Machine Learning (cs.LG)

Abstract: In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of the latent space is empirically pivotal, determining the optimal choice and the process of identifying it remain unclear. In this study, we aim to shed light on this under-explored topic by rethinking the latent space from the perspective of model complexity. Our investigation starts with the classic generative adversarial networks (GANs). Inspired by the GAN training objective, we propose a novel "distance" between the latent and data distributions, whose minimization coincides with that of the generator complexity. The minimizer of this distance is characterized as the optimal data-dependent latent that most effectively capitalizes on the generator's capacity. Then, we consider parameterizing such a latent distribution by an encoder network and propose a two-stage training strategy called Decoupled Autoencoder (DAE), where the encoder is only updated in the first stage with an auxiliary decoder and then frozen in the second stage while the actual decoder is being trained. DAE can improve the latent distribution and as a result, improve the generative performance. Our theoretical analyses are corroborated by comprehensive experiments on various models such as VQGAN and Diffusion Transformer, where our modifications yield significant improvements in sample quality with decreased model complexity.

Abstract: Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the spawning and permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.

Abstract: This paper shows that time series forecasting Transformer (TSFT) suffers from severe over-fitting problem caused by improper initialization method of unknown decoder inputs, esp. when handling non-stationary time series. Based on this observation, we propose GBT, a novel two-stage Transformer framework with Good Beginning. It decouples the prediction process of TSFT into two stages, including Auto-Regression stage and Self-Regression stage to tackle the problem of different statistical properties between input and prediction sequences.Prediction results of Auto-Regression stage serve as a Good Beginning, i.e., a better initialization for inputs of Self-Regression stage. We also propose Error Score Modification module to further enhance the forecasting capability of the Self-Regression stage in GBT. Extensive experiments on seven benchmark datasets demonstrate that GBT outperforms SOTA TSFTs (FEDformer, Pyraformer, ETSformer, etc.) and many other forecasting models (SCINet, N-HiTS, etc.) with only canonical attention and convolution while owning less time and space complexity. It is also general enough to couple with these models to strengthen their forecasting capability. The source code is available at: https://github.com/OrigamiSL/GBT

Abstract: As a distributed learning, Federated Learning (FL) faces two challenges: the unbalanced distribution of training data among participants, and the model attack by Byzantine nodes. In this paper, we consider the long-tailed distribution with the presence of Byzantine nodes in the FL scenario. A novel two-layer aggregation method is proposed for the rejection of malicious models and the advisable selection of valuable models containing tail class data information. We introduce the concept of think tank to leverage the wisdom of all participants. Preliminary experiments validate that the think tank can make effective model selections for global aggregation.

Abstract: Adversarial attacks are a type of attack on machine learning models where an attacker deliberately modifies the inputs to cause the model to make incorrect predictions. Adversarial attacks can have serious consequences, particularly in applications such as autonomous vehicles, medical diagnosis, and security systems. Work on the vulnerability of deep learning models to adversarial attacks has shown that it is very easy to make samples that make a model predict things that it doesn't want to. In this work, we analyze the impact of model interpretability due to adversarial attacks on text classification problems. We develop an ML-based classification model for text data. Then, we introduce the adversarial perturbations on the text data to understand the classification performance after the attack. Subsequently, we analyze and interpret the model's explainability before and after the attack

Abstract: This paper presents RAYEN, a framework to impose hard convex constraints on the output or latent variable of a neural network. RAYEN guarantees that, for any input or any weights of the network, the constraints are satisfied at all times. Compared to other approaches, RAYEN does not perform a computationally-expensive orthogonal projection step onto the feasible set, does not rely on soft constraints (which do not guarantee the satisfaction of the constraints at test time), does not use conservative approximations of the feasible set, and does not perform a potentially slow inner gradient descent correction to enforce the constraints. RAYEN supports any combination of linear, convex quadratic, second-order cone (SOC), and linear matrix inequality (LMI) constraints, achieving a very small computational overhead compared to unconstrained networks. For example, it is able to impose 1K quadratic constraints on a 1K-dimensional variable with an overhead of less than 8 ms, and an LMI constraint with 300x300 dense matrices on a 10K-dimensional variable in less than 12 ms. When used in neural networks that approximate the solution of constrained optimization problems, RAYEN achieves computation times between 20 and 7468 times faster than state-of-the-art algorithms, while guaranteeing the satisfaction of the constraints at all times and obtaining a cost very close to the optimal one.

