreted as eliciting a kind of in-context learning. We suggest that this perspective helps to unify the broad set of in-context abilities that language models exhibit x2014 such as adapting to tasks from instructions or role play, or extrapolating time series. This perspective also sheds light on potential roots of in-context learning in lower-level processing of linguistic dependencies (e.g. coreference or parallel structures). Finally, taking this perspective highlights the importance of generalization, which we suggest can be studied along several dimensions: not only the ability to learn something novel, but also flexibility in learning from different presentations, and in applying what is learned. We discuss broader connections to past literature in meta-learning and goal-conditioned agents, and other perspectives on learning and adaptation. We close by suggesting that research on in-context learning should consider this broader spectrum of in-context capabilities and types of generalization.

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the "generalization gap" phenomena. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase. We find that the weight distance from its initialization grows logarithmically with the number of weight updates. We therefore propose a "random walk on random landscape" statistical model which is known to exhibit similar "ultra-slow" diffusion behavior. Following this hypothesis we conducted experiments to show empirically that the "generalization gap" stems from the relatively small number of updates rather than the batch size, and can be completely eliminated by adapting the training regime used. We further investigate different techniques to train models in the large-batch regime and present a novel algorithm named "Ghost Batch Normalization" which enables significant decrease in the generalization gap without increasing the number of updates. To validate our findings we conduct several additional experiments on MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices and beliefs concerning training of deep models and suggest they may not be optimal to achieve good generalization.

Modern text-to-image models have achieved strong visual synthesis, yet remain unreliable when prompts require implicit visual constraints, relational reasoning, or external knowledge. Existing retrieval-augmented and agentic generation methods mitigate this issue by acquiring external knowledge, references, or refined prompts for the current request, yet they typically treat each generation as an isolated episode and do not systematically preserve past successes or failures for future use. In this work, we ask whether a text-to-image system can continually improve from its own generation experience without updating the underlying generator. We propose MemoGen, a training-free framework that augments existing image generators with an agentic evolution layer. For each task, MemoGen explicitly infers visual requirements, retrieves external evidence and references when necessary, translates them into executable generation constraints, evaluates the generated result, and stores task understanding, reference choices, visual feedback, successful strategies, and failure lessons as reusable experience memory. Across evolution rounds, the agent retrieves relevant experience to improve similar future generations, selectively repairing previously failed cases while preserving successful ones, thereby enabling test-time self-evolution without parameter updates. Extensive experiments on knowledge-intensive and reasoning-oriented benchmarks demonstrate the effectiveness of this paradigm: after only two evolution rounds, MemoGen built upon the open-source Qwen-Image backbone surpasses strong proprietary systems such as Nano Banana Pro and GPT-Image-1 on WISE and Mind-Bench, showing that explicit experience memory can serve as a powerful continual learning signal for reliable text-to-image generation.

Recent advancements in large language models (LLMs) reveal a perplexing phenomenon in continual learning: despite extensive training, models experience significant performance declines, raising questions about task alignment and underlying knowledge retention. This study first explores the concept of "spurious forgetting", proposing that such performance drops often reflect a decline in task alignment rather than true knowledge loss. Through controlled experiments with a synthesized dataset, we investigate the dynamics of model performance during the initial training phases of new tasks, discovering that early optimization steps can disrupt previously established task alignments. Our theoretical analysis connects these shifts to orthogonal updates in model weights, providing a robust framework for understanding this behavior. Ultimately, we introduce a Freezing strategy that fix the bottom layers of the model, leading to substantial improvements in four continual learning scenarios. Our findings underscore the critical distinction between task alignment and knowledge retention, paving the way for more effective strategies in continual learning.

The use of episodic memory in continual learning has demonstrated effectiveness for alleviating catastrophic forgetting. In recent studies, gradient-based approaches have been developed to make more efficient use of compact episodic memory. Such approaches refine the gradients resulting from new samples by those from memorized samples, aiming to reduce the diversity of gradients from different tasks. In this paper, we clarify the relation between diversity of gradients and discriminativeness of representations, showing shared as well as conflicting interests between Deep Metric Learning and continual learning, thus demonstrating pros and cons of learning discriminative representations in continual learning. Based on these findings, we propose a simple method -- Semi-Discriminative Representation Loss (SDRL) -- for continual learning. In comparison with state-of-the-art methods, SDRL shows better performance with low computational cost on multiple benchmark tasks in the setting of online continual learning.

Memory-augmented LLM agents offer an appealing shortcut to continual learning: rather than updating model parameters, they accumulate experience in external memory, seemingly sidestepping the stability-plasticity dilemma of parametric learning. We show that this challenge does not disappear but resurfaces at the memory level. Under a limited context window, old and new experiences compete during retrieval, relocating the continual-learning bottleneck from parameter updates to memory access. To study this phenomenon, we introduce a (k,v) framework that disentangles two fundamental design axes of external memory: how experience is represented and how it is organized for retrieval. Across sequential-task experiments in ALFWorld and BabyAI, we find that abstract procedural memories transfer more reliably than detailed trajectories, while negative transfer disproportionately harms the hard cases. Moreover, finer-grained memory organization is not universally beneficial: designs that yield strong forward transfer can simultaneously induce severe forgetting. Together, these results reveal that external memory does not resolve the continual-learning problem; it reshapes it into a problem of memory representation and retrieval design.

Continual learning is a promising machine learning paradigm to learn new tasks while retaining previously learned knowledge over streaming training data. Till now, rehearsal-based methods, keeping a small part of data from old tasks as a memory buffer, have shown good performance in mitigating catastrophic forgetting for previously learned knowledge. However, most of these methods typically treat each new task equally, which may not adequately consider the relationship or similarity between old and new tasks. Furthermore, these methods commonly neglect sample importance in the continual training process and result in sub-optimal performance on certain tasks. To address this challenging problem, we propose Relational Experience Replay (RER), a bi-level learning framework, to adaptively tune task-wise relationships and sample importance within each task to achieve a better `stability' and `plasticity' trade-off. As such, the proposed method is capable of accumulating new knowledge while consolidating previously learned old knowledge during continual learning. Extensive experiments conducted on three publicly available datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) show that the proposed method can consistently improve the performance of all baselines and surpass current state-of-the-art methods.

