Machine Learning (cs.LG)

Abstract: Previous research has shown that fully-connected networks with small initialization and gradient-based training methods exhibit a phenomenon known as condensation during training. This phenomenon refers to the input weights of hidden neurons condensing into isolated orientations during training, revealing an implicit bias towards simple solutions in the parameter space. However, the impact of neural network structure on condensation has not been investigated yet. In this study, we focus on the investigation of convolutional neural networks (CNNs). Our experiments suggest that when subjected to small initialization and gradient-based training methods, kernel weights within the same CNN layer also cluster together during training, demonstrating a significant degree of condensation. Theoretically, we demonstrate that in a finite training period, kernels of a two-layer CNN with small initialization will converge to one or a few directions. This work represents a step towards a better understanding of the non-linear training behavior exhibited by neural networks with specialized structures.

Abstract: We study the consistency of surrogate risks for robust binary classification. It is common to learn robust classifiers by adversarial training, which seeks to minimize the expected $0$-$1$ loss when each example can be maliciously corrupted within a small ball. We give a simple and complete characterization of the set of surrogate loss functions that are \emph{consistent}, i.e., that can replace the $0$-$1$ loss without affecting the minimizing sequences of the original adversarial risk, for any data distribution. We also prove a quantitative version of adversarial consistency for the $\rho$-margin loss. Our results reveal that the class of adversarially consistent surrogates is substantially smaller than in the standard setting, where many common surrogates are known to be consistent.

Abstract: Graph neural networks (GNNs) realize great success in graph learning but suffer from performance loss when meeting heterophily, i.e. neighboring nodes are dissimilar, due to their local and uniform aggregation. Existing attempts in incoorporating global aggregation for heterophilous GNNs usually require iteratively maintaining and updating full-graph information, which entails $\mathcal{O}(n^2)$ computation efficiency for a graph with $n$ nodes, leading to weak scalability to large graphs. In this paper, we propose SIMGA, a GNN structure integrating SimRank structural similarity measurement as global aggregation. The design of SIMGA is simple, yet it leads to promising results in both efficiency and effectiveness. The simplicity of SIMGA makes it the first heterophilous GNN model that can achieve a propagation efficiency near-linear to $n$. We theoretically demonstrate its effectiveness by treating SimRank as a new interpretation of GNN and prove that the aggregated node representation matrix has expected grouping effect. The performances of SIMGA are evaluated with 11 baselines on 12 benchmark datasets, usually achieving superior accuracy compared with the state-of-the-art models. Efficiency study reveals that SIMGA is up to 5$\times$ faster than the state-of-the-art method on the largest heterophily dataset pokec with over 30 million edges.

Abstract: Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of algorithms such as ADAM or AdaGrad. In this paper, we propose a novel algorithm for adaptive step length selection in the classical SGD framework, which can be readily adapted to other stochastic algorithms. Our proposed algorithm is inspired by traditional nonlinear optimization techniques and is supported by analytical findings. We show that under reasonable conditions, the algorithm produces step lengths in line with well-established theoretical requirements, and generates iterates that converge to a stationary neighborhood of a solution in expectation. We test the proposed algorithm on logistic regressions and deep neural networks and demonstrate that the algorithm can generate step lengths comparable to the best step length obtained from manual tuning.

Abstract: We introduce Reprompting, an iterative sampling algorithm that searches for the Chain-of-Thought (CoT) recipes for a given task without human intervention. Through Gibbs sampling, we infer CoT recipes that work consistently well for a set of training samples. Our method iteratively samples new recipes using previously sampled solutions as parent prompts to solve other training problems. On five Big-Bench Hard tasks that require multi-step reasoning, Reprompting achieves consistently better performance than the zero-shot, few-shot, and human-written CoT baselines. Reprompting can also facilitate transfer of knowledge from a stronger model to a weaker model leading to substantially improved performance of the weaker model. Overall, Reprompting brings up to +17 point improvements over the previous state-of-the-art method that uses human-written CoT prompts.

