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Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of a family of models with the symmetries of that family's internal representation of data. We do this by calculating a set of fundamental symmetry groups, which we call the intertwiner groups of the model. We connect intertwiner groups to a model's internal representations of data through a range of experiments that probe similarities between hidden states across models with the same architecture. Our work suggests that the symmetries of a network are propagated into the symmetries in that network's representation of data, providing us with a better understanding of how architecture affects the learning and prediction process. Finally, we speculate that for ReLU networks, the intertwiner groups may provide a justification for the common practice of concentrating model interpretability exploration on the activation basis in hidden layers rather than arbitrary linear combinations thereof.

It is important to quantify the uncertainty of input samples, especially in mission-critical domains such as autonomous driving and healthcare, where failure predictions on out-of-distribution (OOD) data are likely to cause big problems. OOD detection problem fundamentally begins in that the model cannot express what it is not aware of. Post-hoc OOD detection approaches are widely explored because they do not require an additional re-training process which might degrade the model's performance and increase the training cost. In this study, from the perspective of neurons in the deep layer of the model representing high-level features, we introduce a new aspect for analyzing the difference in model outputs between in-distribution data and OOD data. We propose a novel method, Leveraging Important Neurons (LINe), for post-hoc Out of distribution detection. Shapley value-based pruning reduces the effects of noisy outputs by selecting only high-contribution neurons for predicting specific classes of input data and masking the rest. Activation clipping fixes all values above a certain threshold into the same value, allowing LINe to treat all the class-specific features equally and just consider the difference between the number of activated feature differences between in-distribution and OOD data. Comprehensive experiments verify the effectiveness of the proposed method by outperforming state-of-the-art post-hoc OOD detection methods on CIFAR-10, CIFAR-100, and ImageNet datasets.

Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational invariants and relational procedure specs, which in turn enables automation and modular reasoning. Alignment has been explored in terms of trace pairs, deductive rules of relational Hoare logics (RHL), and several forms of product automata. This article shows how a simple extension of Kleene Algebra with Tests (KAT), called BiKAT, subsumes prior formulations, including alignment witnesses for forall-exists properties, which brings to light new RHL-style rules for such properties. Alignments can be discovered algorithmically or devised manually but, in either case, their adequacy with respect to the original programs must be proved; an explicit algebra enables constructive proof by equational reasoning. Furthermore our approach inherits algorithmic benefits from existing KAT-based techniques and tools, which are applicable to a range of semantic models.

Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics such as the likelihood and average time of events (predictions). Here we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a data set of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.

Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future.

Security and privacy are important concerns in machine learning. End user devices often contain a wealth of data and this information is sensitive and should not be shared with servers or enterprises. As a result, federated learning was introduced to enable machine learning over large decentralized datasets while promising privacy by eliminating the need for data sharing. However, prior work has shown that shared gradients often contain private information and attackers can gain knowledge either through malicious modification of the architecture and parameters or by using optimization to approximate user data from the shared gradients. Despite this, most attacks have so far been limited in scale of number of clients, especially failing when client gradients are aggregated together using secure model aggregation. The attacks that still function are strongly limited in the number of clients attacked, amount of training samples they leak, or number of iterations they take to be trained. In this work, we introduce MANDRAKE, an attack that overcomes previous limitations to directly leak large amounts of client data even under secure aggregation across large numbers of clients. Furthermore, we break the anonymity of aggregation as the leaked data is identifiable and directly tied back to the clients they come from. We show that by sending clients customized convolutional parameters, the weight gradients of data points between clients will remain separate through aggregation. With an aggregation across many clients, prior work could only leak less than 1% of images. With the same number of non-zero parameters, and using only a single training iteration, MANDRAKE leaks 70-80% of data samples.

When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This paper proposes a systematic modular procedure for the dynamic modeling of branched robots comprising several subsystems, each composed of an arbitrary number of rigid bodies, providing the final dynamic model by reusing previous models of each branch. Unlike previous approaches, the proposed strategy is applicable even if some subsystems are regarded as black boxes, requiring only twists and wrenches at the connection points between them. To help in the model composition, we also propose a weighted directed graph representation where the weights encode the propagation of twists and wrenches between the subsystems. A simple linear operation on the graph interconnection matrix provides the dynamics of the whole system. Numerical results using a 38-DoF fixed-base branched robot composed of nine subsystems show that the proposed formalism is as accurate as a state-of-the-art library for robotic dynamic modeling. Additional results using a 39-DoF holonomic branched mobile manipulator composed of ten subsystems demonstrate the fidelity of our model to a modern robotics simulator.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Inferring missing links in knowledge graphs (KG) has attracted a lot of attention from the research community. In this paper, we tackle a practical query answering task involving predicting the relation of a given entity pair. We frame this prediction problem as an inference problem in a probabilistic graphical model and aim at resolving it from a variational inference perspective. In order to model the relation between the query entity pair, we assume that there exists an underlying latent variable (paths connecting two nodes) in the KG, which carries the equivalent semantics of their relations. However, due to the intractability of connections in large KGs, we propose to use variation inference to maximize the evidence lower bound. More specifically, our framework (\textsc{Diva}) is composed of three modules, i.e. a posterior approximator, a prior (path finder), and a likelihood (path reasoner). By using variational inference, we are able to incorporate them closely into a unified architecture and jointly optimize them to perform KG reasoning. With active interactions among these sub-modules, \textsc{Diva} is better at handling noise and coping with more complex reasoning scenarios. In order to evaluate our method, we conduct the experiment of the link prediction task on multiple datasets and achieve state-of-the-art performances on both datasets.