Despite their recent successes, Transformer-based large language models show surprising failure modes. A well-known example of such failure modes is their inability to length-generalize: solving problem instances at inference time that are longer than those seen during training. In this work, we further explore the root cause of this failure by performing a detailed analysis of model behaviors on the simple parity task. Our analysis suggests that length generalization failures are intricately related to a model's inability to perform random memory accesses within its context window. We present supporting evidence for this hypothesis by demonstrating the effectiveness of methodologies that circumvent the need for indexing or that enable random token access indirectly, through content-based addressing. We further show where and how the failure to perform random memory access manifests through attention map visualizations.

Large language model (LLM) agents increasingly rely on accumulated memory to solve long-horizon decision-making tasks. However, most existing approaches store memory in fixed representations and reuse it at a single or implicit level of abstraction, which limits generalization and often leads to negative transfer when distribution shift. This paper proposes the Meta-Cognitive Memory Abstraction method (MCMA), which treats memory abstraction as a learnable cognitive skill rather than a fixed design choice. MCMA decouples task execution from memory management by combining a frozen task model with a learned memory copilot. The memory copilot is trained using direct preference optimization, it determines how memories should be structured, abstracted, and reused. Memories are further organized into a hierarchy of abstraction levels, enabling selective reuse based on task similarity. When no memory is transferable, MCMA transfers the ability to abstract and manage memory by transferring the memory copilot. Experiments on ALFWorld, ScienceWorld, and BabyAI demonstrate substantial improvements in performance, out-of-distribution generalization, and cross-task transfer over several baselines.

Continual pre-training has increasingly become the predominant approach for adapting Large Language Models (LLMs) to new domains. This process involves updating the pre-trained LLM with a corpus from a new domain, resulting in a shift in the training distribution. To study the behavior of LLMs during this shift, we measured the model's performance throughout the continual pre-training process. we observed a temporary performance drop at the beginning, followed by a recovery phase, a phenomenon known as the "stability gap," previously noted in vision models classifying new classes. To address this issue and enhance LLM performance within a fixed compute budget, we propose three effective strategies: (1) Continually pre-training the LLM on a subset with a proper size for multiple epochs, resulting in faster performance recovery than pre-training the LLM on a large corpus in a single epoch; (2) Pre-training the LLM only on high-quality sub-corpus, which rapidly boosts domain performance; and (3) Using a data mixture similar to the pre-training data to reduce distribution gap. We conduct various experiments on Llama-family models to validate the effectiveness of our strategies in both medical continual pre-training and instruction tuning. For example, our strategies improve the average medical task performance of the OpenLlama-3B model from 36.2% to 40.7% with only 40% of the original training budget and enhance the average general task performance without causing forgetting. Furthermore, we apply our strategies to the Llama-3-8B model. The resulting model, Llama-3-Physician, achieves the best medical performance among current open-source models, and performs comparably to or even better than GPT-4 on several medical benchmarks. We release our models at https://huggingface.co/YiDuo1999/Llama-3-Physician-8B-Instruct.

We study the performance of transformers as a function of the number of repetitions of training examples with algorithmically generated datasets. On three problems of mathematics: the greatest common divisor, modular multiplication, and matrix eigenvalues, we show that for a fixed number of training steps, models trained on smaller sets of repeated examples outperform models trained on larger sets of single-use examples. We also demonstrate that two-set training - repeated use of a small random subset of examples, along normal sampling on the rest of the training set - provides for faster learning and better performance. This highlights that the benefits of repetition can outweigh those of data diversity. These datasets and problems provide a controlled setting to shed light on the still poorly understood interplay between generalization and memorization in deep learning.

Large Language Models (LLMs) frequently memorize long sequences verbatim, often with serious legal and privacy implications. Much prior work has studied such verbatim memorization using observational data. To complement such work, we develop a framework to study verbatim memorization in a controlled setting by continuing pre-training from Pythia checkpoints with injected sequences. We find that (1) non-trivial amounts of repetition are necessary for verbatim memorization to happen; (2) later (and presumably better) checkpoints are more likely to verbatim memorize sequences, even for out-of-distribution sequences; (3) the generation of memorized sequences is triggered by distributed model states that encode high-level features and makes important use of general language modeling capabilities. Guided by these insights, we develop stress tests to evaluate unlearning methods and find they often fail to remove the verbatim memorized information, while also degrading the LM. Overall, these findings challenge the hypothesis that verbatim memorization stems from specific model weights or mechanisms. Rather, verbatim memorization is intertwined with the LM's general capabilities and thus will be very difficult to isolate and suppress without degrading model quality.

Curriculum learning (CL), motivated by the intuition that learning in increasing order of difficulty should ease generalization, is commonly adopted both in pre-training and post-training of large language models (LLMs). The intuition of CL is particularly compelling for compositional reasoning, where complex problems are built from elementary inference rules; however, the actual impact of CL on such tasks remains largely underexplored. We present a systematic empirical study of CL for post-training of LLMs, using synthetic arithmetic and logical benchmarks where difficulty is characterized by reasoning complexity rather than surface-level proxies. Surprisingly, across multiple model families and curriculum schedules, we find no robust advantage in difficulty-based sequencing over standard random sampling in either accuracy or response length. These findings persist across both supervised fine-tuning (SFT) and reinforcement learning (RL) methods. Our study suggests that, in the context of deductive reasoning, the specific ordering of training examples plays a negligible role in achieving compositional generalization, challenging the practical utility of curriculum-based post-training.