Abstract: Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence, obtaining a model with high performance is exceedingly time-consuming and occasionally impossible. Optimizing the parameters of the deep networks, therefore, requires improved optimization algorithms with high convergence rates. The single objective-based optimization methods generally used are mostly time-consuming and do not guarantee optimum performance in all cases. Mathematical optimization problems containing multiple objective functions that must be optimized simultaneously fall under the category of multi-objective optimization sometimes referred to as Pareto optimization. Multi-objective optimization problems form one of the alternatives yet useful options for parameter optimization. However, this domain is a bit less explored. In this survey, we focus on exploring the effectiveness of multi-objective optimization strategies for parameter optimization in conjunction with deep neural networks. The case studies used in this study focus on how the two methods are combined to provide valuable insights into the generation of predictions and analysis in multiple applications.

Abstract: Solving partial differential equations (PDEs) has been a fundamental problem in computational science and of wide applications for both scientific and engineering research. Due to its universal approximation property, neural network is widely used to approximate the solutions of PDEs. However, existing works are incapable of solving high-order PDEs due to insufficient calculation accuracy of higher-order derivatives, and the final network is a black box without explicit explanation. To address these issues, we propose a deep learning framework to solve high-order PDEs, named SHoP. Specifically, we derive the high-order derivative rule for neural network, to get the derivatives quickly and accurately; moreover, we expand the network into a Taylor series, providing an explicit solution for the PDEs. We conduct experimental validations four high-order PDEs with different dimensions, showing that we can solve high-order PDEs efficiently and accurately.

Abstract: Predictive Maintenance (PdM) methods aim to facilitate the scheduling of maintenance work before equipment failure. In this context, detecting early faults in automated teller machines (ATMs) has become increasingly important since these machines are susceptible to various types of unpredictable failures. ATMs track execution status by generating massive event-log data that collect system messages unrelated to the failure event. Predicting machine failure based on event logs poses additional challenges, mainly in extracting features that might represent sequences of events indicating impending failures. Accordingly, feature learning approaches are currently being used in PdM, where informative features are learned automatically from minimally processed sensor data. However, a gap remains to be seen on how these approaches can be exploited for deriving relevant features from event-log-based data. To fill this gap, we present a predictive model based on a convolutional kernel (MiniROCKET and HYDRA) to extract features from the original event-log data and a linear classifier to classify the sample based on the learned features. The proposed methodology is applied to a significant real-world collected dataset. Experimental results demonstrated how one of the proposed convolutional kernels (i.e. HYDRA) exhibited the best classification performance (accuracy of 0.759 and AUC of 0.693). In addition, statistical analysis revealed that the HYDRA and MiniROCKET models significantly overcome one of the established state-of-the-art approaches in time series classification (InceptionTime), and three non-temporal ML methods from the literature. The predictive model was integrated into a container-based decision support system to support operators in the timely maintenance of ATMs.

Abstract: The so-called black-box deep learning (DL) models are increasingly used in classification tasks across many scientific disciplines, including wireless communications domain. In this trend, supervised DL models appear as most commonly proposed solutions to domain-related classification problems. Although they are proven to have unmatched performance, the necessity for large labeled training data and their intractable reasoning, as two major drawbacks, are constraining their usage. The self-supervised architectures emerged as a promising solution that reduces the size of the needed labeled data, but the explainability problem remains. In this paper, we propose a methodology for explaining deep clustering, self-supervised learning architectures comprised of a representation learning part based on a Convolutional Neural Network (CNN) and a clustering part. For the state of the art representation learning part, our methodology employs Guided Backpropagation to interpret the regions of interest of the input data. For the clustering part, the methodology relies on Shallow Trees to explain the clustering result using optimized depth decision tree. Finally, a data-specific visualizations part enables connection for each of the clusters to the input data trough the relevant features. We explain on a use case of wireless spectrum activity clustering how the CNN-based, deep clustering architecture reasons.

Abstract: We prove Wasserstein inverse reinforcement learning enables the learner's reward values to imitate the expert's reward values in a finite iteration for multi-objective optimizations. Moreover, we prove Wasserstein inverse reinforcement learning enables the learner's optimal solutions to imitate the expert's optimal solutions for multi-objective optimizations with lexicographic order.

