Bayesian experimental design (BED) provides a powerful and general framework for optimizing the design of experiments. However, its deployment often poses substantial computational challenges that can undermine its practical use. In this review, we outline how recent advances have transformed our ability to overcome these challenges and thus utilize BED effectively, before discussing some key areas for future development in the field.
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In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric, and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added.
Bounded Model Checking (BMC) is a powerful technique for proving reachability of error states, i.e., unsafety. However, finding deep counterexamples that require a large bound is challenging for BMC. On the other hand, acceleration techniques compute "shortcuts" that "compress" many execution steps into a single one. In this paper, we tightly integrate acceleration techniques into SMT-based bounded model checking. By adding suitable "shortcuts" to the SMT-problem on the fly, our approach can quickly detect deep counterexamples, even when only using small bounds. Moreover, using so-called blocking clauses, our approach can prove safety of examples where BMC diverges. An empirical comparison with other state-of-the-art techniques shows that our approach is highly competitive for proving unsafety, and orthogonal to existing techniques for proving safety.
Inspired by the concept of fault tolerance quantum computation, this article proposes a framework dubbed Exact Homomorphic Encryption, EHE, enabling exact computations on encrypted data without the need for pre-decryption. The introduction of quantum gates is a critical step in constructing the message encryption and the computation encryption within the framework. Of significance is that both encryptions are respectively accomplished in a multivariate polynomial set generated by quantum gates. Two fundamental traits of quantum gates, the invertibility and the noncommutativity, establish the success of EHE. The employment of invertible gates allows exact decryptions for both an encrypted message and encrypted computation. The encrypted computation is exact as well because its encryption transformation is conducted with invertible gates. The second trait of noncommutativity among applied quantum gates brings forth the security for the two encryptions. In the message encryption, a plaintext is encoded into a ciphertext via a polynomial set generated by a product of noncommuting gates randomly chosen. Toward the computation encryption, a desired operation is encoded into an encrypted polynomial set generated by another product of noncommuting gates. The encrypted computation is then the evaluation of the encrypted polynomial set on the ciphertext and is referred to as the cryptovaluation. EHE is not only attainable on quantum computers, but also straightforwardly realizable on traditional computing environments. Surpassing the standard security 2^128 of quantum resilience, both the encryptions further reach a security greater than the suggested threshold 2^1024 and are characterized as hyper quantum-resilient. Thanks to the two essential traits of quantum gates, this framework can be regarded as the initial tangible manifestation of the concept noncommutative cryptography.
Breakthroughs in machine learning in the last decade have led to `digital intelligence', i.e. machine learning models capable of learning from vast amounts of labeled data to perform several digital tasks such as speech recognition, face recognition, machine translation and so on. The goal of this thesis is to make progress towards designing algorithms capable of `physical intelligence', i.e. building intelligent autonomous navigation agents capable of learning to perform complex navigation tasks in the physical world involving visual perception, natural language understanding, reasoning, planning, and sequential decision making. Despite several advances in classical navigation methods in the last few decades, current navigation agents struggle at long-term semantic navigation tasks. In the first part of the thesis, we discuss our work on short-term navigation using end-to-end reinforcement learning to tackle challenges such as obstacle avoidance, semantic perception, language grounding, and reasoning. In the second part, we present a new class of navigation methods based on modular learning and structured explicit map representations, which leverage the strengths of both classical and end-to-end learning methods, to tackle long-term navigation tasks. We show that these methods are able to effectively tackle challenges such as localization, mapping, long-term planning, exploration and learning semantic priors. These modular learning methods are capable of long-term spatial and semantic understanding and achieve state-of-the-art results on various navigation tasks.