Multimodal Continual Instruction Tuning (MCIT) aims to enable Multimodal Large Language Models (MLLMs) to incrementally learn new tasks without catastrophic forgetting. In this paper, we explore forgetting in this context, categorizing it into superficial forgetting and essential forgetting. Superficial forgetting refers to cases where the model's knowledge may not be genuinely lost, but its responses to previous tasks deviate from expected formats due to the influence of subsequent tasks' answer styles, making the results unusable. By contrast, essential forgetting refers to situations where the model provides correctly formatted but factually inaccurate answers, indicating a true loss of knowledge. Assessing essential forgetting necessitates addressing superficial forgetting first, as severe superficial forgetting can obscure the model's knowledge state. Hence, we first introduce the Answer Style Diversification (ASD) paradigm, which defines a standardized process for transforming data styles across different tasks, unifying their training sets into similarly diversified styles to prevent superficial forgetting caused by style shifts. Building on this, we propose RegLoRA to mitigate essential forgetting. RegLoRA stabilizes key parameters where prior knowledge is primarily stored by applying regularization, enabling the model to retain existing competencies. Experimental results demonstrate that our overall method, SEFE, achieves state-of-the-art performance.

Continual learning is a setting where machine learning models learn novel concepts from continuously shifting training data, while simultaneously avoiding degradation of knowledge on previously seen classes which may disappear from the training data for extended periods of time (a phenomenon known as the catastrophic forgetting problem). Current approaches for continual learning of a single expanding task (aka class-incremental continual learning) require extensive rehearsal of previously seen data to avoid this degradation of knowledge. Unfortunately, rehearsal comes at a cost to memory, and it may also violate data-privacy. Instead, we explore combining knowledge distillation and parameter regularization in new ways to achieve strong continual learning performance without rehearsal. Specifically, we take a deep dive into common continual learning techniques: prediction distillation, feature distillation, L2 parameter regularization, and EWC parameter regularization. We first disprove the common assumption that parameter regularization techniques fail for rehearsal-free continual learning of a single, expanding task. Next, we explore how to leverage knowledge from a pre-trained model in rehearsal-free continual learning and find that vanilla L2 parameter regularization outperforms EWC parameter regularization and feature distillation. Finally, we explore the recently popular ImageNet-R benchmark, and show that L2 parameter regularization implemented in self-attention blocks of a ViT transformer outperforms recent popular prompting for continual learning methods.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

Modern large language models excel in knowledge-intensive tasks, yet how transformers acquire (store) knowledge during pre-training and extract (retrieve) it during post-fine-tuning inference remains theoretically opaque. While prior theoretical work has begun to investigate these questions through the analysis of training dynamics, such studies are limited to single-layer, attention-only architectures. However, most existing studies suggest that MLPs are the most contributing components for storing knowledge in transformer-based language models. Meanwhile, our empirical investigations reveal that such simplified models, when trained using standard next-token prediction objectives, may be incapable of acquiring or extracting factual knowledge. To overcome this limitation, we introduce a tractable one-layer transformer framework that crucially incorporates both self-attention and MLP modules. By tracking its gradient dynamics, we establish convergence and generalization guarantees that illuminate the ability of knowledge acquisition and extraction. We prove that 1) Transformers can achieve near-optimal training loss during pre-training, signifying effective knowledge acquisition; 2) With a large fine-tuning dataset and specific data multiplicity conditions met, transformers can achieve low generalization error when tested on factual knowledge learned during pre-training but not reinforced during the fine-tuning, indicating successful knowledge extraction; 3) When the conditions are not satisfied, transformers exhibit high generalization loss, resulting in hallucinations. Our analysis includes both full fine-tuning and low-rank fine-tuning. Furthermore, our analysis offers theoretical insights into several pertinent empirical phenomena, such as the role of learning rate schedules. Experiments on synthetic and real-world PopQA datasets with GPT-2 and Llama-3.2-1B validate our results.

Adapting general large language models (LLMs) to specialized domains presents great challenges due to varied data distributions. This adaptation typically requires continual pre-training on massive domain-specific corpora to facilitate knowledge memorization, followed by training to apply this knowledge following human instructions and preferences. However, this method may result in inefficient knowledge memorization due to a lack of awareness of knowledge utilization and imposes substantial demands on LLMs to simultaneously learn knowledge utilization and format alignment with limited training samples. To facilitate the domain adaptation of LLM, we revise this process and propose a new domain adaptation framework including domain knowledge learning and general format alignment, called Mix-CPT. Specifically, we first conduct a knowledge mixture continual pre-training that concurrently focuses on knowledge memorization and utilization, allowing for mutual reinforcement. To avoid catastrophic forgetting during the continual pre-training process, we further incorporate a logit swap self-distillation constraint. Subsequently, leveraging the knowledge and capabilities acquired during continual pre-training, we efficiently perform instruction tuning and alignment with a few general training samples to achieve format alignment. Extensive experiments demonstrate that our proposed Mix-CPT framework can simultaneously improve the task-solving capabilities of LLMs on the target and general domains compared to the traditional adaptation methods.

The learning trajectories of linguistic phenomena in humans provide insight into linguistic representation, beyond what can be gleaned from inspecting the behavior of an adult speaker. To apply a similar approach to analyze neural language models (NLM), it is first necessary to establish that different models are similar enough in the generalizations they make. In this paper, we show that NLMs with different initialization, architecture, and training data acquire linguistic phenomena in a similar order, despite their different end performance. These findings suggest that there is some mutual inductive bias that underlies these models' learning of linguistic phenomena. Taking inspiration from psycholinguistics, we argue that studying this inductive bias is an opportunity to study the linguistic representation implicit in NLMs. Leveraging these findings, we compare the relative performance on different phenomena at varying learning stages with simpler reference models. Results suggest that NLMs exhibit consistent "developmental" stages. Moreover, we find the learning trajectory to be approximately one-dimensional: given an NLM with a certain overall performance, it is possible to predict what linguistic generalizations it has already acquired. Initial analysis of these stages presents phenomena clusters (notably morphological ones), whose performance progresses in unison, suggesting a potential link between the generalizations behind them.

