Cross Attention is a popular method for retrieving information from a set of context tokens for making predictions. At inference time, for each prediction, Cross Attention scans the full set of $\mathcal{O}(N)$ tokens. In practice, however, often only a small subset of tokens are required for good performance. Methods such as Perceiver IO are cheap at inference as they distill the information to a smaller-sized set of latent tokens $L < N$ on which cross attention is then applied, resulting in only $\mathcal{O}(L)$ complexity. However, in practice, as the number of input tokens and the amount of information to distill increases, the number of latent tokens needed also increases significantly. In this work, we propose Tree Cross Attention (TCA) - a module based on Cross Attention that only retrieves information from a logarithmic $\mathcal{O}(\log(N))$ number of tokens for performing inference. TCA organizes the data in a tree structure and performs a tree search at inference time to retrieve the relevant tokens for prediction. Leveraging TCA, we introduce ReTreever, a flexible architecture for token-efficient inference. We show empirically that Tree Cross Attention (TCA) performs comparable to Cross Attention across various classification and uncertainty regression tasks while being significantly more token-efficient. Furthermore, we compare ReTreever against Perceiver IO, showing significant gains while using the same number of tokens for inference.

Neural Processes (NPs) are popular meta-learning methods for efficiently modelling predictive uncertainty. Recent state-of-the-art methods, however, leverage expensive attention mechanisms, limiting their applications, particularly in low-resource settings. In this work, we propose Constant Memory Attentive Neural Processes (CMANPs), an NP variant that only requires constant memory. To do so, we first propose an efficient update operation for Cross Attention. Leveraging the update operation, we propose Constant Memory Attention Block (CMAB), a novel attention block that (i) is permutation invariant, (ii) computes its output in constant memory, and (iii) performs constant computation updates. Finally, building on CMAB, we detail Constant Memory Attentive Neural Processes. Empirically, we show CMANPs achieve state-of-the-art results on popular NP benchmarks while being significantly more memory efficient than prior methods.

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the paper, we show that different choices of penalties define the regions of the input space where the property is observed. As such, previous methods result in models that are monotonic only in a small volume of the input space. We thus propose an approach that uses mixtures of training instances and random points to populate the space and enforce the penalty in a much larger region. As a second set of contributions, we introduce regularization strategies that enforce other notions of monotonicity in different settings. In this case, we consider applications, such as image classification and generative modeling, where monotonicity is not a hard constraint but can help improve some aspects of the model. Namely, we show that inducing monotonicity can be beneficial in applications such as: (1) allowing for controllable data generation, (2) defining strategies to detect anomalous data, and (3) generating explanations for predictions. Our proposed approaches do not introduce relevant computational overhead while leading to efficient procedures that provide extra benefits over baseline models.

We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substantially improves practical performance, and analyze the rate of convergence of the SAGA variant under non-uniform sampling. Our experimental results reveal that our method significantly outperforms existing methods in terms of the training objective, and performs as well or better than optimally-tuned stochastic gradient methods in terms of test error.

We present and analyze several strategies for improving the performance ofstochastic variance-reduced gradient (SVRG) methods. We first show that theconvergence rate of these methods can be preserved under a decreasing sequenceof errors in the control variate, and use this to derive variants of SVRG that usegrowing-batch strategies to reduce the number of gradient calculations requiredin the early iterations. We further (i) show how to exploit support vectors to reducethe number of gradient computations in the later iterations, (ii) prove that thecommonly–used regularized SVRG iteration is justified and improves the convergencerate, (iii) consider alternate mini-batch selection strategies, and (iv) considerthe generalization error of the method.

Power line communications (PLC) has attracted considerable attention for supporting smart grid applications. Since it reuses the existing grid infrastructure, it offers cost advantages over alternative communications methods and gives electric utilities control over the communications medium. Furthermore, the "through-the-grid" property of PLC extends its possible use beyond mere communications. Since the PLC signals are bound to travel through the power grid, they can also be used for inference tasks, such as online diagnostics of power line integrity. In this paper, we consider such an inference application of PLC, enabled by modern signal processing. We assume a power grid at whose edges PLC devices are deployed to form a PLC network for purposes such as advanced meter reading. We are interested in retrieving the physical power-grid topology, i.e., the connections and lengths of power lines reaching to the locations of the PLC devices. To this end, we propose the combination of PLC-based ranging with inference based on end-to-end measurements. In the context of communication networks, the latter is known as tomography and hence, we refer to the developed method as power grid tomography. For the purpose of ranging we formulate a new super-resolution ranging algorithm specifically tailored for signal propagation through power lines. Numerical results for low-voltage distribution grid examples demonstrate the successful reconstruction of the grid topology by the proposed power grid tomography method.

Frequency Domain Reflectometry (FDR) is a technique that was proposed for fault detection in Digital Subscriber Line (DSL) cables. In this paper, we describe how FDR can be used to determine the topology of power line networks. To this end, we first infer distance information from the multiple signal reflections measured and processed with FDR. Then, we present an algorithm that uses these distance measurements to reconstruct the topology step by step operating on a network graph. Numerical results for sets of sample networks demonstrate the effectiveness of the proposed topology-inference approach.