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We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done right$\unicode{x2014}$by which we mean using specific insights from the optimisation and kernel communities$\unicode{x2014}$this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

A principal seeks to learn about a binary state and can do so by enlisting an agent to acquire information over time using a Poisson information arrival technology. The agent learns about this state privately, and his effort choices are unobserved by the principal. The principal can reward the agent with a prize of fixed value as a function of the agent's sequence of reports and the realized state. We identify conditions that each individually ensure that the principal cannot do better than by eliciting a single report from the agent after all information has been acquired. We also show that such a static contract is suboptimal under sufficiently strong violations of these conditions. We contrast our solution to the case where the agent acquires information "all at once;" notably, the optimal contract in the dynamic environment may provide strictly positive base rewards to the agent even if his prediction about the state is incorrect.

In Reinforcement Learning, agents learn policies by exploring and interacting with the environment. Due to the curse of dimensionality, learning policies that map high-dimensional sensory input to motor output is particularly challenging. During training, state of the art methods (SAC, PPO, etc.) explore the environment by perturbing the actuation with independent Gaussian noise. While this unstructured exploration has proven successful in numerous tasks, it can be suboptimal for overactuated systems. When multiple actuators, such as motors or muscles, drive behavior, uncorrelated perturbations risk diminishing each other's effect, or modifying the behavior in a task-irrelevant way. While solutions to introduce time correlation across action perturbations exist, introducing correlation across actuators has been largely ignored. Here, we propose LATent TIme-Correlated Exploration (Lattice), a method to inject temporally-correlated noise into the latent state of the policy network, which can be seamlessly integrated with on- and off-policy algorithms. We demonstrate that the noisy actions generated by perturbing the network's activations can be modeled as a multivariate Gaussian distribution with a full covariance matrix. In the PyBullet locomotion tasks, Lattice-SAC achieves state of the art results, and reaches 18% higher reward than unstructured exploration in the Humanoid environment. In the musculoskeletal control environments of MyoSuite, Lattice-PPO achieves higher reward in most reaching and object manipulation tasks, while also finding more energy-efficient policies with reductions of 20-60%. Overall, we demonstrate the effectiveness of structured action noise in time and actuator space for complex motor control tasks. The code is available at: //github.com/amathislab/lattice.

Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian Recursive Update Filter (BRUF), a Kalman filter that uses a recursive approach to incorporate information from nonlinear measurements. The BRUF relaxes the measurement linearity assumption of the Extended Kalman Filter (EKF) by dividing the measurement update into a user-defined number of steps. The proposed technique is extended for ensemble filters in the Bayesian Recursive Update Ensemble Kalman Filter (BRUEnKF). The performance of both filters is demonstrated in numerical examples, and new filters are introduced which exploit the theoretical foundation of the BRUF in different ways. A comparison between the BRUEnKF and Gromov flow, a popular particle flow algorithm, is presented in detail. Finally, the BRUEnKF is shown to outperform the EnKF for a very high-dimensional system.

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to efficiently decode classical random linear codes (RLCs) performing near the maximum rate of the finite blocklength regime. By using noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, provided that a simple code membership test exists. These conditions are particularly suitable for quantum systems, and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum-GRAND, this work shows that it is possible to decode QECCs that are easy to adapt to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum-GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding.

Large Language Models (LLMs) have significantly advanced natural language processing (NLP) with their impressive language understanding and generation capabilities. However, their performance may be suboptimal for long-tail or domain-specific tasks due to limited exposure to domain-specific knowledge and vocabulary. Additionally, the lack of transparency of most state-of-the-art (SOTA) LLMs, which can only be accessed via APIs, impedes further fine-tuning with custom data. Moreover, data privacy is a significant concern. To address these challenges, we propose the novel Parametric Knowledge Guiding (PKG) framework, which equips LLMs with a knowledge-guiding module to access relevant knowledge at runtime without altering the LLMs' parameters. Our PKG is based on open-source "white-box" small language models, allowing offline storage of any knowledge that LLMs require. We demonstrate that our PKG framework can enhance the performance of "black-box" LLMs on a range of long-tail and domain-specific downstream tasks requiring factual, tabular, medical, and multimodal knowledge.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.

We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.