Machine Learning (cs.LG)

Abstract: The success of the Adam optimizer on a wide array of architectures has made it the default in settings where stochastic gradient descent (SGD) performs poorly. However, our theoretical understanding of this discrepancy is lagging, preventing the development of significant improvements on either algorithm. Recent work advances the hypothesis that Adam and other heuristics like gradient clipping outperform SGD on language tasks because the distribution of the error induced by sampling has heavy tails. This suggests that Adam outperform SGD because it uses a more robust gradient estimate. We evaluate this hypothesis by varying the batch size, up to the entire dataset, to control for stochasticity. We present evidence that stochasticity and heavy-tailed noise are not major factors in the performance gap between SGD and Adam. Rather, Adam performs better as the batch size increases, while SGD is less effective at taking advantage of the reduction in noise. This raises the question as to why Adam outperforms SGD in the full-batch setting. Through further investigation of simpler variants of SGD, we find that the behavior of Adam with large batches is similar to sign descent with momentum.

Abstract: Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a $\textbf{mo}$derately $\textbf{d}$istributional $\textbf{e}$xploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty $\textit{subset}$ that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

Abstract: Distributed learning paradigms, such as federated or decentralized learning, allow a collection of agents to solve global learning and optimization problems through limited local interactions. Most such strategies rely on a mixture of local adaptation and aggregation steps, either among peers or at a central fusion center. Classically, aggregation in distributed learning is based on averaging, which is statistically efficient, but susceptible to attacks by even a small number of malicious agents. This observation has motivated a number of recent works, which develop robust aggregation schemes by employing robust variations of the mean. We present a new attack based on sensitivity curve maximization (SCM), and demonstrate that it is able to disrupt existing robust aggregation schemes by injecting small, but effective perturbations.

Abstract: Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

Abstract: Despite the huge recent breakthroughs in neural networks (NNs) for artificial intelligence (specifically deep convolutional networks) such NNs do not achieve human-level performance: they can be hacked by images that would fool no human and lack `common sense'. It has been argued that a basis of human-level intelligence is mankind's ability to perform relational reasoning: the comparison of different objects, measuring similarity, grasping of relations between objects and the converse, figuring out the odd one out in a set of objects. Mankind can even do this with objects they have never seen before. Here we show how ClusterFlow, a semi-supervised hierarchical clustering framework can operate on trained NNs utilising the rich multi-dimensional class and feature data found at the pre-SoftMax layer to build a hyperspacial map of classes/features and this adds more human-like functionality to modern deep convolutional neural networks. We demonstrate this with 3 tasks. 1. the statistical learning based `mistakes' made by infants when attending to images of cats and dogs. 2. improving both the resilience to hacking images and the accurate measure of certainty in deep-NNs. 3. Relational reasoning over sets of images, including those not known to the NN nor seen before. We also demonstrate that ClusterFlow can work on non-NN data and deal with missing data by testing it on a Chemistry dataset. This work suggests that modern deep NNs can be made more human-like without re-training of the NNs. As it is known that some methods used in deep and convolutional NNs are not biologically plausible or perhaps even the best approach: the ClusterFlow framework can sit on top of any NN and will be a useful tool to add as NNs are improved in this regard.

Abstract: This paper introduces JaxPruner, an open-source JAX-based pruning and sparse training library for machine learning research. JaxPruner aims to accelerate research on sparse neural networks by providing concise implementations of popular pruning and sparse training algorithms with minimal memory and latency overhead. Algorithms implemented in JaxPruner use a common API and work seamlessly with the popular optimization library Optax, which, in turn, enables easy integration with existing JAX based libraries. We demonstrate this ease of integration by providing examples in four different codebases: Scenic, t5x, Dopamine and FedJAX and provide baseline experiments on popular benchmarks.

Abstract: Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

Abstract: We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of $\mathbb{R}^{n}$ for the groups $S_n$, $O(n)$, $Sp(n)$, and $SO(n)$. By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.

Abstract: The learnable, linear neural network layers between tensor power spaces of $\mathbb{R}^{n}$ that are equivariant to the orthogonal group, $O(n)$, the special orthogonal group, $SO(n)$, and the symplectic group, $Sp(n)$, were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, $S_n$, recovering the algorithm of arXiv:2303.06208 in the process.

