Test-Time Robust Personalization for Federated LearningLiangze Jiang, Tao Lin
Federated Learning (FL) is a machine learning paradigm where many clients collaboratively learn a shared global model with decentralized training data. Personalized FL additionally adapts the global model to different clients, achieving promising results on consistent local training and test distributions. However, for real-world personalized FL applications, it is crucial to go one step further: robustifying FL models under the evolving local test set during deployment, where various distribution shifts can arise. In this work, we identify the pitfalls of existing works under test-time distribution shifts and propose Federated Test-time Head Ensemble plus tuning(FedTHE+), which personalizes FL models with robustness to various test-time distribution shifts. We illustrate the advancement of FedTHE+ (and its computationally efficient variant FedTHE) over strong competitors, by training various neural architectures (CNN, ResNet, and Transformer) on CIFAR10 andImageNet with various test distributions. Along with this, we build a benchmark for assessing the performance and robustness of personalized FL methods during deployment. Code: https://github.com/LINs-lab/FedTHE.
FedBR: Improving Federated Learning on Heterogeneous Data via Local Learning Bias ReductionYongxin Guo, Xiaoying Tang, Tao Lin
Federated Learning (FL) is a way for machines to learn from data that is kept locally, in order to protect the privacy of clients. This is typically done using local SGD, which helps to improve communication efficiency. However, such a scheme is currently constrained by slow and unstable convergence due to the variety of data on different clients' devices. In this work, we identify three under-explored phenomena of biased local learning that may explain these challenges caused by local updates in supervised FL. As a remedy, we propose FedBR, a novel unified algorithm that reduces the local learning bias on features and classifiers to tackle these challenges. FedBR has two components. The first component helps to reduce bias in local classifiers by balancing the output of the models. The second component helps to learn local features that are similar to global features, but different from those learned from other data sources. We conducted several experiments to test \algopt and found that it consistently outperforms other SOTA FL methods. Both of its components also individually show performance gains. Our code is available at https://github.com/lins-lab/fedbr.
FedRC: Tackling Diverse Distribution Shifts Challenge in Federated Learning by Robust ClusteringYongxin Guo, Xiaoying Tang, Tao Lin
Federated Learning (FL) is a machine learning paradigm that safeguards privacy by retaining client data on edge devices. However, optimizing FL in practice can be challenging due to the diverse and heterogeneous nature of the learning system. Though recent research has focused on improving the optimization of FL when distribution shifts occur among clients, ensuring global performance when multiple types of distribution shifts occur simultaneously among clients -- such as feature distribution shift, label distribution shift, and concept shift -- remain under-explored. In this paper, we identify the learning challenges posed by the simultaneous occurrence of diverse distribution shifts and propose a clustering principle to overcome these challenges. Through our research, we find that existing methods fail to address the clustering principle. Therefore, we propose a novel clustering algorithm framework, dubbed as FedRC, which adheres to our proposed clustering principle by incorporating a bi-level optimization problem and a novel objective function. Extensive experiments demonstrate that FedRC significantly outperforms other SOTA cluster-based FL methods. Our code is available at \url{https://github.com/LINs-lab/FedRC}.
No Fear of Classifier Biases: Neural Collapse Inspired Federated Learning with Synthetic and Fixed ClassifierZexi Li, Xinyi Shang, Rui He et al.
Data heterogeneity is an inherent challenge that hinders the performance of federated learning (FL). Recent studies have identified the biased classifiers of local models as the key bottleneck. Previous attempts have used classifier calibration after FL training, but this approach falls short in improving the poor feature representations caused by training-time classifier biases. Resolving the classifier bias dilemma in FL requires a full understanding of the mechanisms behind the classifier. Recent advances in neural collapse have shown that the classifiers and feature prototypes under perfect training scenarios collapse into an optimal structure called simplex equiangular tight frame (ETF). Building on this neural collapse insight, we propose a solution to the FL's classifier bias problem by utilizing a synthetic and fixed ETF classifier during training. The optimal classifier structure enables all clients to learn unified and optimal feature representations even under extremely heterogeneous data. We devise several effective modules to better adapt the ETF structure in FL, achieving both high generalization and personalization. Extensive experiments demonstrate that our method achieves state-of-the-art performances on CIFAR-10, CIFAR-100, and Tiny-ImageNet.
28.2LGMay 3, 2022
Adversarial Training for High-Stakes ReliabilityDaniel M. Ziegler, Seraphina Nix, Lawrence Chan et al.
