Xin Yu Zhou

Xin Zhou, Ling Chen, Houming Wu

As the size of models and datasets grows, it has become increasingly common to train models in parallel. However, existing distributed stochastic gradient descent (SGD) algorithms suffer from insufficient utilization of computational resources and poor convergence in heterogeneous clusters. In this paper, we propose a delayed synchronous SGD algorithm with adaptive batch size (ABS-SGD) for heterogeneous GPU clusters. In ABS-SGD, workers perform global synchronization to accumulate delayed gradients and use the accumulated delayed gradients to update parameters. While workers are performing global synchronization for delayed gradients, they perform the computation of the next batch without specifying batch size in advance, which lasts until the next global synchronization starts, realizing the full utilization of computational resources. Since the gradient delay is only one iteration, the stale gradient problem can be alleviated. We theoretically prove the convergence of ABS-SGD in heterogeneous clusters. Extensive experiments in three types of heterogeneous clusters demonstrate that ABS-SGD can make full use of computational resources and accelerate model convergence: When training ResNet18 network with 4 workers, ABS-SGD increases the convergence speed by 1.30x on average compared with the best baseline algorithm.

Conor Snedeker, Xinyu Zhou, Raef Bassily

We study model personalization under user-level differential privacy (DP) in the shared representation framework. In this problem, there are $n$ users whose data is statistically heterogeneous, and their optimal parameters share an unknown embedding $U^* \in\mathbb{R}^{d\times k}$ that maps the user parameters in $\mathbb{R}^d$ to low-dimensional representations in $\mathbb{R}^k$, where $k\ll d$. Our goal is to privately recover the shared embedding and the local low-dimensional representations with small excess risk in the federated setting. We propose a private, efficient federated learning algorithm to learn the shared embedding based on the FedRep algorithm in [CHM+21]. Unlike [CHM+21], our algorithm satisfies differential privacy, and our results hold for the case of noisy labels. In contrast to prior work on private model personalization [JRS+21], our utility guarantees hold under a larger class of users' distributions (sub-Gaussian instead of Gaussian distributions). Additionally, in natural parameter regimes, we improve the privacy error term in [JRS+21] by a factor of $\widetilde{O}(dk)$. Next, we consider the binary classification setting. We present an information-theoretic construction to privately learn the shared embedding and derive a margin-based accuracy guarantee that is independent of $d$. Our method utilizes the Johnson-Lindenstrauss transform to reduce the effective dimensions of the shared embedding and the users' data. This result shows that dimension-independent risk bounds are possible in this setting under a margin loss.

Yi Lu, Wanxu Zhao, Xin Zhou et al.

Large Language Models (LLMs) often struggle to process and generate coherent context when the number of input tokens exceeds the pre-trained length. Recent advancements in long-context extension have significantly expanded the context window of LLMs but require expensive overhead to train the large-scale models with longer context. In this work, we propose Dimension-Wise Positional Embeddings Manipulation (DPE), a training-free framework to extrapolate the context window of LLMs by diving into RoPE's different hidden dimensions. Instead of manipulating all dimensions equally, DPE detects the effective length for every dimension and finds the key dimensions for context extension. We reuse the original position indices with their embeddings from the pre-trained model and manipulate the key dimensions' position indices to their most effective lengths. In this way, DPE adjusts the pre-trained models with minimal modifications while ensuring that each dimension reaches its optimal state for extrapolation. DPE significantly surpasses well-known baselines such as YaRN and Self-Extend. DPE enables Llama3-8k 8B to support context windows of 128k tokens without continual training and integrates seamlessly with Flash Attention 2. In addition to its impressive extrapolation capability, DPE also dramatically improves the models' performance within training length, such as Llama3.1 70B, by over 18 points on popular long-context benchmarks RULER. When compared with commercial models, Llama 3.1 70B with DPE even achieves better performance than GPT-4-128K.