Abstract: The recent proliferation of large-scale text-to-image models has led to growing concerns that such models may be misused to generate harmful, misleading, and inappropriate content. Motivated by this issue, we derive a technique inspired by continual learning to selectively forget concepts in pretrained deep generative models. Our method, dubbed Selective Amnesia, enables controllable forgetting where a user can specify how a concept should be forgotten. Selective Amnesia can be applied to conditional variational likelihood models, which encompass a variety of popular deep generative frameworks, including variational autoencoders and large-scale text-to-image diffusion models. Experiments across different models demonstrate that our approach induces forgetting on a variety of concepts, from entire classes in standard datasets to celebrity and nudity prompts in text-to-image models. Our code is publicly available at https://github.com/clear-nus/selective-amnesia.

Abstract: Structure-based drug design powered by deep generative models have attracted increasing research interest in recent years. Language models have demonstrated a robust capacity for generating valid molecules in 2D structures, while methods based on geometric deep learning can directly produce molecules with accurate 3D coordinates. Inspired by both methods, this article proposes a pocket-based 3D molecule generation method that leverages the language model with the ability to generate 3D coordinates. High quality protein-ligand complex data are insufficient; hence, a perturbation and restoration pre-training task is designed that can utilize vast amounts of small-molecule data. A new molecular representation, a fragment-based SMILES with local and global coordinates, is also presented, enabling the language model to learn molecular topological structures and spatial position information effectively. Ultimately, CrossDocked and DUD-E dataset is employed for evaluation and additional metrics are introduced. This method achieves state-of-the-art performance in nearly all metrics, notably in terms of binding patterns, drug-like properties, rational conformations, and inference speed. Our model is available as an online service to academic users via sw3dmg.stonewise.cn

Abstract: Recent work provides promising evidence that Physics-informed neural networks (PINN) can efficiently solve partial differential equations (PDE). However, previous works have failed to provide guarantees on the worst-case residual error of a PINN across the spatio-temporal domain - a measure akin to the tolerance of numerical solvers - focusing instead on point-wise comparisons between their solution and the ones obtained by a solver on a set of inputs. In real-world applications, one cannot consider tests on a finite set of points to be sufficient grounds for deployment, as the performance could be substantially worse on a different set. To alleviate this issue, we establish tolerance-based correctness conditions for PINNs over the entire input domain. To verify the extent to which they hold, we introduce $\partial$-CROWN: a general, efficient and scalable post-training framework to bound PINN residual errors. We demonstrate its effectiveness in obtaining tight certificates by applying it to two classically studied PDEs - Burgers' and Schr\"odinger's equations -, and two more challenging ones with real-world applications - the Allan-Cahn and Diffusion-Sorption equations.

Abstract: Recently, a simple yet effective algorithm -- goal-conditioned supervised-learning (GCSL) -- was proposed to tackle goal-conditioned reinforcement-learning. GCSL is based on the principle of hindsight learning: by observing states visited in previously executed trajectories and treating them as attained goals, GCSL learns the corresponding actions via supervised learning. However, GCSL only learns a goal-conditioned policy, discarding other information in the process. Our insight is that the same hindsight principle can be used to learn to predict goal-conditioned sub-goals from the same trajectory. Based on this idea, we propose Trajectory Iterative Learner (TraIL), an extension of GCSL that further exploits the information in a trajectory, and uses it for learning to predict both actions and sub-goals. We investigate the settings in which TraIL can make better use of the data, and discover that for several popular problem settings, replacing real goals in GCSL with predicted TraIL sub-goals allows the agent to reach a greater set of goal states using the exact same data as GCSL, thereby improving its overall performance.

