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Publications
Lower and Upper Bounds on the Pseudo-Dimension of Tensor Network Models
Tensor network (TN) methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the mac… (voir plus)hine learning community for their ability to compactly represent very high-dimensional objects. TN methods can for example be used to efficiently learn linear models in exponentially large feature spaces [56]. In this work, we derive upper and lower bounds on the VC-dimension and pseudo-dimension of a large class of TN models for classification, regression and completion. Our upper bounds hold for linear models parameterized by arbitrary TN structures, and we derive lower bounds for common tensor decomposition models (CP, Tensor Train, Tensor Ring and Tucker) showing the tightness of our general upper bound. These results are used to derive a generalization bound which can be applied to classification with low-rank matrices as well as linear classifiers based on any of the commonly used tensor decomposition models. As a corollary of our results, we obtain a bound on the VC-dimension of the matrix product state classifier introduced in [56] as a function of the so-called bond dimension (i.e. tensor train rank), which answers an open problem listed by Cirac, Garre-Rubio and Pérez-García in [13].
Visual environments are structured, consisting of distinct objects or entities. These entities have properties---visible or latent---that d… (voir plus)etermine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be. Second, GNNs do not factorize knowledge about interactions in an entity-conditional manner. As an alternative, we take inspiration from cognitive science and resurrect a classic approach, production systems, which consist of a set of rule templates that are applied by binding placeholder variables in the rules to specific entities. Rules are scored on their match to entities, and the best fitting rules are applied to update entity properties. In a series of experiments, we demonstrate that this architecture achieves a flexible, dynamic flow of control and serves to factorize entity-specific and rule-based information. This disentangling of knowledge achieves robust future-state prediction in rich visual environments, outperforming state-of-the-art methods using GNNs, and allows for the extrapolation from simple (few object) environments to more complex environments.
Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and … (voir plus)the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is known to converge to a stationary point for specific classes of games, but current convergence analyses require a bounded variance assumption. SCO is used successfully for solving large-scale adversarial problems, but its convergence guarantees are limited to its deterministic variant. In this work, we introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO under this condition for solving a class of stochastic variational inequality problems that are potentially non-monotone. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size, and we propose insightful stepsize-switching rules to guarantee convergence to the exact solution. In addition, our convergence guarantees hold under the arbitrary sampling paradigm, and as such, we give insights into the complexity of minibatching.
One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mech… (voir plus)anisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An important property of many kinds of neural networks is universal approximability: the ability to approximate any function to arbitrary precision. Given this property, one may be tempted to surmise that a collection of neural nets is capable of learning any SCM by training on data generated by that SCM. In this paper, we show this is not the case by disentangling the notions of expressivity and learnability. Specifically, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits of what can be learned from data, still holds for neural models. For instance, an arbitrarily complex and expressive neural net is unable to predict the effects of interventions given observational data alone. Given this result, we introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences. Building on this new class of models, we focus on solving two canonical tasks found in the literature known as causal identification and estimation. Leveraging the neural toolbox, we develop an algorithm that is both sufficient and necessary to determine whether a causal effect can be learned from data (i.e., causal identifiability); it then estimates the effect whenever identifiability holds (causal estimation). Simulations corroborate the proposed approach.
The visual system of mammals is comprised of parallel, hierarchical specialized pathways. Different pathways are specialized in so far as th… (voir plus)ey use representations that are more suitable for supporting specific downstream behaviours. In particular, the clearest example is the specialization of the ventral (“what”) and dorsal (“where”) pathways of the visual cortex. These two pathways support behaviours related to visual recognition and movement, respectively. To-date, deep neural networks have mostly been used as models of the ventral, recognition pathway. However, it is unknown whether both pathways can be modelled with a single deep ANN. Here, we ask whether a single model with a single loss function can capture the properties of both the ventral and the dorsal pathways. We explore this question using data from mice, who like other mammals, have specialized pathways that appear to support recognition and movement behaviours. We show that when we train a deep neural network architecture with two parallel pathways using a self-supervised predictive loss function, we can outperform other models in fitting mouse visual cortex. Moreover, we can model both the dorsal and ventral pathways. These results demonstrate that a self-supervised predictive learning approach applied to parallel pathway architectures can account for some of the functional specialization seen in mammalian visual systems.
Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an explan… (voir plus)ation for their classification results. Machine learning models that are interpretable are usually linear or piecewise linear and yield inferior performance. Non-linear models achieve much better classification performance, but it is usually hard to explain their classification results. As a counter-example, an interpretable feedforward neural network (IFFNN) is proposed to achieve both high classification performance and interpretability for malware detection. If the IFFNN can perform well in a more flexible and general form for other classification tasks while providing meaningful explanations, it may be of great interest to the applied machine learning community. In this paper, we propose a way to generalize the interpretable feedforward neural network to multi-class classification scenarios and any type of feedforward neural networks, and evaluate its classification performance and interpretability on interpretable datasets. We conclude by finding that the generalized IFFNNs achieve comparable classification performance to their normal feedforward neural network counterparts and provide meaningful explanations. Thus, this kind of neural network architecture has great practical use.
Key Points Inhibition of RAB protein function mediates the anti–acute myeloid leukemia activity of statins. Statin sensitivity is associat… (voir plus)ed with enhanced vesicle-mediated traffic.
Key Points Inhibition of RAB protein function mediates the anti–acute myeloid leukemia activity of statins. Statin sensitivity is associat… (voir plus)ed with enhanced vesicle-mediated traffic.
In this work, we introduce back-training, an alternative to self-training for unsupervised domain adaptation (UDA). While self-training gene… (voir plus)rates synthetic training data where natural inputs are aligned with noisy outputs, back-training results in natural outputs aligned with noisy inputs. This significantly reduces the gap between target domain and synthetic data distribution, and reduces model overfitting to source domain. We run UDA experiments on question generation and passage retrieval from the Natural Questions domain to machine learning and biomedical domains. We find that back-training vastly outperforms self-training by a mean improvement of 7.8 BLEU-4 points on generation, and 17.6% top-20 retrieval accuracy across both domains. We further propose consistency filters to remove low-quality synthetic data before training. We also release a new domain-adaptation dataset - MLQuestions containing 35K unaligned questions, 50K unaligned passages, and 3K aligned question-passage pairs.
2021-11-01
Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing (publié)