A prevailing narrative in LLM post-training holds that supervised finetuning (SFT) memorizes while reinforcement learning (RL) generalizes. We revisit this claim for reasoning SFT with long chain-of-thought (CoT) supervision and find that cross-domain generalization is not absent but conditional, jointly shaped by optimization dynamics, training data, and base-model capability. Some reported failures are under-optimization artifacts: cross-domain performance first degrades before recovering and improving with extended training (a dip-and-recovery pattern), so shorttraining checkpoints can underestimate generalization. Data quality and structure both matter: low-quality solutions broadly hurt generalization,while verified long-CoT traces yield consistent cross-domain gains. Model capability is essential: stronger models internalize transferable procedural patterns (e.g., backtracking) even from a toy arithmetic game, while weaker ones imitate surface verbosity. This generalization is asymmetric, however: reasoning improves while safety degrades, reframing the question from whether reasoning SFT generalizes to under what conditions and at what cost.

Understanding memorisation in language models has practical and societal implications, e.g., studying models' training dynamics or preventing copyright infringements. Prior work defines memorisation as the causal effect of training with an instance on the model's ability to predict that instance. This definition relies on a counterfactual: the ability to observe what would have happened had the model not seen that instance. Existing methods struggle to provide computationally efficient and accurate estimates of this counterfactual. Further, they often estimate memorisation for a model architecture rather than for a specific model instance. This paper fills an important gap in the literature, proposing a new, principled, and efficient method to estimate memorisation based on the difference-in-differences design from econometrics. Using this method, we characterise a model's memorisation profile--its memorisation trends across training--by only observing its behaviour on a small set of instances throughout training. In experiments with the Pythia model suite, we find that memorisation (i) is stronger and more persistent in larger models, (ii) is determined by data order and learning rate, and (iii) has stable trends across model sizes, thus making memorisation in larger models predictable from smaller ones.

We investigate the generalization capabilities of small language models under two popular adaptation paradigms: few-shot prompting and supervised fine-tuning. While prompting is often favored for its parameter efficiency and flexibility, it remains unclear how robust this approach is in low-resource settings and under distributional shifts. This paper presents a comparative study of prompting and fine-tuning across task formats, prompt styles, and model scales, with a focus on their behavior in both in-distribution and out-of-distribution (OOD) settings. Beyond accuracy, we analyze the internal representations learned by each approach to assess the stability and abstraction of task-specific features. Our findings highlight critical differences in how small models internalize and generalize knowledge under different adaptation strategies. This work offers practical guidance for model selection in low-data regimes and contributes empirical insight into the ongoing debate over prompting versus fine-tuning. Code for the experiments is available at the following

One major obstacle towards AI is the poor ability of models to solve new problems quicker, and without forgetting previously acquired knowledge. To better understand this issue, we study the problem of continual learning, where the model observes, once and one by one, examples concerning a sequence of tasks. First, we propose a set of metrics to evaluate models learning over a continuum of data. These metrics characterize models not only by their test accuracy, but also in terms of their ability to transfer knowledge across tasks. Second, we propose a model for continual learning, called Gradient Episodic Memory (GEM) that alleviates forgetting, while allowing beneficial transfer of knowledge to previous tasks. Our experiments on variants of the MNIST and CIFAR-100 datasets demonstrate the strong performance of GEM when compared to the state-of-the-art.

Large language models (LLMs) such as GPT-4 sometimes appear to be creative, solving novel tasks often with a few demonstrations in the prompt. These tasks require the models to generalize on distributions different from those from training data -- which is known as out-of-distribution (OOD) generalization. Despite the tremendous success of LLMs, how they approach OOD generalization remains an open and underexplored question. We examine OOD generalization in settings where instances are generated according to hidden rules, including in-context learning with symbolic reasoning. Models are required to infer the hidden rules behind input prompts without any fine-tuning. We empirically examined the training dynamics of Transformers on a synthetic example and conducted extensive experiments on a variety of pretrained LLMs, focusing on a type of components known as induction heads. We found that OOD generalization and composition are tied together -- models can learn rules by composing two self-attention layers, thereby achieving OOD generalization. Furthermore, a shared latent subspace in the embedding (or feature) space acts as a bridge for composition by aligning early layers and later layers, which we refer to as the common bridge representation hypothesis.

Reliable generalization lies at the heart of safe ML and AI. However, understanding when and how neural networks generalize remains one of the most important unsolved problems in the field. In this work, we conduct an extensive empirical study (20'910 models, 15 tasks) to investigate whether insights from the theory of computation can predict the limits of neural network generalization in practice. We demonstrate that grouping tasks according to the Chomsky hierarchy allows us to forecast whether certain architectures will be able to generalize to out-of-distribution inputs. This includes negative results where even extensive amounts of data and training time never lead to any non-trivial generalization, despite models having sufficient capacity to fit the training data perfectly. Our results show that, for our subset of tasks, RNNs and Transformers fail to generalize on non-regular tasks, LSTMs can solve regular and counter-language tasks, and only networks augmented with structured memory (such as a stack or memory tape) can successfully generalize on context-free and context-sensitive tasks.

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These include theorem proving, solving quantitative mathematics problems, and reading/summarizing novels. In this paper, we run careful empirical studies exploring the length generalization capabilities of transformer-based language models. We first establish that naively finetuning transformers on length generalization tasks shows significant generalization deficiencies independent of model scale. We then show that combining pretrained large language models' in-context learning abilities with scratchpad prompting (asking the model to output solution steps before producing an answer) results in a dramatic improvement in length generalization. We run careful failure analyses on each of the learning modalities and identify common sources of mistakes that highlight opportunities in equipping language models with the ability to generalize to longer problems.