Abstract: Large language models (LLMs) have brought about significant transformations in human society. Among the crucial computations in LLMs, the softmax unit holds great importance. Its helps the model generating a probability distribution on potential subsequent words or phrases, considering a series of input words. By utilizing this distribution, the model selects the most probable next word or phrase, based on the assigned probabilities. The softmax unit assumes a vital function in LLM training as it facilitates learning from data through the adjustment of neural network weights and biases. With the development of the size of LLMs, computing the gradient becomes expensive. However, Zero-th Order method can approximately compute the gradient with only forward passes. In this paper, we present a Zero-th Order algorithm specifically tailored for Softmax optimization. We demonstrate the convergence of our algorithm, highlighting its effectiveness in efficiently computing gradients for large-scale LLMs. By leveraging the Zeroth-Order method, our work contributes to the advancement of optimization techniques in the context of complex language models.

Abstract: In this paper, we propose an online convex optimization method with two different levels of adaptivity. On a higher level, our method is agnostic to the specific type and curvature of the loss functions, while at a lower level, it can exploit the niceness of the environments and attain problem-dependent guarantees. To be specific, we obtain $\mathcal{O}(\ln V_T)$, $\mathcal{O}(d \ln V_T)$ and $\hat{\mathcal{O}}(\sqrt{V_T})$ regret bounds for strongly convex, exp-concave and convex loss functions, respectively, where $d$ is the dimension, $V_T$ denotes problem-dependent gradient variations and $\hat{\mathcal{O}}(\cdot)$-notation omits logarithmic factors on $V_T$. Our result finds broad implications and applications. It not only safeguards the worst-case guarantees, but also implies the small-loss bounds in analysis directly. Besides, it draws deep connections with adversarial/stochastic convex optimization and game theory, further validating its practical potential. Our method is based on a multi-layer online ensemble incorporating novel ingredients, including carefully-designed optimism for unifying diverse function types and cascaded corrections for algorithmic stability. Remarkably, despite its multi-layer structure, our algorithm necessitates only one gradient query per round, making it favorable when the gradient evaluation is time-consuming. This is facilitated by a novel regret decomposition equipped with customized surrogate losses.

Abstract: Automated machine learning (AutoML) systems commonly ensemble models post hoc to improve predictive performance, typically via greedy ensemble selection (GES). However, we believe that GES may not always be optimal, as it performs a simple deterministic greedy search. In this work, we introduce two novel population-based ensemble selection methods, QO-ES and QDO-ES, and compare them to GES. While QO-ES optimises solely for predictive performance, QDO-ES also considers the diversity of ensembles within the population, maintaining a diverse set of well-performing ensembles during optimisation based on ideas of quality diversity optimisation. The methods are evaluated using 71 classification datasets from the AutoML benchmark, demonstrating that QO-ES and QDO-ES often outrank GES, albeit only statistically significant on validation data. Our results further suggest that diversity can be beneficial for post hoc ensembling but also increases the risk of overfitting.

Abstract: Accurate battery lifetime prediction is important for preventative maintenance, warranties, and improved cell design and manufacturing. However, manufacturing variability and usage-dependent degradation make life prediction challenging. Here, we investigate new features derived from capacity-voltage data in early life to predict the lifetime of cells cycled under widely varying charge rates, discharge rates, and depths of discharge. Features were extracted from regularly scheduled reference performance tests (i.e., low rate full cycles) during cycling. The early-life features capture a cell's state of health and the rate of change of component-level degradation modes, some of which correlate strongly with cell lifetime. Using a newly generated dataset from 225 nickel-manganese-cobalt/graphite Li-ion cells aged under a wide range of conditions, we demonstrate a lifetime prediction of in-distribution cells with 15.1% mean absolute percentage error using no more than the first 15% of data, for most cells. Further testing using a hierarchical Bayesian regression model shows improved performance on extrapolation, achieving 21.8% mean absolute percentage error for out-of-distribution cells. Our approach highlights the importance of using domain knowledge of lithium-ion battery degradation modes to inform feature engineering. Further, we provide the community with a new publicly available battery aging dataset with cells cycled beyond 80% of their rated capacity.

Abstract: Predicting emissions for gas turbines is critical for monitoring harmful pollutants being released into the atmosphere. In this study, we evaluate the performance of machine learning models for predicting emissions for gas turbines. We compare an existing predictive emissions model, a first principles-based Chemical Kinetics model, against two machine learning models we developed based on SAINT and XGBoost, to demonstrate improved predictive performance of nitrogen oxides (NOx) and carbon monoxide (CO) using machine learning techniques. Our analysis utilises a Siemens Energy gas turbine test bed tabular dataset to train and validate the machine learning models. Additionally, we explore the trade-off between incorporating more features to enhance the model complexity, and the resulting presence of increased missing values in the dataset.