Abstract: Cluster separation in scatterplots is a task that is typically tackled by widely used clustering techniques, such as for instance k-means or DBSCAN. However, as these algorithms are based on non-perceptual metrics, their output often does not reflect human cluster perception. To bridge the gap between human cluster perception and machine-computed clusters, we propose a learning strategy which directly operates on scattered data. To learn perceptual cluster separation on this data, we crowdsourced a large scale dataset, consisting of 7,320 point-wise cluster affiliations for bivariate data, which has been labeled by 384 human crowd workers. Based on this data, we were able to train ClusterNet, a point-based deep learning model, trained to reflect human perception of cluster separability. In order to train ClusterNet on human annotated data, we omit rendering scatterplots on a 2D canvas, but rather use a PointNet++ architecture enabling inference on point clouds directly. In this work, we provide details on how we collected our dataset, report statistics of the resulting annotations, and investigate perceptual agreement of cluster separation for real-world data. We further report the training and evaluation protocol of ClusterNet and introduce a novel metric, that measures the accuracy between a clustering technique and a group of human annotators. Finally, we compare our approach against existing state-of-the-art clustering techniques.

Abstract: We use a binary attribute representation (BAR) model to describe a data set of Netflix viewers' ratings of movies. We classify the viewers with discrete bits rather than continuous parameters, which makes the representation compact and transparent. The attributes are easy to interpret, and we need far fewer attributes than similar methods do to achieve the same level of error. We also take advantage of the nonuniform distribution of ratings among the movies in the data set to train on a small selection of movies without compromising performance on the rest of the movies.

Abstract: The goal of the linear law-based feature space transformation (LLT) algorithm is to assist with the classification of univariate and multivariate time series. The presented R package, called LLT, implements this algorithm in a flexible yet user-friendly way. This package first splits the instances into training and test sets. It then utilizes time-delay embedding and spectral decomposition techniques to identify the governing patterns (called linear laws) of each input sequence (initial feature) within the training set. Finally, it applies the linear laws of the training set to transform the initial features of the test set. These steps are performed by three separate functions called trainTest, trainLaw, and testTrans. Their application requires a predefined data structure; however, for fast calculation, they use only built-in functions. The LLT R package and a sample dataset with the appropriate data structure are publicly available on GitHub.

Abstract: Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled. Approaches to identifying dynamical systems from such data typically use interpolation, imputation or subsampling to reorganize or modify the training data $\textit{prior}$ to learning. Partial physical knowledge may also be available $\textit{a priori}$ (accurately or approximately), and data-driven techniques can complement this knowledge. Here we exploit neural network architectures based on numerical integration methods and $\textit{a priori}$ physical knowledge to identify the right-hand side of the underlying governing differential equations. Iterates of such neural-network models allow for learning from data sampled at arbitrary time points $\textit{without}$ data modification. Importantly, we integrate the network with available partial physical knowledge in "physics informed gray-boxes"; this enables learning unknown kinetic rates or microbial growth functions while simultaneously estimating experimental parameters.

Abstract: Self-distillation relies on its own information to improve the generalization ability of the model and has a bright future. Existing self-distillation methods either require additional models, model modification, or batch size expansion for training, which increases the difficulty of use, memory consumption, and computational cost. This paper developed Self-discipline on multiple channels(SMC), which combines consistency regularization with self-distillation using the concept of multiple channels. Conceptually, SMC consists of two steps: 1) each channel data is simultaneously passed through the model to obtain its corresponding soft label, and 2) the soft label saved in the previous step is read together with the soft label obtained from the current channel data through the model to calculate the loss function. SMC uses consistent regularization and self-distillation to improve the generalization ability of the model and the robustness of the model to noisy labels. We named the SMC containing only two channels as SMC-2. Comparative experimental results on both datasets show that SMC-2 outperforms Label Smoothing Regularizaion and Self-distillation From The Last Mini-batch on all models, and outperforms the state-of-the-art Sharpness-Aware Minimization method on 83% of the models.Compatibility of SMC-2 and data augmentation experimental results show that using both SMC-2 and data augmentation improves the generalization ability of the model between 0.28% and 1.80% compared to using only data augmentation. Ultimately, the results of the label noise interference experiments show that SMC-2 curbs the tendency that the model's generalization ability decreases in the late training period due to the interference of label noise. The code is available at https://github.com/JiuTiannn/SMC-Self-discipline-on-multiple-channels.