Abstract: Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

Abstract: Attention-based models have been a key element of many recent breakthroughs in deep learning. Two key components of Attention are the structure of its input (which consists of keys, values and queries) and the computations by which these three are combined. In this paper we explore the space of models that share said input structure but are not restricted to the computations of Attention. We refer to this space as Keys-Values-Queries (KVQ) Space. Our goal is to determine whether there are any other stackable models in KVQ Space that Attention cannot efficiently approximate, which we can implement with our current deep learning toolbox and that solve problems that are interesting to the community. Maybe surprisingly, the solution to the standard least squares problem satisfies these properties. A neural network module that is able to compute this solution not only enriches the set of computations that a neural network can represent but is also provably a strict generalisation of Linear Attention. Even more surprisingly the computational complexity of this module is exactly the same as that of Attention, making it a suitable drop in replacement. With this novel connection between classical machine learning (least squares) and modern deep learning (Attention) established we justify a variation of our model which generalises regular Attention in the same way. Both new modules are put to the test an a wide spectrum of tasks ranging from few-shot learning to policy distillation that confirm their real-worlds applicability.

Abstract: Works in quantum machine learning (QML) over the past few years indicate that QML algorithms can function just as well as their classical counterparts, and even outperform them in some cases. Among the corpus of recent work, many current QML models take advantage of variational quantum algorithm (VQA) circuits, given that their scale is typically small enough to be compatible with NISQ devices and the method of automatic differentiation for optimizing circuit parameters is familiar to machine learning (ML). While the results bear interesting promise for an era when quantum machines are more readily accessible, if one can achieve similar results through non-quantum methods then there may be a more near-term advantage available to practitioners. To this end, the nature of this work is to investigate the utilization of stochastic methods inspired by a variational quantum version of the long short-term memory (LSTM) model in an attempt to approach the reported successes in performance and rapid convergence. By analyzing the performance of classical, stochastic, and quantum methods, this work aims to elucidate if it is possible to achieve some of QML's major reported benefits on classical machines by incorporating aspects of its stochasticity.

Abstract: This paper investigates the differences in data organization between contrastive and supervised learning methods, focusing on the concept of locally dense clusters. We introduce a novel metric, Relative Local Density (RLD), to quantitatively measure local density within clusters. Visual examples are provided to highlight the distinctions between locally dense clusters and globally dense ones. By comparing the clusters formed by contrastive and supervised learning, we reveal that contrastive learning generates locally dense clusters without global density, while supervised learning creates clusters with both local and global density. We further explore the use of a Graph Convolutional Network (GCN) classifier as an alternative to linear classifiers for handling locally dense clusters. Finally, we utilize t-SNE visualizations to substantiate the differences between the features generated by contrastive and supervised learning methods. We conclude by proposing future research directions, including the development of efficient classifiers tailored to contrastive learning and the creation of innovative augmentation algorithms.

Abstract: Self-supervised learning aims to extract meaningful features from unlabeled data for further downstream tasks. In this paper, we consider classification as a downstream task in phase 2 and develop rigorous theories to realize the factors that implicitly influence the general loss of this classification task. Our theories signify that sharpness-aware feature extractors benefit the classification task in phase 2 and the existing data shift between the ideal (i.e., the ideal one used in theory development) and practical (i.e., the practical one used in implementation) distributions to generate positive pairs also remarkably affects this classification task. Further harvesting these theoretical findings, we propose to minimize the sharpness of the feature extractor and a new Fourier-based data augmentation technique to relieve the data shift in the distributions generating positive pairs, reaching Sharpness & Shift-Aware Contrastive Learning (SSA-CLR). We conduct extensive experiments to verify our theoretical findings and demonstrate that sharpness & shift-aware contrastive learning can remarkably boost the performance as well as obtaining more robust extracted features compared with the baselines.

Abstract: The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSIMCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We meticulously investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by systematically adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm, employing rigorous scientific methodologies throughout the process. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves the existing algorithm significantly when the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

Abstract: This paper studies tabular reinforcement learning (RL) in the hybrid setting, which assumes access to both an offline dataset and online interactions with the unknown environment. A central question boils down to how to efficiently utilize online data collection to strengthen and complement the offline dataset and enable effective policy fine-tuning. Leveraging recent advances in reward-agnostic exploration and model-based offline RL, we design a three-stage hybrid RL algorithm that beats the best of both worlds -- pure offline RL and pure online RL -- in terms of sample complexities. The proposed algorithm does not require any reward information during data collection. Our theory is developed based on a new notion called single-policy partial concentrability, which captures the trade-off between distribution mismatch and miscoverage and guides the interplay between offline and online data.

