Why Transformers Need Adam: A Hessian Perspective

SGD performs worse than Adam by a significant margin on Transformers, but the reason remains unclear. In this work, we provide an explanation of SGD's failure on Transformers through the lens of Hessian: (i) Transformers are ``heterogeneous'': the Hessian spectrum across parameter blocks vary dramatically, a phenomenon we call ``block heterogeneity"; (ii) Heterogeneity hampers SGD: SGD performs badly on problems with block heterogeneity. To validate that heterogeneity hampers SGD, we check various Transformers, CNNs, MLPs, and quadratic problems, and find that SGD works well on problems without block heterogeneity but performs badly when the heterogeneity exists. Our initial theoretical analysis indicates that SGD fails because it applies one single learning rate for all blocks, which cannot handle the heterogeneity among blocks. The failure could be rescued if we could assign different learning rates across blocks, as designed in Adam.

Communication Efficiency Optimization of Federated Learning for Computing and Network Convergence of 6G Networks

Federated learning effectively addresses issues such as data privacy by collaborating across participating devices to train global models. However, factors such as network topology and device computing power can affect its training or communication process in complex network environments. A new network architecture and paradigm with computing-measurable, perceptible, distributable, dispatchable, and manageable capabilities, computing and network convergence (CNC) of 6G networks can effectively support federated learning training and improve its communication efficiency. By guiding the participating devices' training in federated learning based on business requirements, resource load, network conditions, and arithmetic power of devices, CNC can reach this goal. In this paper, to improve the communication efficiency of federated learning in complex networks, we study the communication efficiency optimization of federated learning for computing and network convergence of 6G networks, methods that gives decisions on its training process for different network conditions and arithmetic power of participating devices in federated learning. The experiments address two architectures that exist for devices in federated learning and arrange devices to participate in training based on arithmetic power while achieving optimization of communication efficiency in the process of transferring model parameters. The results show that the method we proposed can (1) cope well with complex network situations (2) effectively balance the delay distribution of participating devices for local training (3) improve the communication efficiency during the transfer of model parameters (4) improve the resource utilization in the network.

ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models

Alignment is of critical importance for training large language models (LLMs). The predominant strategy to address this is through Reinforcement Learning from Human Feedback (RLHF), where PPO serves as the de-facto algorithm. Yet, PPO is known to suffer from computational inefficiency, which is a challenge that this paper aims to address. We identify three important properties in RLHF tasks: fast simulation, deterministic transitions, and trajectory-level rewards, which are not leveraged in PPO. Based on such observations, we develop a new algorithm tailored for RLHF, called ReMax. The algorithm design of ReMax is built on a celebrated algorithm REINFORCE but is equipped with a new variance-reduction technique. Our method has three-fold advantages over PPO: first, ReMax is simple to implement and removes many hyper-parameters in PPO, which are scale-sensitive and laborious to tune. Second, ReMax saves about 50% memory usage in principle. As a result, PPO runs out-of-memory when fine-tuning a Llama2 (7B) model on 8xA100-40GB GPUs, whereas ReMax can afford training. This memory improvement is achieved by removing the value model in PPO. Third, based on our calculations, we find that even assuming PPO can afford the training of Llama2 (7B), it would still run about 2x slower than ReMax. This is due to the computational overhead of the value model, which does not exist in ReMax. Importantly, the above computational improvements do not sacrifice the performance. We hypothesize these advantages can be maintained in larger-scaled models. Our implementation of ReMax is available at https://github.com/liziniu/ReMax

Uncertainty and Explainable Analysis of Machine Learning Model for Reconstruction of Sonic Slowness Logs