Abstract: Deep learning (DL) has been a revolutionary technique in various domains. To facilitate the model development and deployment, many deep learning frameworks are proposed, among which PyTorch is one of the most popular solutions. The performance of ecosystem around PyTorch is critically important, which saves the costs of training models and reduces the response time of model inferences. In this paper, we propose TorchBench, a novel benchmark suite to study the performance of PyTorch software stack. Unlike existing benchmark suites, TorchBench encloses many representative models, covering a large PyTorch API surface. TorchBench is able to comprehensively characterize the performance of the PyTorch software stack, guiding the performance optimization across models, PyTorch framework, and GPU libraries. We show two practical use cases of TorchBench. (1) We profile TorchBench to identify GPU performance inefficiencies in PyTorch. We are able to optimize many performance bugs and upstream patches to the official PyTorch repository. (2) We integrate TorchBench into PyTorch continuous integration system. We are able to identify performance regression in multiple daily code checkins to prevent PyTorch repository from introducing performance bugs. TorchBench is open source and keeps evolving.

Abstract: Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to expectations of well-known distributions. We can then directly write the update by simply ``reading-off'' the terms in front of those expectations. The recipe makes the derivation easier, faster, shorter, and more general.

Abstract: Traditional models of glucose-insulin dynamics rely on heuristic parameterizations chosen to fit observations within a laboratory setting. However, these models cannot describe glucose dynamics in daily life. One source of failure is in their descriptions of glucose absorption rates after meal events. A meal's macronutritional content has nuanced effects on the absorption profile, which is difficult to model mechanistically. In this paper, we propose to learn the effects of macronutrition content from glucose-insulin data and meal covariates. Given macronutrition information and meal times, we use a neural network to predict an individual's glucose absorption rate. We use this neural rate function as the control function in a differential equation of glucose dynamics, enabling end-to-end training. On simulated data, our approach is able to closely approximate true absorption rates, resulting in better forecast than heuristic parameterizations, despite only observing glucose, insulin, and macronutritional information. Our work readily generalizes to meal events with higher-dimensional covariates, such as images, setting the stage for glucose dynamics models that are personalized to each individual's daily life.

Abstract: We study online learning in episodic constrained Markov decision processes (CMDPs), where the goal of the learner is to collect as much reward as possible over the episodes, while guaranteeing that some long-term constraints are satisfied during the learning process. Rewards and constraints can be selected either stochastically or adversarially, and the transition function is not known to the learner. While online learning in classical unconstrained MDPs has received considerable attention over the last years, the setting of CMDPs is still largely unexplored. This is surprising, since in real-world applications, such as, e.g., autonomous driving, automated bidding, and recommender systems, there are usually additional constraints and specifications that an agent has to obey during the learning process. In this paper, we provide the first best-of-both-worlds algorithm for CMDPs with long-term constraints. Our algorithm is capable of handling settings in which rewards and constraints are selected either stochastically or adversarially, without requiring any knowledge of the underling process. Moreover, our algorithm matches state-of-the-art regret and constraint violation bounds for settings in which constraints are selected stochastically, while it is the first to provide guarantees in the case in which they are chosen adversarially.

Abstract: Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test points. In this work, we tackle the problem of developing machine learning systems that retain the power of overparameterized function approximators while enabling extrapolation to out-of-support test points when possible. This is accomplished by noting that under certain conditions, a "transductive" reparameterization can convert an out-of-support extrapolation problem into a problem of within-support combinatorial generalization. We propose a simple strategy based on bilinear embeddings to enable this type of combinatorial generalization, thereby addressing the out-of-support extrapolation problem under certain conditions. We instantiate a simple, practical algorithm applicable to various supervised learning and imitation learning tasks.