Abstract: We propose a novel training algorithm called DualFL (Dualized Federated Learning), for solving a distributed optimization problem in federated learning. Our approach is based on a specific dual formulation of the federated learning problem. DualFL achieves communication acceleration under various settings on smoothness and strong convexity of the problem. Moreover, it theoretically guarantees the use of inexact local solvers, preserving its optimal communication complexity even with inexact local solutions. DualFL is the first federated learning algorithm that achieves communication acceleration, even when the cost function is either nonsmooth or non-strongly convex. Numerical results demonstrate that the practical performance of DualFL is comparable to those of state-of-the-art federated learning algorithms, and it is robust with respect to hyperparameter tuning.

Abstract: Lithium-ion batteries are widely used in various applications, including portable electronic devices, electric vehicles, and renewable energy storage systems. Accurately estimating the remaining useful life of these batteries is crucial for ensuring their optimal performance, preventing unexpected failures, and reducing maintenance costs. In this paper, we present a comprehensive review of the existing approaches for estimating the remaining useful life of lithium-ion batteries, including data-driven methods, physics-based models, and hybrid approaches. We also propose a novel approach based on machine learning techniques for accurately predicting the remaining useful life of lithium-ion batteries. Our approach utilizes various battery performance parameters, including voltage, current, and temperature, to train a predictive model that can accurately estimate the remaining useful life of the battery. We evaluate the performance of our approach on a dataset of lithium-ion battery cycles and compare it with other state-of-the-art methods. The results demonstrate the effectiveness of our proposed approach in accurately estimating the remaining useful life of lithium-ion batteries.

Abstract: Tabular data is the most widely used data format in machine learning (ML). While tree-based methods outperform DL-based methods in supervised learning, recent literature reports that self-supervised learning with Transformer-based models outperforms tree-based methods. In the existing literature on self-supervised learning for tabular data, contrastive learning is the predominant method. In contrastive learning, data augmentation is important to generate different views. However, data augmentation for tabular data has been difficult due to the unique structure and high complexity of tabular data. In addition, three main components are proposed together in existing methods: model structure, self-supervised learning methods, and data augmentation. Therefore, previous works have compared the performance without comprehensively considering these components, and it is not clear how each component affects the actual performance. In this study, we focus on data augmentation to address these issues. We propose a novel data augmentation method, $\textbf{M}$ask $\textbf{T}$oken $\textbf{R}$eplacement ($\texttt{MTR}$), which replaces the mask token with a portion of each tokenized column; $\texttt{MTR}$ takes advantage of the properties of Transformer, which is becoming the predominant DL-based architecture for tabular data, to perform data augmentation for each column embedding. Through experiments with 13 diverse public datasets in both supervised and self-supervised learning scenarios, we show that $\texttt{MTR}$ achieves competitive performance against existing data augmentation methods and improves model performance. In addition, we discuss specific scenarios in which $\texttt{MTR}$ is most effective and identify the scope of its application. The code is available at https://github.com/somaonishi/MTR/.

Abstract: Meta-learning algorithms are able to learn a new task using previously learned knowledge, but they often require a large number of meta-training tasks which may not be readily available. To address this issue, we propose a method for few-shot learning with fewer tasks, which we call MetaModulation. The key idea is to use a neural network to increase the density of the meta-training tasks by modulating batch normalization parameters during meta-training. Additionally, we modify parameters at various network levels, rather than just a single layer, to increase task diversity. To account for the uncertainty caused by the limited training tasks, we propose a variational MetaModulation where the modulation parameters are treated as latent variables. We also introduce learning variational feature hierarchies by the variational MetaModulation, which modulates features at all layers and can consider task uncertainty and generate more diverse tasks. The ablation studies illustrate the advantages of utilizing a learnable task modulation at different levels and demonstrate the benefit of incorporating probabilistic variants in few-task meta-learning. Our MetaModulation and its variational variants consistently outperform state-of-the-art alternatives on four few-task meta-learning benchmarks.

