Continual learning (CL) has emerged as a critical area in machine learning, enabling neural networks to learn from evolving data distributions while mitigating catastrophic forgetting. However, recent research has identified the stability gap -- a phenomenon where models initially lose performance on previously learned tasks before partially recovering during training. Such learning dynamics are contradictory to the intuitive understanding of stability in continual learning where one would expect the performance to degrade gradually instead of rapidly decreasing and then partially recovering later. To better understand and alleviate the stability gap, we investigate it at different levels of the neural network architecture, particularly focusing on the role of the classification head. We introduce the nearest-mean classifier (NMC) as a tool to attribute the influence of the backbone and the classification head on the stability gap. Our experiments demonstrate that NMC not only improves final performance, but also significantly enhances training stability across various continual learning benchmarks, including CIFAR100, ImageNet100, CUB-200, and FGVC Aircrafts. Moreover, we find that NMC also reduces task-recency bias. Our analysis provides new insights into the stability gap and suggests that the primary contributor to this phenomenon is the linear head, rather than the insufficient representation learning.

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 \url{https://huggingface.co/YiDuo1999/Llama-3-Physician-8B-Instruct}.

Recent research identified a temporary performance drop on previously learned tasks when transitioning to a new one. This drop is called the stability gap and has great consequences for continual learning: it complicates the direct employment of continually learning since the worse-case performance at task-boundaries is dramatic, it limits its potential as an energy-efficient training paradigm, and finally, the stability drop could result in a reduced final performance of the algorithm. In this paper, we show that the stability gap also occurs when applying joint incremental training of homogeneous tasks. In this scenario, the learner continues training on the same data distribution and has access to all data from previous tasks. In addition, we show that in this scenario, there exists a low-loss linear path to the next minima, but that SGD optimization does not choose this path. We perform further analysis including a finer batch-wise analysis which could provide insights towards potential solution directions.

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so far. However, we show that even with a perfect approximation to the joint loss, these approaches still suffer from temporary but substantial forgetting when starting to train on a new task. Motivated by this 'stability gap', we propose that continual learning strategies should focus not only on the optimization objective, but also on the way this objective is optimized. While there is some continual learning work that alters the optimization trajectory (e.g., using gradient projection techniques), this line of research is positioned as alternative to improving the optimization objective, while we argue it should be complementary. To evaluate the merits of our proposition, we plan to combine replay-approximated joint objectives with gradient projection-based optimization routines to test whether the addition of the latter provides benefits in terms of (1) alleviating the stability gap, (2) increasing the learning efficiency and (3) improving the final learning outcome.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

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, constraintbased 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. The fast convergence in gradient-based optimization has resulted in many successes with highly overparameterized neural networks (Krizhevsky et al., 2012; Mnih et al., 2013; Devlin et al., 2018). In the standard training paradigm, these results are conditional on having a static data-generating distribution. However, when non-stationarity is introduced by a time-varying data-generating distribution, the gradient-based updates greedily overwrite the parameters of the previous solution. This results in catastrophic forgetting (French, 1999) and is one of the main hurdles in continual or lifelong learning.

While momentum-based methods, in conjunction with stochastic gradient descent (SGD), are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that there exists a convex loss function for which algorithmic stability fails to establish generalization guarantees when SGD with standard heavy-ball momentum (SGDM) is run for multiple epochs. Then, for smooth Lipschitz loss functions, we analyze a modified momentum-based update rule, i.e., SGD with early momentum (SGDEM), and show that it admits an upper-bound on the generalization error. Thus, our results show that machine learning models can be trained for multiple epochs of SGDEM with a guarantee for generalization. Finally, for the special case of strongly convex loss functions, we find a range of momentum such that multiple epochs of standard SGDM, as a special form of SGDEM, also generalizes. Extending our results on generalization, we also develop an upper-bound on the expected true risk, in terms of the number of training steps, the size of the training set, and the momentum parameter. Experimental evaluations verify the consistency between the numerical results and our theoretical bounds and the effectiveness of SGDEM for smooth Lipschitz loss functions.

In this paper we introduce and analyze social distance games, a family of non-transferable utility coalitional games where an agent's utility is a measure of closeness to the other members of the coalition. We study both social welfare maximisation and stability in these games using a graph theoretic perspective. We use the stability gap to investigate the welfare of stable coalition structures, and propose two new solution concepts with improved welfare guarantees. We argue that social distance games are both interesting in themselves, as well as in the context of social networks.

We present and analyze coalitional affinity games, a family of hedonic games that explicitly model the value that an agent receives from being associated with other agents.  We provide a characterization of the social-welfare maximizing coalition structures, and study the stability properties of affinity games, using the core solution concept.  Interestingly, we observe that members of the core do not necessarily maximize social welfare.  We introduce a new measure, the stability-gap to capture this difference.  Using the stability gap, we show that for an interesting class of coalitional affinity games, the difference between the social welfare of a stable coalition structure and a social welfare maximizing coalition structure is bounded by a factor of two, and that this bound is tight.