In the future, powerful AI systems may be deployed in high-stakes settings, where a single failure could be catastrophic. One technique for improving AI safety in high-stakes settings is adversarial training, which uses an adversary to generate examples to train on in order to achieve better worst-case performance. In this work, we used a safe language generation task (``avoid injuries'') as a testbed for achieving high reliability through adversarial training. We created a series of adversarial training techniques -- including a tool that assists human adversaries -- to find and eliminate failures in a classifier that filters text completions suggested by a generator. In our task, we determined that we can set very conservative classifier thresholds without significantly impacting the quality of the filtered outputs. We found that adversarial training increased robustness to the adversarial attacks that we trained on -- doubling the time for our contractors to find adversarial examples both with our tool (from 13 to 26 minutes) and without (from 20 to 44 minutes) -- without affecting in-distribution performance. We hope to see further work in the high-stakes reliability setting, including more powerful tools for enhancing human adversaries and better ways to measure high levels of reliability, until we can confidently rule out the possibility of catastrophic deployment-time failures of powerful models.
16.9LGMay 27, 2022
DELTA: Diverse Client Sampling for Fasting Federated LearningLin Wang, YongXin Guo, Tao Lin et al.
Partial client participation has been widely adopted in Federated Learning (FL) to reduce the communication burden efficiently. However, an inadequate client sampling scheme can lead to the selection of unrepresentative subsets, resulting in significant variance in model updates and slowed convergence. Existing sampling methods are either biased or can be further optimized for faster convergence.In this paper, we present DELTA, an unbiased sampling scheme designed to alleviate these issues. DELTA characterizes the effects of client diversity and local variance, and samples representative clients with valuable information for global model updates. In addition, DELTA is a proven optimal unbiased sampling scheme that minimizes variance caused by partial client participation and outperforms other unbiased sampling schemes in terms of convergence. Furthermore, to address full-client gradient dependence,we provide a practical version of DELTA depending on the available clients' information, and also analyze its convergence. Our results are validated through experiments on both synthetic and real-world datasets.
Increasing Model Capacity for Free: A Simple Strategy for Parameter Efficient Fine-tuningHaobo Song, Hao Zhao, Soumajit Majumder et al.
Fine-tuning large pre-trained foundation models, such as the 175B GPT-3, has attracted more attention for downstream tasks recently. While parameter-efficient fine-tuning methods have been proposed and proven effective without retraining all model parameters, their performance is limited by the capacity of incremental modules, especially under constrained parameter budgets. \\ To overcome this challenge, we propose CapaBoost, a simple yet effective strategy that enhances model capacity by leveraging low-rank updates through parallel weight modules in target layers. By applying static random masks to the shared weight matrix, CapaBoost constructs a diverse set of weight matrices, effectively increasing the rank of incremental weights without adding parameters. Notably, our approach can be seamlessly integrated into various existing parameter-efficient fine-tuning methods. We extensively validate the efficacy of CapaBoost through experiments on diverse downstream tasks, including natural language understanding, question answering, and image classification. Our results demonstrate significant improvements over baselines, without incurring additional computation or storage costs. Our code is available at \url{https://github.com/LINs-lab/CapaBoost}.
Revisiting Weighted Aggregation in Federated Learning with Neural NetworksZexi Li, Tao Lin, Xinyi Shang et al.
In federated learning (FL), weighted aggregation of local models is conducted to generate a global model, and the aggregation weights are normalized (the sum of weights is 1) and proportional to the local data sizes. In this paper, we revisit the weighted aggregation process and gain new insights into the training dynamics of FL. First, we find that the sum of weights can be smaller than 1, causing global weight shrinking effect (analogous to weight decay) and improving generalization. We explore how the optimal shrinking factor is affected by clients' data heterogeneity and local epochs. Second, we dive into the relative aggregation weights among clients to depict the clients' importance. We develop client coherence to study the learning dynamics and find a critical point that exists. Before entering the critical point, more coherent clients play more essential roles in generalization. Based on the above insights, we propose an effective method for Federated Learning with Learnable Aggregation Weights, named as FedLAW. Extensive experiments verify that our method can improve the generalization of the global model by a large margin on different datasets and models.
Towards Robust Multi-Modal Reasoning via Model SelectionXiangyan Liu, Rongxue Li, Wei Ji et al.
