Ghost Noise for Regularizing Deep Neural Networks

Batch Normalization (BN) is widely used to stabilize the optimization process and improve the test performance of deep neural networks. The regularization effect of BN depends on the batch size and explicitly using smaller batch sizes with Batch Normalization, a method known as Ghost Batch Normalization (GBN), has been found to improve generalization in many settings. We investigate the effectiveness of GBN by disentangling the induced "Ghost Noise" from normalization and quantitatively analyzing the distribution of noise as well as its impact on model performance. Inspired by our analysis, we propose a new regularization technique called Ghost Noise Injection (GNI) that imitates the noise in GBN without incurring the detrimental train-test discrepancy effects of small batch training. We experimentally show that GNI can provide a greater generalization benefit than GBN. Ghost Noise Injection can also be beneficial in otherwise non-noisy settings such as layer-normalized networks, providing additional evidence of the usefulness of Ghost Noise in Batch Normalization as a regularizer.

Hardware-Efficient Transformer Training via Piecewise Affine Operations

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

Landmark Attention: Random-Access Infinite Context Length for Transformers

While transformers have shown remarkable success in natural language processing, their attention mechanism's large memory requirements have limited their ability to handle longer contexts. Prior approaches, such as recurrent memory or retrieval-based augmentation, have either compromised the random-access flexibility of attention (i.e., the capability to select any token in the entire context) or relied on separate mechanisms for relevant context retrieval, which may not be compatible with the model's attention. In this paper, we present a novel approach that allows access to the complete context while retaining random-access flexibility, closely resembling running attention on the entire context. Our method uses a landmark token to represent each block of the input and trains the attention to use it for selecting relevant blocks, enabling retrieval of blocks directly through the attention mechanism instead of by relying on a separate mechanism. Our approach seamlessly integrates with specialized data structures and the system's memory hierarchy, enabling processing of arbitrarily long context lengths. We demonstrate that our method can obtain comparable performance with Transformer-XL while significantly reducing the number of retrieved tokens in each step. Finally, we show that fine-tuning LLaMA 7B with our method successfully extends its context length capacity up to 32k tokens, allowing for inference at the context lengths of GPT-4.

Linearization Algorithms for Fully Composite Optimization

In this paper, we study first-order algorithms for solving fully composite optimization problems over bounded sets. We treat the differentiable and non-differentiable parts of the objective separately, linearizing only the smooth components. This provides us with new generalizations of the classical and accelerated Frank-Wolfe methods, that are applicable to non-differentiable problems whenever we can access the structure of the objective. We prove global complexity bounds for our algorithms that are optimal in several settings.

Unified Convergence Theory of Stochastic and Variance-Reduced Cubic Newton Methods

We study the widely known Cubic-Newton method in the stochastic setting and propose a general framework to use variance reduction which we call the helper framework. In all previous work, these methods were proposed with very large batches (both in gradients and Hessians) and with various and often strong assumptions. In this work, we investigate the possibility of using such methods without large batches and use very simple assumptions that are sufficient for all our methods to work. In addition, we study these methods applied to gradient-dominated functions. In the general case, we show improved convergence (compared to first-order methods) to an approximate local minimum, and for gradient-dominated functions, we show convergence to approximate global minima.

Beyond spectral gap (extended): The role of the topology in decentralized learning

In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers communicate over a sparse graph, current theory fails to capture important aspects of real-world behavior. First, the `spectral gap' of the communication graph is not predictive of its empirical performance in (deep) learning. Second, current theory does not explain that collaboration enables larger learning rates than training alone. In fact, it prescribes smaller learning rates, which further decrease as graphs become larger, failing to explain convergence dynamics in infinite graphs. This paper aims to paint an accurate picture of sparsely-connected distributed optimization. We quantify how the graph topology influences convergence in a quadratic toy problem and provide theoretical results for general smooth and (strongly) convex objectives. Our theory matches empirical observations in deep learning, and accurately describes the relative merits of different graph topologies. This paper is an extension of the conference paper by Vogels et. al. (2022). Code: https://github.com/epfml/topology-in-decentralized-learning.

Scalable Collaborative Learning via Representation Sharing

Privacy-preserving machine learning has become a key conundrum for multi-party artificial intelligence. Federated learning (FL) and Split Learning (SL) are two frameworks that enable collaborative learning while keeping the data private (on device). In FL, each data holder trains a model locally and releases it to a central server for aggregation. In SL, the clients must release individual cut-layer activations (smashed data) to the server and wait for its response (during both inference and back propagation). While relevant in several settings, both of these schemes have a high communication cost, rely on server-level computation algorithms and do not allow for tunable levels of collaboration. In this work, we present a novel approach for privacy-preserving machine learning, where the clients collaborate via online knowledge distillation using a contrastive loss (contrastive w.r.t. the labels). The goal is to ensure that the participants learn similar features on similar classes without sharing their input data. To do so, each client releases averaged last hidden layer activations of similar labels to a central server that only acts as a relay (i.e., is not involved in the training or aggregation of the models). Then, the clients download these last layer activations (feature representations) of the ensemble of users and distill their knowledge in their personal model using a contrastive objective. For cross-device applications (i.e., small local datasets and limited computational capacity), this approach increases the utility of the models compared to independent learning and other federated knowledge distillation (FD) schemes, is communication efficient and is scalable with the number of clients. We prove theoretically that our framework is well-posed, and we benchmark its performance against standard FD and FL on various datasets using different model architectures.

Second-order optimization with lazy Hessians

We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the method. This significantly reduces the overall arithmetical complexity of second-order optimization schemes. By using the cubic regularization technique, we establish fast global convergence of our method to a second-order stationary point, while the Hessian does not need to be updated each iteration. For convex problems, we justify global and local superlinear rates for lazy Newton steps with quadratic regularization, which is easier to compute. The optimal frequency for updating the Hessian is once every $d$ iterations, where $d$ is the dimension of the problem. This provably improves the total arithmetical complexity of second-order algorithms by a factor $\sqrt{d}$.

Accuracy Boosters: Epoch-Driven Mixed-Mantissa Block Floating-Point for DNN Training

The unprecedented growth in DNN model complexity, size and the amount of training data have led to a commensurate increase in demand for computing and a search for minimal encoding. Recent research advocates Hybrid Block Floating-Point (HBFP) as a technique that minimizes silicon provisioning in accelerators by converting the majority of arithmetic operations in training to 8-bit fixed-point. In this paper, we perform a full-scale exploration of the HBFP design space including minimal mantissa encoding, varying block sizes, and mixed mantissa bit-width across layers and epochs. We propose Accuracy Boosters, an epoch-driven mixed-mantissa HBFP that uses 6-bit mantissa only in the last epoch and converts $99.7\%$ of all arithmetic operations in training to 4-bit mantissas. Accuracy Boosters enable reducing silicon provisioning for an HBFP training accelerator by $16.98\times$ as compared to FP32, while preserving or outperforming FP32 accuracy.