Large language models exhibit impressive cross-lingual capabilities. However, prior work analyzes this phenomenon through isolated factors and at sparse points during training, limiting our understanding of how cross-lingual generalization emerges--particularly in the early phases of learning. To study the early trajectory of linguistic and translation capabilities, we pretrain a multilingual 1.7B model on nine diverse languages, capturing checkpoints at a much finer granularity. We use word-level translation as a testbed, introducing a novel dataset to trace how translation develops over training through behavioral analyses, model-component analysis, and parameter-based ablations. We find that the model quickly acquires basic linguistic capabilities in parallel with token-level copying, while translation develops in two distinct phases: an initial phase dominated by copying and surface-level similarities, and a second phase in which more generalizing translation mechanisms are developed while copying is refined. Together, these findings provide a fine-grained view of how cross-lingual generalization develops during multilingual pretraining.

Recent diagnostic datasets on compositional generalization, such as SCAN (Lake and Baroni, 2018) and COGS (Kim and Linzen, 2020), expose severe problems in models trained from scratch on these datasets. However, in contrast to this poor performance, state-of-the-art models trained on larger and more general datasets show better generalization ability. In this work, to reconcile this inconsistency, we conduct an empirical analysis by training Transformer models on a variety of training sets with different data factors, including dataset scale, pattern complexity, example difficulty, etc. First, we show that increased dataset complexity can lead to better generalization behavior on multiple different generalization challenges. To further understand this improvement, we show two axes of the benefit from more complex datasets: they provide more diverse examples so compositional understanding becomes more effective, and they also prevent ungeneralizable memorization of the examples due to reduced example repetition frequency. Finally, we explore how training examples of different difficulty levels influence generalization differently. On synthetic datasets, simple examples invoke stronger compositionality than hard examples do. On larger-scale real language datasets, while hard examples become more important potentially to ensure decent data coverage, a balanced mixture of simple and hard examples manages to induce the strongest generalizability. The code and data for this work are available at https://github.com/owenzx/data4comp

According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language processing and also, arguably, for NLP models in the face of out-of-distribution data. However, many neural network models, including Transformers, have been shown to struggle with compositional generalization. In this paper, we hypothesize that forcing models to in-context learn can provide an inductive bias to promote compositional generalization. To test this hypothesis, we train a causal Transformer in a setting that renders ordinary learning very difficult: we present it with different orderings of the training instance and shuffle instance labels. This corresponds to training the model on all possible few-shot learning problems attainable from the dataset. The model can solve the task, however, by utilizing earlier examples to generalize to later ones (i.e. in-context learning). In evaluations on the datasets, SCAN, COGS, and GeoQuery, models trained in this manner indeed show improved compositional generalization. This indicates the usefulness of in-context learning problems as an inductive bias for generalization.

Rapidly learning abstract concepts from limited examples is a hallmark of human intelligence. This work investigates whether gradient-based meta-learning can equip neural networks with inductive biases for efficient few-shot acquisition of discrete concepts. I compare meta-learning methods against a supervised learning baseline on Boolean concepts (logical statements) generated by a probabilistic context-free grammar (PCFG). By systematically varying concept dimensionality (number of features) and recursive compositionality (depth of grammar recursion), I delineate between complexity regimes in which meta-learning robustly improves few-shot concept learning and regimes in which it does not. Meta-learners are much better able to handle compositional complexity than featural complexity. I highlight some reasons for this with a representational analysis of the weights of meta-learners and a loss landscape analysis demonstrating how featural complexity increases the roughness of loss trajectories, allowing curvature-aware optimization to be more effective than first-order methods. I find improvements in out-of-distribution generalization on complex concepts by increasing the number of adaptation steps in meta-SGD, where adaptation acts as a way of encouraging exploration of rougher loss basins. Overall, this work highlights the intricacies of learning compositional versus featural complexity in high dimensional concept spaces and provides a road to understanding the role of 2nd order methods and extended gradient adaptation in few-shot concept learning.

Pre-trained language models demonstrate general intelligence and common sense, but long inputs quickly become a bottleneck for memorizing information at inference time. We resurface a simple method, Memorizing Transformers (Wu et al., 2022), that gives the model access to a bank of pre-computed memories. We show that it is possible to fix many of the shortcomings of the original method, such as the need for fine-tuning, by critically assessing how positional encodings should be updated for the keys and values retrieved. This intuitive method uses the model's own key/query system to select and attend to the most relevant memories at each generation step, rather than using external embeddings. We demonstrate the importance of external information being retrieved in a majority of decoder layers, contrary to previous work. We open source a new counterfactual long-range retrieval benchmark, and show that Extended Mind Transformers outperform today's state of the art by 6% on average.

We investigate the capabilities of transformer large language models (LLMs) on relational reasoning tasks involving abstract symbols. Such tasks have long been studied in the neuroscience literature as fundamental building blocks for more complex abilities in programming, mathematics, and verbal reasoning. For (i) regression tasks, we prove that transformers generalize when trained, but require astonishingly large quantities of training data. For (ii) next-token-prediction tasks with symbolic labels, we show an "inverse scaling law": transformers fail to generalize as their embedding dimension increases. For both settings (i) and (ii), we propose subtle transformer modifications which can reduce the amount of data needed by adding two trainable parameters per head.

A growing number of state-of-the-art transfer learning methods employ language models pretrained on large generic corpora. In this paper we present a conceptually simple and effective transfer learning approach that addresses the problem of catastrophic forgetting. Specifically, we combine the task-specific optimization function with an auxiliary language model objective, which is adjusted during the training process. This preserves language regularities captured by language models, while enabling sufficient adaptation for solving the target task. Our method does not require pretraining or finetuning separate components of the network and we train our models end-to-end in a single step. We present results on a variety of challenging affective and text classification tasks, surpassing well established transfer learning methods with greater level of complexity.