The reasoning capabilities of LLM (Large Language Model) are widely acknowledged in recent research, inspiring studies on tool learning and autonomous agents. LLM serves as the "brain" of the agent, orchestrating multiple tools for collaborative multi-step task solving. Unlike methods invoking tools like calculators or weather APIs for straightforward tasks, multi-modal agents excel by integrating diverse AI models for complex challenges. However, current multi-modal agents neglect the significance of model selection: they primarily focus on the planning and execution phases, and will only invoke predefined task-specific models for each subtask, making the execution fragile. Meanwhile, other traditional model selection methods are either incompatible with or suboptimal for the multi-modal agent scenarios, due to ignorance of dependencies among subtasks arising by multi-step reasoning. To this end, we identify the key challenges therein and propose the $\textit{M}^3$ framework as a plug-in with negligible runtime overhead at test-time. This framework improves model selection and bolsters the robustness of multi-modal agents in multi-step reasoning. In the absence of suitable benchmarks, we create MS-GQA, a new dataset specifically designed to investigate the model selection challenge in multi-modal agents. Our experiments reveal that our framework enables dynamic model selection, considering both user inputs and subtask dependencies, thereby robustifying the overall reasoning process. Our code and benchmark: https://github.com/LINs-lab/M3.
2.0LGJul 16, 2023
Revisiting Implicit Models: Sparsity Trade-offs Capability in Weight-tied Model for Vision TasksHaobo Song, Soumajit Majumder, Tao Lin
Implicit models such as Deep Equilibrium Models (DEQs) have garnered significant attention in the community for their ability to train infinite layer models with elegant solution-finding procedures and constant memory footprint. However, despite several attempts, these methods are heavily constrained by model inefficiency and optimization instability. Furthermore, fair benchmarking across relevant methods for vision tasks is missing. In this work, we revisit the line of implicit models and trace them back to the original weight-tied models. Surprisingly, we observe that weight-tied models are more effective, stable, as well as efficient on vision tasks, compared to the DEQ variants. Through the lens of these simple-yet-clean weight-tied models, we further study the fundamental limits in the model capacity of such models and propose the use of distinct sparse masks to improve the model capacity. Finally, for practitioners, we offer design guidelines regarding the depth, width, and sparsity selection for weight-tied models, and demonstrate the generalizability of our insights to other learning paradigms.
RelaySum for Decentralized Deep Learning on Heterogeneous DataThijs Vogels, Lie He, Anastasia Koloskova et al.
In decentralized machine learning, workers compute model updates on their local data. Because the workers only communicate with few neighbors without central coordination, these updates propagate progressively over the network. This paradigm enables distributed training on networks without all-to-all connectivity, helping to protect data privacy as well as to reduce the communication cost of distributed training in data centers. A key challenge, primarily in decentralized deep learning, remains the handling of differences between the workers' local data distributions. To tackle this challenge, we introduce the RelaySum mechanism for information propagation in decentralized learning. RelaySum uses spanning trees to distribute information exactly uniformly across all workers with finite delays depending on the distance between nodes. In contrast, the typical gossip averaging mechanism only distributes data uniformly asymptotically while using the same communication volume per step as RelaySum. We prove that RelaySGD, based on this mechanism, is independent of data heterogeneity and scales to many workers, enabling highly accurate decentralized deep learning on heterogeneous data. Our code is available at http://github.com/epfml/relaysgd.
KST-GCN: A Knowledge-Driven Spatial-Temporal Graph Convolutional Network for Traffic ForecastingJiawei Zhu, Xin Han, Hanhan Deng et al.
While considering the spatial and temporal features of traffic, capturing the impacts of various external factors on travel is an essential step towards achieving accurate traffic forecasting. However, existing studies seldom consider external factors or neglect the effect of the complex correlations among external factors on traffic. Intuitively, knowledge graphs can naturally describe these correlations. Since knowledge graphs and traffic networks are essentially heterogeneous networks, it is challenging to integrate the information in both networks. On this background, this study presents a knowledge representation-driven traffic forecasting method based on spatial-temporal graph convolutional networks. We first construct a knowledge graph for traffic forecasting and derive knowledge representations by a knowledge representation learning method named KR-EAR. Then, we propose the Knowledge Fusion Cell (KF-Cell) to combine the knowledge and traffic features as the input of a spatial-temporal graph convolutional backbone network. Experimental results on the real-world dataset show that our strategy enhances the forecasting performances of backbones at various prediction horizons. The ablation and perturbation analysis further verify the effectiveness and robustness of the proposed method. To the best of our knowledge, this is the first study that constructs and utilizes a knowledge graph to facilitate traffic forecasting; it also offers a promising direction to integrate external information and spatial-temporal information for traffic forecasting. The source code is available at https://github.com/lehaifeng/T-GCN/tree/master/KST-GCN.