Abstract: It has become a popular paradigm to transfer the knowledge of large-scale pre-trained models to various downstream tasks via fine-tuning the entire model parameters. However, with the growth of model scale and the rising number of downstream tasks, this paradigm inevitably meets the challenges in terms of computation consumption and memory footprint issues. Recently, Parameter-Efficient Fine-Tuning (PEFT) (e.g., Adapter, LoRA, BitFit) shows a promising paradigm to alleviate these concerns by updating only a portion of parameters. Despite these PEFTs having demonstrated satisfactory performance in natural language processing, it remains under-explored for the question of whether these techniques could be transferred to graph-based tasks with Graph Transformer Networks (GTNs). Therefore, in this paper, we fill this gap by providing extensive benchmarks with traditional PEFTs on a range of graph-based downstream tasks. Our empirical study shows that it is sub-optimal to directly transfer existing PEFTs to graph-based tasks due to the issue of feature distribution shift. To address this issue, we propose a novel structure-aware PEFT approach, named G-Adapter, which leverages graph convolution operation to introduce graph structure (e.g., graph adjacent matrix) as an inductive bias to guide the updating process. Besides, we propose Bregman proximal point optimization to further alleviate feature distribution shift by preventing the model from aggressive update. Extensive experiments demonstrate that G-Adapter obtains the state-of-the-art performance compared to the counterparts on nine graph benchmark datasets based on two pre-trained GTNs, and delivers tremendous memory footprint efficiency compared to the conventional paradigm.

Abstract: Persuasion games have been fundamental in economics and AI research, and have significant practical applications. Recent works in this area have started to incorporate natural language, moving beyond the traditional stylized message setting. However, previous research has focused on on-policy prediction, where the train and test data have the same distribution, which is not representative of real-life scenarios. In this paper, we tackle the challenging problem of off-policy evaluation (OPE) in language-based persuasion games. To address the inherent difficulty of human data collection in this setup, we propose a novel approach which combines real and simulated human-bot interaction data. Our simulated data is created by an exogenous model assuming decision makers (DMs) start with a mixture of random and decision-theoretic based behaviors and improve over time. We present a deep learning training algorithm that effectively integrates real interaction and simulated data, substantially improving over models that train only with interaction data. Our results demonstrate the potential of real interaction and simulation mixtures as a cost-effective and scalable solution for OPE in language-based persuasion games.\footnote{Our code and the large dataset we collected and generated are submitted as supplementary material and will be made publicly available upon acceptance.

Abstract: Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR with active learning proposes which experiments to do next. Active learning is done with query by committee, where the Pareto frontier of equations is the committee. The physical constraints improve proposed equations in very low data settings. These approaches reduce the data required for SR and achieves state of the art results in data required to rediscover known equations.

Abstract: Efficiently and reliably estimating uncertainty is an important objective in deep learning. It is especially pertinent to autoregressive sequence tasks, where training and inference costs are typically very high. However, existing research has predominantly focused on tasks with static data such as image classification. In this work, we investigate Ensemble Distribution Distillation (EDD) applied to large-scale natural language sequence-to-sequence data. EDD aims to compress the superior uncertainty performance of an expensive (teacher) ensemble into a cheaper (student) single model. Importantly, the ability to separate knowledge (epistemic) and data (aleatoric) uncertainty is retained. Existing probability-space approaches to EDD, however, are difficult to scale to large vocabularies. We show, for modern transformer architectures on large-scale translation tasks, that modelling the ensemble logits, instead of softmax probabilities, leads to significantly better students. Moreover, the students surprisingly even outperform Deep Ensembles by up to ~10% AUROC on out-of-distribution detection, whilst matching them at in-distribution translation.

