This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying gradients and, therefore, trigger the reuse of outdated gradients. The resultant gradient-based algorithms are termed Lazily Aggregated Gradient --- justifying our acronym LAG used henceforth. Theoretically, the merits of this contribution are: i) the convergence rate is the same as batch gradient descent in strongly-convex, convex, and nonconvex cases; and, ii) if the distributed datasets are heterogeneous (quantified by certain measurable constants), the communication rounds needed to achieve a targeted accuracy are reduced thanks to the adaptive reuse of lagged gradients. Numerical experiments on both synthetic and real data corroborate a significant communication reduction compared to alternatives.

Continual learning (CL) of a sequence of tasks is often accompanied with the catastrophicforgetting(CF)problem.

They split every 2D image into a fixed number of patches, each of which is treated as a token. Generally, representing an image with more tokens would lead tohigher prediction accuracy,while italso results indrastically increased computational cost. To achieve a decent trade-off between accuracy and speed, the number of tokens is empirically set to 16x16 or 14x14. In this paper, we argue that every image has its own characteristics, and ideally the token number should be conditioned on each individual input. In fact, we have observed that there exist aconsiderable number of "easy" images which can be accurately predicted with amere number of4x4tokens, while only asmall fraction of "hard" ones need a finer representation. Inspired by this phenomenon, we propose a Dynamic Transformer to automatically configure a proper number of tokens for each input image. This is achieved by cascading multiple Transformers with increasing numbers of tokens, which are sequentially activated in an adaptive fashion at test time, i.e., the inference is terminated once a sufficiently confident prediction is produced. We further design efficient featurereuseandrelationship reusemechanisms acrossdifferentcomponents ofthe Dynamic Transformer to reduce redundant computations.

With the rapid development of deep learning, the increasing complexity and scale of parameters make training a new model increasingly resource-intensive. In this paper, we start from the classic convolutional neural network (CNN) and explore a paradigm that does not require training to obtain new models. Similar to the birth of CNN inspired by receptive fields in the biological visual system, we draw inspiration from the information subsystem pathways in the biological visual system and propose Model Disassembling and Assembling (MDA). During model disassembling, we introduce the concept of relative contribution and propose a component locating technique to extract task-aware components from trained CNN classifiers. For model assembling, we present the alignment padding strategy and parameter scaling strategy to construct a new model tailored for a specific task, utilizing the disassembled task-aware components.The entire process is akin to playing with LEGO bricks, enabling arbitrary assembly of new models, and providing a novel perspective for model creation and reuse. Extensive experiments showcase that task-aware components disassembled from CNN classifiers or new models assembled using these components closely match or even surpass the performance of the baseline,demonstrating its promising results for model reuse. Furthermore, MDA exhibits diverse potential applications, with comprehensive experiments exploring model decision route analysis, model compression, knowledge distillation, and more.

In deep reinforcement learning, policy optimization methods need to deal with issues such as function approximation and the reuse of off-policy data. Standard policy gradient methods do not handle off-policy data well, leading to premature convergence and instability. This paper introduces a method to stabilize policy optimization when off-policy data are reused. The idea is to include a Bregman divergence between the behavior policy that generates the data and the current policy to ensure small and safe policy updates with off-policy data. The Bregman divergence is calculated between the state distributions of two policies, instead of only on the action probabilities, leading to a divergence augmentation formulation. Empirical experiments on Atari games show that in the data-scarce scenario where the reuse of off-policy data becomes necessary, our method can achieve better performance than other state-of-the-art deep reinforcement learning algorithms.

Excessive reuse of test data has become commonplace in today's machine learning workflows. Popular benchmarks, competitions, industrial scale tuning, among other applications, all involve test data reuse beyond guidance by statistical confidence bounds. Nonetheless, recent replication studies give evidence that popular benchmarks continue to support progress despite years of extensive reuse. We proffer a new explanation for the apparent longevity of test data: Many proposed models are similar in their predictions and we prove that this similarity mitigates overfitting. Specifically, we show empirically that models proposed for the ImageNet ILSVRC benchmark agree in their predictions well beyond what we can conclude from their accuracy levels alone. Likewise, models created by large scale hyperparameter search enjoy high levels of similarity. Motivated by these empirical observations, we give a non-asymptotic generalization bound that takes similarity into account, leading to meaningful confidence bounds in practical settings.

How does a single interconnected neural population perform multiple tasks, each with its own dynamical requirements? The relation between task requirements and neural dynamics in Recurrent Neural Networks (RNNs) has been investigated for single tasks. The forces shaping joint dynamics of multiple tasks, however, are largely unexplored. In this work, we first construct a systematic framework to study multiple tasks in RNNs, minimizing interference from input and output correlations with the hidden representation. This allows us to reveal how RNNs tend to share attractors and reuse dynamics, a tendency we define as the simplicity bias.We find that RNNs develop attractors sequentially during training, preferentially reusing existing dynamics and opting for simple solutions when possible.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves $2$-$3\times$ end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.