Abstract: We analyze the generalization ability of joint-training meta learning algorithms via the Gibbs algorithm. Our exact characterization of the expected meta generalization error for the meta Gibbs algorithm is based on symmetrized KL information, which measures the dependence between all meta-training datasets and the output parameters, including task-specific and meta parameters. Additionally, we derive an exact characterization of the meta generalization error for the super-task Gibbs algorithm, in terms of conditional symmetrized KL information within the super-sample and super-task framework introduced in Steinke and Zakynthinou (2020) and Hellstrom and Durisi (2022) respectively. Our results also enable us to provide novel distribution-free generalization error upper bounds for these Gibbs algorithms applicable to meta learning.

Abstract: As deep learning technology advances and more urban spatial-temporal data accumulates, an increasing number of deep learning models are being proposed to solve urban spatial-temporal prediction problems. However, there are limitations in the existing field, including open-source data being in various formats and difficult to use, few papers making their code and data openly available, and open-source models often using different frameworks and platforms, making comparisons challenging. A standardized framework is urgently needed to implement and evaluate these methods. To address these issues, we provide a comprehensive review of urban spatial-temporal prediction and propose a unified storage format for spatial-temporal data called atomic files. We also propose LibCity, an open-source library that offers researchers a credible experimental tool and a convenient development framework. In this library, we have reproduced 65 spatial-temporal prediction models and collected 55 spatial-temporal datasets, allowing researchers to conduct comprehensive experiments conveniently. Using LibCity, we conducted a series of experiments to validate the effectiveness of different models and components, and we summarized promising future technology developments and research directions for spatial-temporal prediction. By enabling fair model comparisons, designing a unified data storage format, and simplifying the process of developing new models, LibCity is poised to make significant contributions to the spatial-temporal prediction field.

Abstract: We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

Abstract: Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting model is comprised of up to three neural networks, modelling terms representing conservation, dissipation and external forces, and discrete convolution operators that can either be learned or be prior knowledge. We demonstrate numerically the superior performance of PHNN compared to a baseline model that models the full dynamics by a single neural network. Moreover, since the PHNN model consists of three parts with different physical interpretations, these can be studied separately to gain insight into the system, and the learned model is applicable also if external forces are removed or changed.

Abstract: Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional space. Although in practice we usually receive finite observations, they are still high-dimensional and hence dimensionality reduction methods are crucial. In this vein, the main state-of-the-art method for functional data analysis is Functional PCA. Nevertheless, this classic technique assumes that the data lie in a linear manifold, and hence it could have problems when this hypothesis is not fulfilled. In this research, attention has been placed on a non-linear manifold learning method: Diffusion Maps. The article explains how to extend this multivariate method to functional data and compares its behavior against Functional PCA over different simulated and real examples.

Abstract: Deep Learning (DL) can diagnose faults and assess machine health from raw condition monitoring data without manually designed statistical features. However, practical manufacturing applications remain extremely difficult for existing DL methods. Machine data is often unlabeled and from very few health conditions (e.g., only normal operating data). Furthermore, models often encounter shifts in domain as process parameters change and new categories of faults emerge. Traditional supervised learning may struggle to learn compact, discriminative representations that generalize to these unseen target domains since it depends on having plentiful classes to partition the feature space with decision boundaries. Transfer Learning (TL) with domain adaptation attempts to adapt these models to unlabeled target domains but assumes similar underlying structure that may not be present if new faults emerge. This study proposes focusing on maximizing the feature generality on the source domain and applying TL via weight transfer to copy the model to the target domain. Specifically, Self-Supervised Learning (SSL) with Barlow Twins may produce more discriminative features for monitoring health condition than supervised learning by focusing on semantic properties of the data. Furthermore, Federated Learning (FL) for distributed training may also improve generalization by efficiently expanding the effective size and diversity of training data by sharing information across multiple client machines. Results show that Barlow Twins outperforms supervised learning in an unlabeled target domain with emerging motor faults when the source training data contains very few distinct categories. Incorporating FL may also provide a slight advantage by diffusing knowledge of health conditions between machines.