Abstract: Certified defenses against adversarial attacks offer formal guarantees on the robustness of a model, making them more reliable than empirical methods such as adversarial training, whose effectiveness is often later reduced by unseen attacks. Still, the limited certified robustness that is currently achievable has been a bottleneck for their practical adoption. Gowal et al. and Wang et al. have shown that generating additional training data using state-of-the-art diffusion models can considerably improve the robustness of adversarial training. In this work, we demonstrate that a similar approach can substantially improve deterministic certified defenses. In addition, we provide a list of recommendations to scale the robustness of certified training approaches. One of our main insights is that the generalization gap, i.e., the difference between the training and test accuracy of the original model, is a good predictor of the magnitude of the robustness improvement when using additional generated data. Our approach achieves state-of-the-art deterministic robustness certificates on CIFAR-10 for the $\ell_2$ ($\epsilon = 36/255$) and $\ell_\infty$ ($\epsilon = 8/255$) threat models, outperforming the previous best results by $+3.95\%$ and $+1.39\%$, respectively. Furthermore, we report similar improvements for CIFAR-100.

Abstract: We study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is $O(1)$ in the number of nodes. Such graphs are typically known to be locally tree-like. We introduce a notion of Bayes optimality for node classification tasks, called asymptotic local Bayes optimality, and compute the optimal classifier according to this criterion for a fairly general statistical data model with arbitrary distributions of the node features and edge connectivity. The optimal classifier is implementable using a message-passing graph neural network architecture. We then compute the generalization error of this classifier and compare its performance against existing learning methods theoretically on a well-studied statistical model with naturally identifiable signal-to-noise ratios (SNRs) in the data. We find that the optimal message-passing architecture interpolates between a standard MLP in the regime of low graph signal and a typical convolution in the regime of high graph signal. Furthermore, we prove a corresponding non-asymptotic result.

Abstract: Semi-supervised learning has achieved notable success by leveraging very few labeled data and exploiting the wealth of information derived from unlabeled data. However, existing algorithms usually focus on aligning predictions on paired data points augmented from an identical source, and overlook the inter-point relationships within each batch. This paper introduces a novel method, RelationMatch, which exploits in-batch relationships with a matrix cross-entropy (MCE) loss function. Through the application of MCE, our proposed method consistently surpasses the performance of established state-of-the-art methods, such as FixMatch and FlexMatch, across a variety of vision datasets. Notably, we observed a substantial enhancement of 15.21% in accuracy over FlexMatch on the STL-10 dataset using only 40 labels. Moreover, we apply MCE to supervised learning scenarios, and observe consistent improvements as well.

Abstract: We present a novel extension of the traditional neural network approach to classification tasks, referred to as variational classification (VC). By incorporating latent variable modeling, akin to the relationship between variational autoencoders and traditional autoencoders, we derive a training objective based on the evidence lower bound (ELBO), optimized using an adversarial approach. Our VC model allows for more flexibility in design choices, in particular class-conditional latent priors, in place of the implicit assumptions made in off-the-shelf softmax classifiers. Empirical evaluation on image and text classification datasets demonstrates the effectiveness of our approach in terms of maintaining prediction accuracy while improving other desirable properties such as calibration and adversarial robustness, even when applied to out-of-domain data.

Abstract: Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies accordingly. In this context, policy optimization is the \emph{de facto} paradigm to adapt robot policies as a function of task-specific objectives. Most commonly-used motion policies carry particular structures that are often overlooked in policy optimization algorithms. We instead propose to leverage the structure of probabilistic policies by casting the policy optimization as an optimal transport problem. Specifically, we focus on robot motion policies that build on Gaussian mixture models (GMMs) and formulate the policy optimization as a Wassertein gradient flow over the GMMs space. This naturally allows us to constrain the policy updates via the $L^2$-Wasserstein distance between GMMs to enhance the stability of the policy optimization process. Furthermore, we leverage the geometry of the Bures-Wasserstein manifold to optimize the Gaussian distributions of the GMM policy via Riemannian optimization. We evaluate our approach on common robotic settings: Reaching motions, collision-avoidance behaviors, and multi-goal tasks. Our results show that our method outperforms common policy optimization baselines in terms of task success rate and low-variance solutions.