Existing Collaborative Filtering (CF) methods are mostly designed based on the idea of matching, i.e., by learning user and item embeddings from data using shallow or deep models, they try to capture the associative relevance patterns in data, so that a user embedding can be matched with relevant item embeddings using designed or learned similarity functions. However, as a cognition rather than a perception intelligent task, recommendation requires not only the ability of pattern recognition and matching from data, but also the ability of cognitive reasoning in data. In this paper, we propose to advance Collaborative Filtering (CF) to Collaborative Reasoning (CR), which means that each user knows part of the reasoning space, and they collaborate for reasoning in the space to estimate preferences for each other. Technically, we propose a Neural Collaborative Reasoning (NCR) framework to bridge learning and reasoning. Specifically, we integrate the power of representation learning and logical reasoning, where representations capture similarity patterns in data from perceptual perspectives, and logic facilitates cognitive reasoning for informed decision making. An important challenge, however, is to bridge differentiable neural networks and symbolic reasoning in a shared architecture for optimization and inference. To solve the problem, we propose a modularized reasoning architecture, which learns logical operations such as AND ($\wedge$), OR ($\vee$) and NOT ($\neg$) as neural modules for implication reasoning ($\rightarrow$). In this way, logical expressions can be equivalently organized as neural networks, so that logical reasoning and prediction can be conducted in a continuous space. Experiments on real-world datasets verified the advantages of our framework compared with both shallow, deep and reasoning models.
Self-supervised learning has been widely used to obtain transferrable representations from unlabeled images. Especially, recent contrastive learning methods have shown impressive performances on downstream image classification tasks. While these contrastive methods mainly focus on generating invariant global representations at the image-level under semantic-preserving transformations, they are prone to overlook spatial consistency of local representations and therefore have a limitation in pretraining for localization tasks such as object detection and instance segmentation. Moreover, aggressively cropped views used in existing contrastive methods can minimize representation distances between the semantically different regions of a single image. In this paper, we propose a spatially consistent representation learning algorithm (SCRL) for multi-object and location-specific tasks. In particular, we devise a novel self-supervised objective that tries to produce coherent spatial representations of a randomly cropped local region according to geometric translations and zooming operations. On various downstream localization tasks with benchmark datasets, the proposed SCRL shows significant performance improvements over the image-level supervised pretraining as well as the state-of-the-art self-supervised learning methods.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Deep learning methods for graphs achieve remarkable performance on many node-level and graph-level prediction tasks. However, despite the proliferation of the methods and their success, prevailing Graph Neural Networks (GNNs) neglect subgraphs, rendering subgraph prediction tasks challenging to tackle in many impactful applications. Further, subgraph prediction tasks present several unique challenges, because subgraphs can have non-trivial internal topology, but also carry a notion of position and external connectivity information relative to the underlying graph in which they exist. Here, we introduce SUB-GNN, a subgraph neural network to learn disentangled subgraph representations. In particular, we propose a novel subgraph routing mechanism that propagates neural messages between the subgraph's components and randomly sampled anchor patches from the underlying graph, yielding highly accurate subgraph representations. SUB-GNN specifies three channels, each designed to capture a distinct aspect of subgraph structure, and we provide empirical evidence that the channels encode their intended properties. We design a series of new synthetic and real-world subgraph datasets. Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4% over the strongest baseline. SUB-GNN performs exceptionally well on challenging biomedical datasets when subgraphs have complex topology and even comprise multiple disconnected components.
In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.
Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively. However, the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive. To solve this problem, co-attention builds two separate attention distributions for each modality neglecting the interaction between multimodal inputs. In this paper, we propose bilinear attention networks (BAN) that find bilinear attention distributions to utilize given vision-language information seamlessly. BAN considers bilinear interactions among two groups of input channels, while low-rank bilinear pooling extracts the joint representations for each pair of channels. Furthermore, we propose a variant of multimodal residual networks to exploit eight-attention maps of the BAN efficiently. We quantitatively and qualitatively evaluate our model on visual question answering (VQA 2.0) and Flickr30k Entities datasets, showing that BAN significantly outperforms previous methods and achieves new state-of-the-arts on both datasets.
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