PTP: Boosting Stability and Performance of Prompt Tuning with Perturbation-Based Regularizer

Recent studies show that prompt tuning can better leverage the power of large language models than fine-tuning on downstream natural language understanding tasks. However, the existing prompt tuning methods have training instability issues, as the variance of scores under different random seeds is quite large. To address this critical problem, we first investigate and find that the loss landscape of vanilla prompt tuning is precipitous when it is visualized, where a slight change of input data can cause a big fluctuation in the loss landscape. This is an essential factor that leads to the instability of prompt tuning. Based on this observation, we introduce perturbation-based regularizers, which can smooth the loss landscape, into prompt tuning. We propose a new algorithm, called Prompt Tuning with Perturbation-based regularizer~(PTP), which can not only alleviate training instability dramatically but also boost the performance of prompt tuning. We design two kinds of perturbation-based regularizers, including random-noise-based and adversarial-based. In particular, our proposed perturbations are flexible on both text space and embedding space. Extensive experiments show the effectiveness of our proposed methods in stabilizing the training. Our new algorithms improve the state-of-the-art prompt tuning methods by 1.94\% and 2.34\% on SuperGLUE and FewGLUE benchmarks, respectively.

When do you need Chain-of-Thought Prompting for ChatGPT?

Chain-of-Thought (CoT) prompting can effectively elicit complex multi-step reasoning from Large Language Models~(LLMs). For example, by simply adding CoT instruction ``Let's think step-by-step'' to each input query of MultiArith dataset, GPT-3's accuracy can be improved from 17.7\% to 78.7\%. However, it is not clear whether CoT is still effective on more recent instruction finetuned (IFT) LLMs such as ChatGPT. Surprisingly, on ChatGPT, CoT is no longer effective for certain tasks such as arithmetic reasoning while still keeping effective on other reasoning tasks. Moreover, on the former tasks, ChatGPT usually achieves the best performance and can generate CoT even without being instructed to do so. Hence, it is plausible that ChatGPT has already been trained on these tasks with CoT and thus memorized the instruction so it implicitly follows such an instruction when applied to the same queries, even without CoT. Our analysis reflects a potential risk of overfitting/bias toward instructions introduced in IFT, which becomes more common in training LLMs. In addition, it indicates possible leakage of the pretraining recipe, e.g., one can verify whether a dataset and instruction were used in training ChatGPT. Our experiments report new baseline results of ChatGPT on a variety of reasoning tasks and shed novel insights into LLM's profiling, instruction memorization, and pretraining dataset leakage.

Dynamic Voxel Grid Optimization for High-Fidelity RGB-D Supervised Surface Reconstruction

Direct optimization of interpolated features on multi-resolution voxel grids has emerged as a more efficient alternative to MLP-like modules. However, this approach is constrained by higher memory expenses and limited representation capabilities. In this paper, we introduce a novel dynamic grid optimization method for high-fidelity 3D surface reconstruction that incorporates both RGB and depth observations. Rather than treating each voxel equally, we optimize the process by dynamically modifying the grid and assigning more finer-scale voxels to regions with higher complexity, allowing us to capture more intricate details. Furthermore, we develop a scheme to quantify the dynamic subdivision of voxel grid during optimization without requiring any priors. The proposed approach is able to generate high-quality 3D reconstructions with fine details on both synthetic and real-world data, while maintaining computational efficiency, which is substantially faster than the baseline method NeuralRGBD.

Decentralized Riemannian Algorithm for Nonconvex Minimax Problems

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel manifold). Although many optimization algorithms for minimax problems have been developed in the Euclidean setting, it is difficult to convert them into Riemannian cases, and algorithms for nonconvex minimax problems with nonconvex constraints are even rare. On the other hand, to address the big data challenges, decentralized (serverless) training techniques have recently been emerging since they can reduce communications overhead and avoid the bottleneck problem on the server node. Nonetheless, the algorithm for decentralized Riemannian minimax problems has not been studied. In this paper, we study the distributed nonconvex-strongly-concave minimax optimization problem over the Stiefel manifold and propose both deterministic and stochastic minimax methods. The Steifel manifold is a non-convex set. The global function is represented as the finite sum of local functions. For the deterministic setting, we propose DRGDA and prove that our deterministic method achieves a gradient complexity of $O( \epsilon^{-2})$ under mild conditions. For the stochastic setting, we propose DRSGDA and prove that our stochastic method achieves a gradient complexity of $O(\epsilon^{-4})$. The DRGDA and DRSGDA are the first algorithms for distributed minimax optimization with nonconvex constraints with exact convergence. Extensive experimental results on the Deep Neural Networks (DNNs) training over the Stiefel manifold demonstrate the efficiency of our algorithms.

