MoFO: Momentum-Filtered Optimizer for Mitigating Forgetting in LLM Fine-Tuning

Recently, large language models (LLMs) have demonstrated remarkable capabilities in a wide range of tasks. Typically, an LLM is pre-trained on large corpora and subsequently fine-tuned on task-specific datasets. However, during fine-tuning, LLMs may forget the knowledge acquired in the pre-training stage, leading to a decline in general capabilities. To address this issue, we propose a new fine-tuning algorithm termed Momentum-Filtered Optimizer (MoFO). The key idea of MoFO is to iteratively select and update the model parameters with the largest momentum magnitudes. Compared to full-parameter training, MoFO achieves similar fine-tuning performance while keeping parameters closer to the pre-trained model, thereby mitigating knowledge forgetting. Unlike most existing methods for forgetting mitigation, MoFO combines the following two advantages. First, MoFO does not require access to pre-training data. This makes MoFO particularly suitable for fine-tuning scenarios where pre-training data is unavailable, such as fine-tuning checkpoint-only open-source LLMs. Second, MoFO does not alter the original loss function. This could avoid impairing the model performance on the fine-tuning tasks. We validate MoFO through rigorous convergence analysis and extensive experiments, demonstrating its superiority over existing methods in mitigating forgetting and enhancing fine-tuning performance.

Adam-mini: Use Fewer Learning Rates To Gain More

We propose Adam-mini, an optimizer that achieves on-par or better performance than AdamW with 45% to 50% less memory footprint. Adam-mini reduces memory by cutting down the learning rate resources in Adam (i.e., $1/\sqrt{v}$). We find that $\geq$ 90% of these learning rates in $v$ could be harmlessly removed if we (1) carefully partition the parameters into blocks following our proposed principle on Hessian structure; (2) assign a single but good learning rate to each parameter block. We further find that, for each of these parameter blocks, there exists a single high-quality learning rate that can outperform Adam, provided that sufficient resources are available to search it out. We then provide one cost-effective way to find good learning rates and propose Adam-mini. Empirically, we verify that Adam-mini performs on par or better than AdamW on various language models sized from 125M to 7B for pre-training, supervised fine-tuning, and RLHF. The reduced memory footprint of Adam-mini also alleviates communication overheads among GPUs and CPUs, thereby increasing throughput. For instance, Adam-mini achieves 49.6% higher throughput than AdamW when pre-training Llama2-7B on $2\times$ A800-80GB GPUs, which saves 33% wall-clock time for pre-training.

PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3$\times$ speedup compared to FOMs for large-scale LP problems.

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.

Federated Learning with Lossy Distributed Source Coding: Analysis and Optimization

Recently, federated learning (FL), which replaces data sharing with model sharing, has emerged as an efficient and privacy-friendly paradigm for machine learning (ML). A main challenge of FL is its huge uplink communication cost. In this paper, we tackle this challenge from an information-theoretic perspective. Specifically, we put forth a distributed source coding (DSC) framework for FL uplink, which unifies the encoding, transmission, and aggregation of the local updates as a lossy DSC problem, thus providing a systematic way to exploit the correlation between local updates to improve the uplink efficiency. Under this DSC-FL framework, we propose an FL uplink scheme based on the modified Berger-Tung coding (MBTC), which supports separate encoding and joint decoding by modifying the achievability scheme of the Berger-Tung inner bound. The achievable region of the MBTC-based uplink scheme is also derived. To unleash the potential of the MBTC-based FL scheme, we carry out a convergence analysis and then formulate a convergence rate maximization problem to optimize the parameters of MBTC. To solve this problem, we develop two algorithms, respectively for small- and large-scale FL systems, based on the majorization-minimization (MM) technique. Numerical results demonstrate the superiority of the MBTC-based FL scheme in terms of aggregation distortion, convergence performance, and communication cost, revealing the great potential of the DSC-FL framework.

The Global Landscape of Neural Networks: An Overview

One of the major concerns for neural network training is that the non-convexity of the associated loss functions may cause bad landscape. The recent success of neural networks suggests that their loss landscape is not too bad, but what specific results do we know about the landscape? In this article, we review recent findings and results on the global landscape of neural networks. First, we point out that wide neural nets may have sub-optimal local minima under certain assumptions. Second, we discuss a few rigorous results on the geometric properties of wide networks such as "no bad basin", and some modifications that eliminate sub-optimal local minima and/or decreasing paths to infinity. Third, we discuss visualization and empirical explorations of the landscape for practical neural nets. Finally, we briefly discuss some convergence results and their relation to landscape results.

Sub-Optimal Local Minima Exist for Almost All Over-parameterized Neural Networks

Does over-parameterization eliminate sub-optimal local minima for neural network problems? On one hand, existing positive results do not prove the claim, but often weaker claims. On the other hand, existing negative results have strong assumptions on the activation functions and/or data samples, causing a large gap with positive results. It was unclear before whether there is a clean answer of "yes" or "no". In this paper, we answer this question with a strong negative result. In particular, we prove that for deep and over-parameterized networks, sub-optimal local minima exist for generic input data samples and generic nonlinear activation. This is the setting widely studied in the global landscape of over-parameterized networks, thus our result corrects a possible misconception that "over-parameterization eliminates sub-optimal local-min". Our construction is based on fundamental optimization analysis, and thus rather principled.

Over-Parameterized Deep Neural Networks Have No Strict Local Minima For Any Continuous Activations

In this paper, we study the loss surface of the over-parameterized fully connected deep neural networks. We prove that for any continuous activation functions, the loss function has no bad strict local minimum, both in the regular sense and in the sense of sets. This result holds for any convex and continuous loss function, and the data samples are only required to be distinct in at least one dimension. Furthermore, we show that bad local minima do exist for a class of activation functions.