Abstract: Multivariate time-series anomaly detection is critically important in many applications, including retail, transportation, power grid, and water treatment plants. Existing approaches for this problem mostly employ either statistical models which cannot capture the non-linear relations well or conventional deep learning models (e.g., CNN and LSTM) that do not explicitly learn the pairwise correlations among variables. To overcome these limitations, we propose a novel method, correlation-aware spatial-temporal graph learning (termed CST-GL), for time series anomaly detection. CST-GL explicitly captures the pairwise correlations via a multivariate time series correlation learning module based on which a spatial-temporal graph neural network (STGNN) can be developed. Then, by employing a graph convolution network that exploits one- and multi-hop neighbor information, our STGNN component can encode rich spatial information from complex pairwise dependencies between variables. With a temporal module that consists of dilated convolutional functions, the STGNN can further capture long-range dependence over time. A novel anomaly scoring component is further integrated into CST-GL to estimate the degree of an anomaly in a purely unsupervised manner. Experimental results demonstrate that CST-GL can detect anomalies effectively in general settings as well as enable early detection across different time delays.

Abstract: Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This paper aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

Abstract: Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream tasks. Previous approaches for graph representation learning have focused on either sampling k-hop neighborhoods, akin to breadth-first search, or random walks, akin to depth-first search. However, these methods are computationally expensive and unsuitable for real-time, low-latency inference on dynamic graphs. To overcome these limitations, we propose graph-sprints a general purpose feature extraction framework for continuous-time-dynamic-graphs (CTDGs) that has low latency and is competitive with state-of-the-art, higher latency models. To achieve this, a streaming, low latency approximation to the random-walk based features is proposed. In our framework, time-aware node embeddings summarizing multi-hop information are computed using only single-hop operations on the incoming edges. We evaluate our proposed approach on three open-source datasets and two in-house datasets, and compare with three state-of-the-art algorithms (TGN-attn, TGN-ID, Jodie). We demonstrate that our graph-sprints features, combined with a machine learning classifier, achieve competitive performance (outperforming all baselines for the node classification tasks in five datasets). Simultaneously, graph-sprints significantly reduce inference latencies, achieving close to an order of magnitude speed-up in our experimental setting.

Abstract: Undetected partial discharges (PDs) are a safety critical issue in high voltage (HV) gas insulated systems (GIS). While the diagnosis of PDs under AC voltage is well-established, the analysis of PDs under DC voltage remains an active research field. A key focus of these investigations is the classification of different PD sources to enable subsequent sophisticated analysis. In this paper, we propose and analyze a neural network-based approach for classifying PD signals caused by metallic protrusions and conductive particles on the insulator of HVDC GIS, without relying on pulse sequence analysis features. In contrast to previous approaches, our proposed model can discriminate the studied PD signals obtained at negative and positive potentials, while also generalizing to unseen operating voltage multiples. Additionally, we compare the performance of time- and frequency-domain input signals and explore the impact of different normalization schemes to mitigate the influence of free-space path loss between the sensor and defect location.

Abstract: The more AI-assisted decisions affect people's lives, the more important the fairness of such decisions becomes. In this chapter, we provide an introduction to research on fairness in machine learning. We explain the main fairness definitions and strategies for achieving fairness using concrete examples and place fairness research in the European context. Our contribution is aimed at an interdisciplinary audience and therefore avoids mathematical formulation but emphasizes visualizations and examples. -- Je mehr KI-gest\"utzte Entscheidungen das Leben von Menschen betreffen, desto wichtiger ist die Fairness solcher Entscheidungen. In diesem Kapitel geben wir eine Einf\"uhrung in die Forschung zu Fairness im maschinellen Lernen. Wir erkl\"aren die wesentlichen Fairness-Definitionen und Strategien zur Erreichung von Fairness anhand konkreter Beispiele und ordnen die Fairness-Forschung in den europ\"aischen Kontext ein. Unser Beitrag richtet sich dabei an ein interdisziplin\"ares Publikum und verzichtet daher auf die mathematische Formulierung sondern betont Visualisierungen und Beispiele.

Abstract: In the absence of sensitive race and ethnicity data, researchers, regulators, and firms alike turn to proxies. In this paper, I train a Bidirectional Long Short-Term Memory (BiLSTM) model on a novel dataset of voter registration data from all 50 US states and create an ensemble that achieves up to 36.8% higher out of sample (OOS) F1 scores than the best performing machine learning models in the literature. Additionally, I construct the most comprehensive database of first and surname distributions in the US in order to improve the coverage and accuracy of Bayesian Improved Surname Geocoding (BISG) and Bayesian Improved Firstname Surname Geocoding (BIFSG). Finally, I provide the first high-quality benchmark dataset in order to fairly compare existing models and aid future model developers.