The recent success of large language models (LLMs) trained on static, pre-collected, general datasets has sparked numerous research directions and applications. One such direction addresses the non-trivial challenge of integrating pre-trained LLMs into dynamic data distributions, task structures, and user preferences. Pre-trained LLMs, when tailored for specific needs, often experience significant performance degradation in previous knowledge domains -- a phenomenon known as "catastrophic forgetting". While extensively studied in the continual learning (CL) community, it presents new manifestations in the realm of LLMs. In this survey, we provide a comprehensive overview of the current research progress on LLMs within the context of CL. This survey is structured into four main sections: we first describe an overview of continually learning LLMs, consisting of two directions of continuity: vertical continuity (or vertical continual learning), i.e., continual adaptation from general to specific capabilities, and horizontal continuity (or horizontal continual learning), i.e., continual adaptation across time and domains (Section 3). We then summarize three stages of learning LLMs in the context of modern CL: Continual Pre-Training (CPT), Domain-Adaptive Pre-training (DAP), and Continual Fine-Tuning (CFT) (Section 4). Then we provide an overview of evaluation protocols for continual learning with LLMs, along with the current available data sources (Section 5). Finally, we discuss intriguing questions pertaining to continual learning for LLMs (Section 6). The full list of papers examined in this survey is available at https://github.com/Wang-ML-Lab/llm-continual-learning-survey.

Studying data memorization in neural language models helps us understand the risks (e.g., to privacy or copyright) associated with models regurgitating training data and aids in the development of countermeasures. Many prior works -- and some recently deployed defenses -- focus on "verbatim memorization", defined as a model generation that exactly matches a substring from the training set. We argue that verbatim memorization definitions are too restrictive and fail to capture more subtle forms of memorization. Specifically, we design and implement an efficient defense that perfectly prevents all verbatim memorization. And yet, we demonstrate that this "perfect" filter does not prevent the leakage of training data. Indeed, it is easily circumvented by plausible and minimally modified "style-transfer" prompts -- and in some cases even the non-modified original prompts -- to extract memorized information. We conclude by discussing potential alternative definitions and why defining memorization is a difficult yet crucial open question for neural language models.

Schemata are structured representations of complex tasks that can aid artificial intelligence by allowing models to break down complex tasks into intermediate steps. We propose a novel system that induces schemata from web videos and generalizes them to capture unseen tasks with the goal of improving video retrieval performance. Our system proceeds in three major phases: (1) Given a task with related videos, we construct an initial schema for a task using a joint video-text model to match video segments with text representing steps from wikiHow; (2) We generalize schemata to unseen tasks by leveraging language models to edit the text within existing schemata. Through generalization, we can allow our schemata to cover a more extensive range of tasks with a small amount of learning data; (3) We conduct zero-shot instructional video retrieval with the unseen task names as the queries. Our schema-guided approach outperforms existing methods for video retrieval, and we demonstrate that the schemata induced by our system are better than those generated by other models.

Neural networks often suffer from catastrophic interference (CI): performance on previously learned tasks drops off significantly when learning a new task. This contrasts strongly with humans, who can sequentially learn new tasks without appreciably forgetting previous tasks. Prior work has explored various techniques for mitigating CI such as regularization, rehearsal, generative replay, and distillation methods. The current work takes a different approach, one guided by cognitive science research showing that in naturalistic environments, the probability of encountering a task decreases as a power-law of the time since it was last performed. We argue that a realistic evaluation of techniques for the mitigation of CI should be performed in simulated naturalistic learning environments. Thus, we evaluate the extent of mitigation of CI when training simple rehearsal-based methods in power-law environments similar to the ones humans face. Our work explores this novel rehearsal-based approach for a domain-incremental task: learning permutations in the MNIST task. We compare our rehearsal environment with other baselines to show its efficacy in promoting continual learning. Additionally, we investigate whether this environment shows forward facilitation, i.e., faster learning of later tasks. Next, we explore the robustness of our learning environment to the number of tasks, model size, and amount of data rehearsed after each task. Notably, our results show that the performance is comparable or superior to that of models trained using popular regularization methods and also to rehearsals in non-power-law environments. The benefits of this training paradigm include simplicity and the lack of a need for extra neural circuitry. In addition, because our method is orthogonal to other methods, future research can combine training in power-law environments with other continual learning mechanisms.

We study whether transformers can learn to implicitly reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we consistently find that transformers can learn implicit reasoning, but only through grokking, i.e., extended training far beyond overfitting. The levels of generalization also vary across reasoning types: when faced with out-of-distribution examples, transformers fail to systematically generalize for composition but succeed for comparison. We delve into the model's internals throughout training, conducting analytical experiments that reveal: 1) the mechanism behind grokking, such as the formation of the generalizing circuit and its relation to the relative efficiency of generalizing and memorizing circuits, and 2) the connection between systematicity and the configuration of the generalizing circuit. Our findings guide data and training setup to better induce implicit reasoning and suggest potential improvements to the transformer architecture, such as encouraging cross-layer knowledge sharing. Furthermore, we demonstrate that for a challenging reasoning task with a large search space, GPT-4-Turbo and Gemini-1.5-Pro based on non-parametric memory fail badly regardless of prompting styles or retrieval augmentation, while a fully grokked transformer can achieve near-perfect accuracy, showcasing the power of parametric memory for complex reasoning.

We consider the problem of eliciting compositional generalization capabilities in large language models (LLMs) with a novel type of prompting strategy. Compositional generalization empowers the LLMs to solve problems that are harder than the ones they have seen (i.e., easy-to-hard generalization), which is a critical reasoning capability of human-like intelligence. However, even the current state-of-the-art LLMs still struggle with this form of reasoning. To bridge this gap, we propose skills-in-context (SKiC) prompting, which instructs LLMs how to compose basic skills to resolve more complex problems. We find that it is crucial to demonstrate both the skills and the compositional examples within the same prompting context. With as few as two examplars, our SKiC prompting initiates strong synergies between skills and their composition capabilities. Notably, it empowers LLMs to solve unseen problems that require innovative skill compositions, achieving near-perfect generalization on a broad range of challenging compositionality tasks. Intriguingly, SKiC prompting unlocks the latent potential of LLMs, enabling them to leverage pre-existing internal skills acquired during earlier pre-training stages, even when these skills are not explicitly presented in the prompting context. This results in the capability of LLMs to solve unseen complex problems by activating and composing internal competencies. With such prominent features, SKiC prompting is able to achieve state-of-the-art performance on challenging mathematical reasoning benchmarks (e.g., MATH).