Logs are valuable information for oil and gas fields as they help to determine the lithology of the formations surrounding the borehole and the location and reserves of subsurface oil and gas reservoirs. However, important logs are often missing in horizontal or old wells, which poses a challenge in field applications. In this paper, we utilize data from the 2020 machine learning competition of the SPWLA, which aims to predict the missing compressional wave slowness and shear wave slowness logs using other logs in the same borehole. We employ the NGBoost algorithm to construct an Ensemble Learning model that can predicate the results as well as their uncertainty. Furthermore, we combine the SHAP method to investigate the interpretability of the machine learning model. We compare the performance of the NGBosst model with four other commonly used Ensemble Learning methods, including Random Forest, GBDT, XGBoost, LightGBM. The results show that the NGBoost model performs well in the testing set and can provide a probability distribution for the prediction results. In addition, the variance of the probability distribution of the predicted log can be used to justify the quality of the constructed log. Using the SHAP explainable machine learning model, we calculate the importance of each input log to the predicted results as well as the coupling relationship among input logs. Our findings reveal that the NGBoost model tends to provide greater slowness prediction results when the neutron porosity and gamma ray are large, which is consistent with the cognition of petrophysical models. Furthermore, the machine learning model can capture the influence of the changing borehole caliper on slowness, where the influence of borehole caliper on slowness is complex and not easy to establish a direct relationship. These findings are in line with the physical principle of borehole acoustics.

Adam Can Converge Without Any Modification on Update Rules

Ever since Reddi et al. 2018 pointed out the divergence issue of Adam, many new variants have been designed to obtain convergence. However, vanilla Adam remains exceptionally popular and it works well in practice. Why is there a gap between theory and practice? We point out there is a mismatch between the settings of theory and practice: Reddi et al. 2018 pick the problem after picking the hyperparameters of Adam, i.e., $(\beta_1, \beta_2)$; while practical applications often fix the problem first and then tune $(\beta_1, \beta_2)$. Due to this observation, we conjecture that the empirical convergence can be theoretically justified, only if we change the order of picking the problem and hyperparameter. In this work, we confirm this conjecture. We prove that, when $\beta_2$ is large and $\beta_1 < \sqrt{\beta_2}<1$, Adam converges to the neighborhood of critical points. The size of the neighborhood is propositional to the variance of stochastic gradients. Under an extra condition (strong growth condition), Adam converges to critical points. As $\beta_2$ increases, our convergence result can cover any $\beta_1 \in [0,1)$ including $\beta_1=0.9$, which is the default setting in deep learning libraries. To our knowledge, this is the first result showing that Adam can converge under a wide range of hyperparameters {\it without any modification} on its update rules. Further, our analysis does not require assumptions of bounded gradients or bounded 2nd-order momentum. When $\beta_2$ is small, we further point out a large region of $(\beta_1,\beta_2)$ where Adam can diverge to infinity. Our divergence result considers the same setting as our convergence result, indicating a phase transition from divergence to convergence when increasing $\beta_2$. These positive and negative results can provide suggestions on how to tune Adam hyperparameters.

Provable Adaptivity in Adam

Adaptive Moment Estimation (Adam) optimizer is widely used in deep learning tasks because of its fast convergence properties. However, the convergence of Adam is still not well understood. In particular, the existing analysis of Adam cannot clearly demonstrate the advantage of Adam over SGD. We attribute this theoretical embarrassment to $L$-smooth condition (i.e., assuming the gradient is globally Lipschitz continuous with constant $L$) adopted by literature, which has been pointed out to often fail in practical neural networks. To tackle this embarrassment, we analyze the convergence of Adam under a relaxed condition called $(L_0,L_1)$ smoothness condition, which allows the gradient Lipschitz constant to change with the local gradient norm. $(L_0,L_1)$ is strictly weaker than $L$-smooth condition and it has been empirically verified to hold for practical deep neural networks. Under the $(L_0,L_1)$ smoothness condition, we establish the convergence for Adam with practical hyperparameters. Specifically, we argue that Adam can adapt to the local smoothness condition, justifying the \emph{adaptivity} of Adam. In contrast, SGD can be arbitrarily slow under this condition. Our result might shed light on the benefit of adaptive gradient methods over non-adaptive ones.