Overcoming Long-term Catastrophic Forgetting through Adversarial Neural Pruning and Synaptic ConsolidationJian Peng, Bo Tang, Hao Jiang et al.
Artificial neural networks face the well-known problem of catastrophic forgetting. What's worse, the degradation of previously learned skills becomes more severe as the task sequence increases, known as the long-term catastrophic forgetting. It is due to two facts: first, as the model learns more tasks, the intersection of the low-error parameter subspace satisfying for these tasks becomes smaller or even does not exist; second, when the model learns a new task, the cumulative error keeps increasing as the model tries to protect the parameter configuration of previous tasks from interference. Inspired by the memory consolidation mechanism in mammalian brains with synaptic plasticity, we propose a confrontation mechanism in which Adversarial Neural Pruning and synaptic Consolidation (ANPyC) is used to overcome the long-term catastrophic forgetting issue. The neural pruning acts as long-term depression to prune task-irrelevant parameters, while the novel synaptic consolidation acts as long-term potentiation to strengthen task-relevant parameters. During the training, this confrontation achieves a balance in that only crucial parameters remain, and non-significant parameters are freed to learn subsequent tasks. ANPyC avoids forgetting important information and makes the model efficient to learn a large number of tasks. Specifically, the neural pruning iteratively relaxes the current task's parameter conditions to expand the common parameter subspace of the task; the synaptic consolidation strategy, which consists of a structure-aware parameter-importance measurement and an element-wise parameter updating strategy, decreases the cumulative error when learning new tasks. The full source code is available at https://github.com/GeoX-Lab/ANPyC.
T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic PredictionLing Zhao, Yujiao Song, Chao Zhang et al.
Accurate and real-time traffic forecasting plays an important role in the Intelligent Traffic System and is of great significance for urban traffic planning, traffic management, and traffic control. However, traffic forecasting has always been considered an open scientific issue, owing to the constraints of urban road network topological structure and the law of dynamic change with time, namely, spatial dependence and temporal dependence. To capture the spatial and temporal dependence simultaneously, we propose a novel neural network-based traffic forecasting method, the temporal graph convolutional network (T-GCN) model, which is in combination with the graph convolutional network (GCN) and gated recurrent unit (GRU). Specifically, the GCN is used to learn complex topological structures to capture spatial dependence and the gated recurrent unit is used to learn dynamic changes of traffic data to capture temporal dependence. Then, the T-GCN model is employed to traffic forecasting based on the urban road network. Experiments demonstrate that our T-GCN model can obtain the spatio-temporal correlation from traffic data and the predictions outperform state-of-art baselines on real-world traffic datasets. Our tensorflow implementation of the T-GCN is available at https://github.com/lehaifeng/T-GCN.
On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation ParadigmPeng Sun, Bei Shi, Daiwei Yu et al.
Contemporary machine learning requires training large neural networks on massive datasets and thus faces the challenges of high computational demands. Dataset distillation, as a recent emerging strategy, aims to compress real-world datasets for efficient training. However, this line of research currently struggle with large-scale and high-resolution datasets, hindering its practicality and feasibility. To this end, we re-examine the existing dataset distillation methods and identify three properties required for large-scale real-world applications, namely, realism, diversity, and efficiency. As a remedy, we propose RDED, a novel computationally-efficient yet effective data distillation paradigm, to enable both diversity and realism of the distilled data. Extensive empirical results over various neural architectures and datasets demonstrate the advancement of RDED: we can distill the full ImageNet-1K to a small dataset comprising 10 images per class within 7 minutes, achieving a notable 42% top-1 accuracy with ResNet-18 on a single RTX-4090 GPU (while the SOTA only achieves 21% but requires 6 hours).