To cope with uncertain changes of the external world, intelligent systems must continually learn from complex, evolving environments and respond in real time. This ability, collectively known as general continual learning (GCL), encapsulates practical challenges such as online datastreams and blurry task boundaries. Although leveraging pretrained models (PTMs) has greatly advanced conventional continual learning (CL), these methods remain limited in reconciling the diverse and temporally mixed information along a single pass, resulting in sub-optimal GCL performance. Inspired by meta-plasticity and reconstructive memory in neuroscience, we introduce here an innovative approach named Meta Post-Refinement (MePo) for PTMs-based GCL. This approach constructs pseudo task sequences from pretraining data and develops a bi-level meta-learning paradigm to refine the pretrained backbone, which serves as a prolonged pretraining phase but greatly facilitates rapid adaptation of representation learning to downstream GCL tasks. MePo further initializes a meta covariance matrix as the reference geometry of pretrained representation space, enabling GCL to exploit second-order statistics for robust output alignment. MePo serves as a plug-in strategy that achieves significant performance gains across a variety of GCL benchmarks and pretrained checkpoints in a rehearsal-free manner (e.g., 15.10\%, 13.36\%, and 12.56\% on CIFAR-100, ImageNet-R, and CUB-200 under Sup-21/1K). Our source code is available at https://github.com/SunGL001/MePo{MePo}

Large language models learn and continually learn through the accumulation of gradient-based updates, but how individual pieces of new information affect existing knowledge, leading to both beneficial generalization and problematic hallucination, remains poorly understood. We demonstrate that when learning new information, LLMs exhibit a "priming" effect: learning a new fact can cause the model to inappropriately apply that knowledge in unrelated contexts. To systematically study this phenomenon, we introduce "Outlandish," a carefully curated dataset of 1320 diverse text samples designed to probe how new knowledge permeates through an LLM's existing knowledge base. Using this dataset, we show that the degree of priming after learning new information can be predicted by measuring the token probability of key words before learning. This relationship holds robustly across different model architectures (PALM-2, Gemma, Llama), sizes, and training stages. Finally, we develop two novel techniques to modulate how new knowledge affects existing model behavior: (1) a ``stepping-stone'' text augmentation strategy and (2) an ``ignore-k'' update pruning method. These approaches reduce undesirable priming effects by 50-95\% while preserving the model's ability to learn new information. Our findings provide both empirical insights into how LLMs learn and practical tools for improving the specificity of knowledge insertion in language models. Further materials: https://sunchipsster1.github.io/projects/outlandish/

Modern recommender systems employ various sequential modules such as self-attention to learn dynamic user interests. However, these methods are less effective in capturing collaborative and transitional signals within user interaction sequences. First, the self-attention architecture uses the embedding of a single item as the attention query, making it challenging to capture collaborative signals. Second, these methods typically follow an auto-regressive framework, which is unable to learn global item transition patterns. To overcome these limitations, we propose a new method called Multi-Query Self-Attention with Transition-Aware Embedding Distillation (MQSA-TED). First, we propose an L-query self-attention module that employs flexible window sizes for attention queries to capture collaborative signals. In addition, we introduce a multi-query self-attention method that balances the bias-variance trade-off in modeling user preferences by combining long and short-query self-attentions. Second, we develop a transition-aware embedding distillation module that distills global item-to-item transition patterns into item embeddings, which enables the model to memorize and leverage transitional signals and serves as a calibrator for collaborative signals. Experimental results on four real-world datasets demonstrate the effectiveness of the proposed modules.

Meta-training, which fine-tunes the language model (LM) on various downstream tasks by maximizing the likelihood of the target label given the task instruction and input instance, has improved the zero-shot task generalization performance. However, meta-trained LMs still struggle to generalize to challenging tasks containing novel labels unseen during meta-training. In this paper, we propose Flipped Learning, an alternative method of meta-training which trains the LM to generate the task instruction given the input instance and label. During inference, the LM trained with Flipped Learning, referred to as Flipped, selects the label option that is most likely to generate the task instruction. On 14 tasks of the BIG-bench benchmark, the 11B-sized Flipped outperforms zero-shot T0-11B and even a 16 times larger 3-shot GPT-3 (175B) on average by 8.4% and 9.7% points, respectively. Flipped gives particularly large improvements on tasks with unseen labels, outperforming T0-11B by up to +20% average F1 score. This indicates that the strong task generalization of Flipped comes from improved generalization to novel labels. We release our code at https://github.com/seonghyeonye/Flipped-Learning.

The impressive capability of modern text-to-image models to generate realistic visuals has come with a serious drawback: they can be misused to create harmful, deceptive or unlawful content. This has accelerated the push for machine unlearning. This new field seeks to selectively remove specific knowledge from a model's training data without causing a drop in its overall performance. However, it turns out that actually forgetting a given concept is an extremely difficult task. Models exposed to attacks using adversarial prompts show the ability to generate so-called unlearned concepts, which can be not only harmful but also illegal. In this paper, we present considerations regarding the ability of models to forget and recall knowledge, introducing the Memory Self-Regeneration task. Furthermore, we present MemoRa strategy, which we consider to be a regenerative approach supporting the effective recovery of previously lost knowledge. Moreover, we propose that robustness in knowledge retrieval is a crucial yet underexplored evaluation measure for developing more robust and effective unlearning techniques. Finally, we demonstrate that forgetting occurs in two distinct ways: short-term, where concepts can be quickly recalled, and long-term, where recovery is more challenging.

