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We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and derive explicit bounds on the finite sample performance of the test. We demonstrate the empirical performance of the procedure in comparison to existing sequential and non-sequential independence tests. Furthermore, since the proposed test is distribution free under the null hypothesis, we empirically simulate the gap due to Ville's inequality, the supermartingale analogue of Markov's inequality, that is commonly applied to control type I error in anytime-valid inference, and apply this to construct a truncated sequential test.

Methods for 3D reconstruction from posed frames require prior knowledge about the scene metric range, usually to recover matching cues along the epipolar lines and narrow the search range. However, such prior might not be directly available or estimated inaccurately in real scenarios -- e.g., outdoor 3D reconstruction from video sequences -- therefore heavily hampering performance. In this paper, we focus on multi-view depth estimation without requiring prior knowledge about the metric range of the scene by proposing RAMDepth, an efficient and purely 2D framework that reverses the depth estimation and matching steps order. Moreover, we demonstrate the capability of our framework to provide rich insights about the quality of the views used for prediction. Additional material can be found on our project page //andreaconti.github.io/projects/range_agnostic_multi_view_depth.

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in ``software'', it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of ``self-organization''. The latter means that the initial configuration does not have to encode an infinite hierarchy -- this will be built up over time. This is a corrected and strengthened version of the journal paper of 2001.

Efficient implementation of massive multiple-input-multiple-output (MIMO) transceivers is essential for the next-generation wireless networks. To reduce the high computational complexity of the massive MIMO transceiver, in this paper, we propose a new massive MIMO architecture using finite-precision arithmetic. First, we conduct the rounding error analysis and derive the lower bound of the achievable rate for single-input-multiple-output (SIMO) using maximal ratio combining (MRC) and multiple-input-single-output (MISO) systems using maximal ratio transmission (MRT) with finite-precision arithmetic. Then, considering the multi-user scenario, the rounding error analysis of zero-forcing (ZF) detection and precoding is derived by using the normal equations (NE) method. The corresponding lower bounds of the achievable sum rate are also derived and asymptotic analyses are presented. Built upon insights from these analyses and lower bounds, we propose a mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic. The corresponding analysis of rounding errors and computational costs is obtained. Simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of machine learning models is essential to the development of trustworthy machine-learning-based systems. A burgeoning body of research seeks to define the goals and methods of explainability in machine learning. In this paper, we seek to review and categorize research on counterfactual explanations, a specific class of explanation that provides a link between what could have happened had input to a model been changed in a particular way. Modern approaches to counterfactual explainability in machine learning draw connections to the established legal doctrine in many countries, making them appealing to fielded systems in high-impact areas such as finance and healthcare. Thus, we design a rubric with desirable properties of counterfactual explanation algorithms and comprehensively evaluate all currently-proposed algorithms against that rubric. Our rubric provides easy comparison and comprehension of the advantages and disadvantages of different approaches and serves as an introduction to major research themes in this field. We also identify gaps and discuss promising research directions in the space of counterfactual explainability.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.