Abstract: We design a novel algorithm for optimal transport by drawing from the entropic optimal transport, mirror descent and conjugate gradients literatures. Our algorithm is able to compute optimal transport costs with arbitrary accuracy without running into numerical stability issues. The algorithm is implemented efficiently on GPUs and is shown empirically to converge more quickly than traditional algorithms such as Sinkhorn's Algorithm both in terms of number of iterations and wall-clock time in many cases. We pay particular attention to the entropy of marginal distributions and show that high entropy marginals make for harder optimal transport problems, for which our algorithm is a good fit. We provide a careful ablation analysis with respect to algorithm and problem parameters, and present benchmarking over the MNIST dataset. The results suggest that our algorithm can be a useful addition to the practitioner's optimal transport toolkit. Our code is open-sourced at https://github.com/adaptive-agents-lab/MDOT-PNCG .

Abstract: In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.

Abstract: In the last few decades we have witnessed a significant development in Artificial Intelligence (AI) thanks to the availability of a variety of testbeds, mostly based on simulated environments and video games. Among those, roguelike games offer a very good trade-off in terms of complexity of the environment and computational costs, which makes them perfectly suited to test AI agents generalization capabilities. In this work, we present LuckyMera, a flexible, modular, extensible and configurable AI framework built around NetHack, a popular terminal-based, single-player roguelike video game. This library is aimed at simplifying and speeding up the development of AI agents capable of successfully playing the game and offering a high-level interface for designing game strategies. LuckyMera comes with a set of off-the-shelf symbolic and neural modules (called "skills"): these modules can be either hard-coded behaviors, or neural Reinforcement Learning approaches, with the possibility of creating compositional hybrid solutions. Additionally, LuckyMera comes with a set of utility features to save its experiences in the form of trajectories for further analysis and to use them as datasets to train neural modules, with a direct interface to the NetHack Learning Environment and MiniHack. Through an empirical evaluation we validate our skills implementation and propose a strong baseline agent that can reach state-of-the-art performances in the complete NetHack game. LuckyMera is open-source and available at https://github.com/Pervasive-AI-Lab/LuckyMera.

Abstract: Coping with distributional shifts is an important part of transfer learning methods in order to perform well in real-life tasks. However, most of the existing approaches in this area either focus on an ideal scenario in which the data does not contain noises or employ a complicated training paradigm or model design to deal with distributional shifts. In this paper, we revisit the robustness of the minimum error entropy (MEE) criterion, a widely used objective in statistical signal processing to deal with non-Gaussian noises, and investigate its feasibility and usefulness in real-life transfer learning regression tasks, where distributional shifts are common. Specifically, we put forward a new theoretical result showing the robustness of MEE against covariate shift. We also show that by simply replacing the mean squared error (MSE) loss with the MEE on basic transfer learning algorithms such as fine-tuning and linear probing, we can achieve competitive performance with respect to state-of-the-art transfer learning algorithms. We justify our arguments on both synthetic data and 5 real-world time-series data.

Abstract: Data heterogeneity across clients is one of the key challenges in Federated Learning (FL), which may slow down the global model convergence and even weaken global model performance. Most existing approaches tackle the heterogeneity by constraining local model updates through reference to global information provided by the server. This can alleviate the performance degradation on the aggregated global model. Different from existing methods, we focus the information exchange between clients, which could also enhance the effectiveness of local training and lead to generate a high-performance global model. Concretely, we propose a novel FL framework named FedCME by client matching and classifier exchanging. In FedCME, clients with large differences in data distribution will be matched in pairs, and then the corresponding pair of clients will exchange their classifiers at the stage of local training in an intermediate moment. Since the local data determines the local model training direction, our method can correct update direction of classifiers and effectively alleviate local update divergence. Besides, we propose feature alignment to enhance the training of the feature extractor. Experimental results demonstrate that FedCME performs better than FedAvg, FedProx, MOON and FedRS on popular federated learning benchmarks including FMNIST and CIFAR10, in the case where data are heterogeneous.