The objective of digital forgetting is, given a model with undesirable knowledge or behavior, obtain a new model where the detected issues are no longer present. The motivations for forgetting include privacy protection, copyright protection, elimination of biases and discrimination, and prevention of harmful content generation. Effective digital forgetting has to be effective (meaning how well the new model has forgotten the undesired knowledge/behavior), retain the performance of the original model on the desirable tasks, and be scalable (in particular forgetting has to be more efficient than retraining from scratch on just the tasks/data to be retained). This survey focuses on forgetting in large language models (LLMs). We first provide background on LLMs, including their components, the types of LLMs, and their usual training pipeline. Second, we describe the motivations, types, and desired properties of digital forgetting. Third, we introduce the approaches to digital forgetting in LLMs, among which unlearning methodologies stand out as the state of the art. Fourth, we provide a detailed taxonomy of machine unlearning methods for LLMs, and we survey and compare current approaches. Fifth, we detail datasets, models and metrics used for the evaluation of forgetting, retaining and runtime. Sixth, we discuss challenges in the area. Finally, we provide some concluding remarks.

Classical continual learning (CL) has primarily focused on enabling models to update and retain knowledge through parameter-centric mechanisms, e.g., training strategies, architectural designs, and weight adaptation. However, emerging paradigms are reshaping the scope of CL beyond this traditional model adaptation view. For instance, on-policy learning broadens the space of update mechanisms; test-time training extends CL from the training phase to inference; and external harness components such as memory, skill libraries, and interaction protocols extend the evolutionary boundaries of model capabilities far beyond the static parameter space. Collectively, these developments indicate a transition from parameter-centric learning toward system-level adaptation. To characterize this transition, we examine the evolution of continual learning through three dimensions: When, How, and Where learning occurs. The How dimension encompasses off-policy, on-policy, and beyond-gradient optimization mechanics. The When dimension captures evolution across pre-training, post-training, and inference-time stages. The Where dimension delineates updates occurring within internal parameters versus external structural constraints. Anchored by this tri-axial framework, we systematically survey representative methods, trace the ongoing transition of continual learning, and discuss the key challenges, broader implications, and future directions arising from this paradigm shift.

Adapting one's thought process based on corrective feedback is an essential ability in human learning, particularly in collaborative settings. In contrast, the current large language model training paradigm relies heavily on modeling vast, static corpora. While effective for knowledge acquisition, it overlooks the interactive feedback loops essential for models to adapt dynamically to their context. In this work, we propose a framework that treats this interactive in-context learning ability not as an emergent property, but as a distinct, trainable skill. We introduce a scalable method that transforms single-turn verifiable tasks into multi-turn didactic interactions driven by information asymmetry. We first show that current flagship models struggle to integrate corrective feedback on hard reasoning tasks. We then demonstrate that models trained with our approach dramatically improve the ability to interactively learn from language feedback. More specifically, the multi-turn performance of a smaller model nearly reaches that of a model an order of magnitude larger. We also observe robust out-of-distribution generalization: interactive training on math problems transfers to diverse domains like coding, puzzles and maze navigation. Our qualitative analysis suggests that this improvement is due to an enhanced in-context plasticity. Finally, we show that this paradigm offers a unified path to self-improvement. By training the model to predict the teacher's critiques, effectively modeling the feedback environment, we convert this external signal into an internal capability, allowing the model to self-correct even without a teacher.

People can learn a new concept and use it compositionally, understanding how to "blicket twice" after learning how to "blicket." In contrast, powerful sequence-to-sequence (seq2seq) neural networks fail such tests of compositionality, especially when composing new concepts together with existing concepts. In this paper, I show how memory-augmented neural networks can be trained to generalize compositionally through meta seq2seq learning. In this approach, models train on a series of seq2seq problems to acquire the compositional skills needed to solve new seq2seq problems. Meta se2seq learning solves several of the SCAN tests for compositional learning and can learn to apply implicit rules to variables.

Large language models have achieved significant reasoning improvements through reinforcement learning with verifiable rewards (RLVR). Yet as model capabilities grow, constructing high-quality reward signals becomes increasingly difficult, making it essential to understand when RLVR can succeed under weaker forms of supervision. We conduct a systematic empirical study across diverse model families and reasoning domains under three weak supervision settings: scarce data, noisy rewards, and self-supervised proxy rewards. We find that generalization is governed by training reward saturation dynamics: models that generalize exhibit a prolonged pre-saturation phase during which training reward and downstream performance climb together, while models that saturate rapidly memorize rather than learn. We identify reasoning faithfulness, defined as the extent to which intermediate steps logically support the final answer, as the pre-RL property that predicts which regime a model falls into, while output diversity alone is uninformative. Motivated by these findings, we disentangle the contributions of continual pre-training and supervised fine-tuning, finding that SFT on explicit reasoning traces is necessary for generalization under weak supervision, while continual pre-training on domain data amplifies the effect. Applied together to Llama3.2-3B-Base, these interventions enable generalization across all three settings where the base model previously failed.

In settings such as fine-tuning and reinforcement learning, neural networks are often adapted under distribution shift. Standard adaptation methods typically optimize the target objective directly, inducing an abrupt change from the source training objective. This abrupt transition can distort learned representations, including features that may still be useful for the new task. We investigate whether a more gradual transition can improve adaptation. We propose loss smoothing, a simple approach that interpolates between the source and target training objectives at the start of adaptation. This smooth transition helps to preserve useful features from the source distribution while still enabling the model to specialize to the target distribution. Across controlled supervised shifts, pretrained vision adaptation, offline-to-online and online reinforcement learning, and language model fine-tuning, we find that loss smoothing consistently improves performance, suggesting that smoother objective transitions are a broadly useful tool for model adaptation.