1.8LGJul 26, 2022
Sample Complexity of Forecast AggregationTao Lin, Yiling Chen
We consider a Bayesian forecast aggregation model where $n$ experts, after observing private signals about an unknown binary event, report their posterior beliefs about the event to a principal, who then aggregates the reports into a single prediction for the event. The signals of the experts and the outcome of the event follow a joint distribution that is unknown to the principal, but the principal has access to i.i.d. "samples" from the distribution, where each sample is a tuple of the experts' reports (not signals) and the realization of the event. Using these samples, the principal aims to find an $\varepsilon$-approximately optimal aggregator, where optimality is measured in terms of the expected squared distance between the aggregated prediction and the realization of the event. We show that the sample complexity of this problem is at least $\tilde Ω(m^{n-2} / \varepsilon)$ for arbitrary discrete distributions, where $m$ is the size of each expert's signal space. This sample complexity grows exponentially in the number of experts $n$. But, if the experts' signals are independent conditioned on the realization of the event, then the sample complexity is significantly reduced, to $\tilde O(1 / \varepsilon^2)$, which does not depend on $n$. Our results can be generalized to non-binary events. The proof of our results uses a reduction from the distribution learning problem and reveals the fact that forecast aggregation is almost as difficult as distribution learning.
3.1LGNov 21, 2021
Learning by Active Forgetting for Neural NetworksJian Peng, Xian Sun, Min Deng et al.
Remembering and forgetting mechanisms are two sides of the same coin in a human learning-memory system. Inspired by human brain memory mechanisms, modern machine learning systems have been working to endow machine with lifelong learning capability through better remembering while pushing the forgetting as the antagonist to overcome. Nevertheless, this idea might only see the half picture. Up until very recently, increasing researchers argue that a brain is born to forget, i.e., forgetting is a natural and active process for abstract, rich, and flexible representations. This paper presents a learning model by active forgetting mechanism with artificial neural networks. The active forgetting mechanism (AFM) is introduced to a neural network via a "plug-and-play" forgetting layer (P\&PF), consisting of groups of inhibitory neurons with Internal Regulation Strategy (IRS) to adjust the extinction rate of themselves via lateral inhibition mechanism and External Regulation Strategy (ERS) to adjust the extinction rate of excitatory neurons via inhibition mechanism. Experimental studies have shown that the P\&PF offers surprising benefits: self-adaptive structure, strong generalization, long-term learning and memory, and robustness to data and parameter perturbation. This work sheds light on the importance of forgetting in the learning process and offers new perspectives to understand the underlying mechanisms of neural networks.
4.4LGAug 28, 2021
Representation Memorization for Fast Learning New Knowledge without ForgettingFei Mi, Tao Lin, Boi Faltings
The ability to quickly learn new knowledge (e.g. new classes or data distributions) is a big step towards human-level intelligence. In this paper, we consider scenarios that require learning new classes or data distributions quickly and incrementally over time, as it often occurs in real-world dynamic environments. We propose "Memory-based Hebbian Parameter Adaptation" (Hebb) to tackle the two major challenges (i.e., catastrophic forgetting and sample efficiency) towards this goal in a unified framework. To mitigate catastrophic forgetting, Hebb augments a regular neural classifier with a continuously updated memory module to store representations of previous data. To improve sample efficiency, we propose a parameter adaptation method based on the well-known Hebbian theory, which directly "wires" the output network's parameters with similar representations retrieved from the memory. We empirically verify the superior performance of Hebb through extensive experiments on a wide range of learning tasks (image classification, language model) and learning scenarios (continual, incremental, online). We demonstrate that Hebb effectively mitigates catastrophic forgetting, and it indeed learns new knowledge better and faster than the current state-of-the-art.
15.3LGNov 22, 2020
AST-GCN: Attribute-Augmented Spatiotemporal Graph Convolutional Network for Traffic ForecastingJiawei Zhu, Chao Tao, Hanhan Deng et al.
Traffic forecasting is a fundamental and challenging task in the field of intelligent transportation. Accurate forecasting not only depends on the historical traffic flow information but also needs to consider the influence of a variety of external factors, such as weather conditions and surrounding POI distribution. Recently, spatiotemporal models integrating graph convolutional networks and recurrent neural networks have become traffic forecasting research hotspots and have made significant progress. However, few works integrate external factors. Therefore, based on the assumption that introducing external factors can enhance the spatiotemporal accuracy in predicting traffic and improving interpretability, we propose an attribute-augmented spatiotemporal graph convolutional network (AST-GCN). We model the external factors as dynamic attributes and static attributes and design an attribute-augmented unit to encode and integrate those factors into the spatiotemporal graph convolution model. Experiments on real datasets show the effectiveness of considering external information on traffic forecasting tasks when compared to traditional traffic prediction methods. Moreover, under different attribute-augmented schemes and prediction horizon settings, the forecasting accuracy of the AST-GCN is higher than that of the baselines.