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms, yet it is underexplored in the Federated Learning setting. It is unclear how the challenges of Federated Learning affect the convergence of bilevel algorithms. In this work, we study Federated Bilevel Optimization problems. We first propose the FedBiO algorithm that solves the hyper-gradient estimation problem efficiently, then we propose FedBiOAcc to accelerate FedBiO. FedBiO has communication complexity $O(\epsilon^{-1.5})$ with linear speed up, while FedBiOAcc achieves communication complexity $O(\epsilon^{-1})$, sample complexity $O(\epsilon^{-1.5})$ and also the linear speed up. We also study Federated Bilevel Optimization problems with local lower level problems, and prove that FedBiO and FedBiOAcc converges at the same rate with some modification.

FedDA: Faster Framework of Local Adaptive Gradient Methods via Restarted Dual Averaging

Federated learning (FL) is an emerging learning paradigm to tackle massively distributed data. In Federated Learning, a set of clients jointly perform a machine learning task under the coordination of a server. The FedAvg algorithm is one of the most widely used methods to solve Federated Learning problems. In FedAvg, the learning rate is a constant rather than changing adaptively. The adaptive gradient methods show superior performance over the constant learning rate schedule; however, there is still no general framework to incorporate adaptive gradient methods into the federated setting. In this paper, we propose \textbf{FedDA}, a novel framework for local adaptive gradient methods. The framework adopts a restarted dual averaging technique and is flexible with various gradient estimation methods and adaptive learning rate formulations. In particular, we analyze \textbf{FedDA-MVR}, an instantiation of our framework, and show that it achieves gradient complexity $\tilde{O}(\epsilon^{-1.5})$ and communication complexity $\tilde{O}(\epsilon^{-1})$ for finding a stationary point $\epsilon$. This matches the best known rate for first-order FL algorithms and \textbf{FedDA-MVR} is the first adaptive FL algorithm that achieves this rate. We also perform extensive numerical experiments to verify the efficacy of our method.

A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier-augmented Lagrangian method for finding an approximate SOSP of this problem. Under some mild assumptions, we show that our method enjoys a total inner iteration complexity of $\widetilde{\cal O}(\epsilon^{-11/2})$ and an operation complexity of $\widetilde{\cal O}(\epsilon^{-11/2}\min\{n,\epsilon^{-5/4}\})$ for finding an $(\epsilon,\sqrt{\epsilon})$-SOSP of general nonconvex conic optimization with high probability. Moreover, under a constraint qualification, these complexity bounds are improved to $\widetilde{\cal O}(\epsilon^{-7/2})$ and $\widetilde{\cal O}(\epsilon^{-7/2}\min\{n,\epsilon^{-3/4}\})$, respectively. To the best of our knowledge, this is the first study on the complexity of finding an approximate SOSP of general nonconvex conic optimization. Preliminary numerical results are presented to demonstrate superiority of the proposed method over first-order methods in terms of solution quality.

Adversarial Weight Perturbation Improves Generalization in Graph Neural Network

A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we minimize the loss w.r.t. a bounded worst-case perturbation of the model parameters thereby favoring local minima with a small loss in a neighborhood around them. The benefits of AWP, and more generally the connections between flatness and generalization, have been extensively studied for i.i.d. data such as images. In this paper, we extensively study this phenomenon for graph data. Along the way, we first derive a generalization bound for non-i.i.d. node classification tasks. Then we identify a vanishing-gradient issue with all existing formulations of AWP and we propose a new Weighted Truncated AWP (WT-AWP) to alleviate this issue. We show that regularizing graph neural networks with WT-AWP consistently improves both natural and robust generalization across many different graph learning tasks and models.

Faster Adaptive Federated Learning

Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, the federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples $O(\epsilon^{-3})$ and $O(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms.

Towards Robust Dataset Learning

Adversarial training has been actively studied in recent computer vision research to improve the robustness of models. However, due to the huge computational cost of generating adversarial samples, adversarial training methods are often slow. In this paper, we study the problem of learning a robust dataset such that any classifier naturally trained on the dataset is adversarially robust. Such a dataset benefits the downstream tasks as natural training is much faster than adversarial training, and demonstrates that the desired property of robustness is transferable between models and data. In this work, we propose a principled, tri-level optimization to formulate the robust dataset learning problem. We show that, under an abstraction model that characterizes robust vs. non-robust features, the proposed method provably learns a robust dataset. Extensive experiments on MNIST, CIFAR10, and TinyImageNet demostrate the effectiveness of our algorithm with different network initializations and architectures.