Abstract: Despite tremendous advancements in Artificial Intelligence, learning from large sets of data in an unsupervised manner remains a significant challenge. Classical clustering algorithms often fail to discover complex dependencies in large datasets, especially considering sparse, high-dimensional spaces. However, deep learning techniques proved to be successful when dealing with large quantities of data, efficiently reducing their dimensionality without losing track of underlying information. Several interesting advancements have already been made to combine deep learning and clustering. Still, the idea of enhancing the clustering results by combining multiple views of the data generated by deep neural networks appears to be insufficiently explored yet. This paper aims to investigate this direction and bridge the gap between deep neural networks, clustering techniques and ensemble learning methods. To achieve this goal, we propose a novel deep clustering ensemble method - Snapshot Spectral Clustering, designed to maximize the gain from combining multiple data views while minimizing the computational costs of creating the ensemble. Comparative analysis and experiments described in this paper prove the proposed concept, while the conducted hyperparameter study provides a valuable intuition to follow when selecting proper values.

Abstract: The concept of sustainable intensification in agriculture necessitates the implementation of management practices that prioritize sustainability without compromising productivity. However, the effects of such practices are known to depend on environmental conditions, and are therefore expected to change as a result of a changing climate. We study the impact of crop diversification on productivity in the context of climate change. We leverage heterogeneous Earth Observation data and contribute a data-driven approach based on causal machine learning for understanding how crop diversification impacts may change in the future. We apply this method to the country of Cyprus throughout a 4-year period. We find that, on average, crop diversification significantly benefited the net primary productivity of crops, increasing it by 2.8%. The effect generally synergized well with higher maximum temperatures and lower soil moistures. In a warmer and more drought-prone climate, we conclude that crop diversification exhibits promising adaptation potential and is thus a sensible policy choice with regards to agricultural productivity for present and future.

Abstract: This work analyzes and parallelizes LearnedSort, the novel algorithm that sorts using machine learning models based on the cumulative distribution function. LearnedSort is analyzed under the lens of algorithms with predictions, and it is argued that LearnedSort is a learning-augmented SampleSort. A parallel LearnedSort algorithm is developed combining LearnedSort with the state-of-the-art SampleSort implementation, IPS4o. Benchmarks on synthetic and real-world datasets demonstrate improved parallel performance for parallel LearnedSort compared to IPS4o and other sorting algorithms.

Abstract: Corruption is frequently observed in collected data and has been extensively studied in machine learning under different corruption models. Despite this, there remains a limited understanding of how these models relate such that a unified view of corruptions and their consequences on learning is still lacking. In this work, we formally analyze corruption models at the distribution level through a general, exhaustive framework based on Markov kernels. We highlight the existence of intricate joint and dependent corruptions on both labels and attributes, which are rarely touched by existing research. Further, we show how these corruptions affect standard supervised learning by analyzing the resulting changes in Bayes Risk. Our findings offer qualitative insights into the consequences of "more complex" corruptions on the learning problem, and provide a foundation for future quantitative comparisons. Applications of the framework include corruption-corrected learning, a subcase of which we study in this paper by theoretically analyzing loss correction with respect to different corruption instances.

Abstract: Batch effects (BEs) refer to systematic technical differences in data collection unrelated to biological variations whose noise is shown to negatively impact machine learning (ML) model generalizability. Here we release CohortFinder, an open-source tool aimed at mitigating BEs via data-driven cohort partitioning. We demonstrate CohortFinder improves ML model performance in downstream medical image processing tasks. CohortFinder is freely available for download at cohortfinder.com.

Abstract: Scaling Transformers to longer sequence lengths has been a major problem in the last several years, promising to improve performance in language modeling and high-resolution image understanding, as well as to unlock new applications in code, audio, and video generation. The attention layer is the main bottleneck in scaling to longer sequences, as its runtime and memory increase quadratically in the sequence length. FlashAttention exploits the asymmetric GPU memory hierarchy to bring significant memory saving (linear instead of quadratic) and runtime speedup (2-4$\times$ compared to optimized baselines), with no approximation. However, FlashAttention is still not nearly as fast as optimized matrix-multiply (GEMM) operations, reaching only 25-40\% of the theoretical maximum FLOPs/s. We observe that the inefficiency is due to suboptimal work partitioning between different thread blocks and warps on the GPU, causing either low-occupancy or unnecessary shared memory reads/writes. We propose FlashAttention-2, with better work partitioning to address these issues. In particular, we (1) tweak the algorithm to reduce the number of non-matmul FLOPs (2) parallelize the attention computation, even for a single head, across different thread blocks to increase occupancy, and (3) within each thread block, distribute the work between warps to reduce communication through shared memory. These yield around 2$\times$ speedup compared to FlashAttention, reaching 50-73\% of the theoretical maximum FLOPs/s on A100 and getting close to the efficiency of GEMM operations. We empirically validate that when used end-to-end to train GPT-style models, FlashAttention-2 reaches training speed of up to 225 TFLOPs/s per A100 GPU (72\% model FLOPs utilization).