XCM: An Explainable Convolutional Neural Network for Multivariate Time Series ClassificationKevin Fauvel, Tao Lin, Véronique Masson et al.
Multivariate Time Series (MTS) classification has gained importance over the past decade with the increase in the number of temporal datasets in multiple domains. The current state-of-the-art MTS classifier is a heavyweight deep learning approach, which outperforms the second-best MTS classifier only on large datasets. Moreover, this deep learning approach cannot provide faithful explanations as it relies on post hoc model-agnostic explainability methods, which could prevent its use in numerous applications. In this paper, we present XCM, an eXplainable Convolutional neural network for MTS classification. XCM is a new compact convolutional neural network which extracts information relative to the observed variables and time directly from the input data. Thus, XCM architecture enables a good generalization ability on both large and small datasets, while allowing the full exploitation of a faithful post hoc model-specific explainability method (Gradient-weighted Class Activation Mapping) by precisely identifying the observed variables and timestamps of the input data that are important for predictions. We first show that XCM outperforms the state-of-the-art MTS classifiers on both the large and small public UEA datasets. Then, we illustrate how XCM reconciles performance and explainability on a synthetic dataset and show that XCM enables a more precise identification of the regions of the input data that are important for predictions compared to the current deep learning MTS classifier also providing faithful explainability. Finally, we present how XCM can outperform the current most accurate state-of-the-art algorithm on a real-world application while enhancing explainability by providing faithful and more informative explanations.
31.9CLApr 26, 2020
Masking as an Efficient Alternative to Finetuning for Pretrained Language ModelsMengjie Zhao, Tao Lin, Fei Mi et al.
We present an efficient method of utilizing pretrained language models, where we learn selective binary masks for pretrained weights in lieu of modifying them through finetuning. Extensive evaluations of masking BERT and RoBERTa on a series of NLP tasks show that our masking scheme yields performance comparable to finetuning, yet has a much smaller memory footprint when several tasks need to be inferred simultaneously. Through intrinsic evaluations, we show that representations computed by masked language models encode information necessary for solving downstream tasks. Analyzing the loss landscape, we show that masking and finetuning produce models that reside in minima that can be connected by a line segment with nearly constant test accuracy. This confirms that masking can be utilized as an efficient alternative to finetuning.
22.3LGMay 28, 2019
Exploring Interpretable LSTM Neural Networks over Multi-Variable DataTian Guo, Tao Lin, Nino Antulov-Fantulin
For recurrent neural networks trained on time series with target and exogenous variables, in addition to accurate prediction, it is also desired to provide interpretable insights into the data. In this paper, we explore the structure of LSTM recurrent neural networks to learn variable-wise hidden states, with the aim to capture different dynamics in multi-variable time series and distinguish the contribution of variables to the prediction. With these variable-wise hidden states, a mixture attention mechanism is proposed to model the generative process of the target. Then we develop associated training methods to jointly learn network parameters, variable and temporal importance w.r.t the prediction of the target variable. Extensive experiments on real datasets demonstrate enhanced prediction performance by capturing the dynamics of different variables. Meanwhile, we evaluate the interpretation results both qualitatively and quantitatively. It exhibits the prospect as an end-to-end framework for both forecasting and knowledge extraction over multi-variable data.
16.9LGApr 4, 2018
Training DNNs with Hybrid Block Floating PointMario Drumond, Tao Lin, Martin Jaggi et al.
The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full precision floating-point arithmetic to maximize performance per area. Ongoing research efforts seek to further increase that performance density by replacing floating-point with fixed-point arithmetic. However, a significant roadblock for these attempts has been fixed point's narrow dynamic range, which is insufficient for DNN training convergence. We identify block floating point (BFP) as a promising alternative representation since it exhibits wide dynamic range and enables the majority of DNN operations to be performed with fixed-point logic. Unfortunately, BFP alone introduces several limitations that preclude its direct applicability. In this work, we introduce HBFP, a hybrid BFP-FP approach, which performs all dot products in BFP and other operations in floating point. HBFP delivers the best of both worlds: the high accuracy of floating point at the superior hardware density of fixed point. For a wide variety of models, we show that HBFP matches floating point's accuracy while enabling hardware implementations that deliver up to 8.5x higher throughput.