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This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due to decentralization and a detrimental impact of poorly-connected communication graphs on generalization. On the contrary, we show, for convex, strongly convex and non-convex functions, that D-SGD can always recover generalization bounds analogous to those of classical SGD, suggesting that the choice of graph does not matter. We then argue that this result is coming from a worst-case analysis, and we provide a refined data-dependent generalization bound for general convex functions. This new bound reveals that the choice of graph can in fact improve the worst-case bound in certain regimes, and that surprisingly, a poorly-connected graph can even be beneficial.

To evaluate code large language models (LLMs), research has relied on a few small manually curated benchmarks, such as HumanEval and MBPP, which represent a narrow part of the real-world software domains. In this work, we introduce round-trip correctness (RTC) as an alternative evaluation method. RTC allows Code LLM evaluation on a broader spectrum of real-world software domains without the need for costly human curation. RTC rests on the idea that we can ask a model to make a prediction (e.g., describe some code using natural language), feed that prediction back (e.g., synthesize code from the predicted description), and check if this round-trip leads to code that is semantically equivalent to the original input. We show how to employ RTC to evaluate code synthesis and editing. We find that RTC strongly correlates with model performance on existing narrow-domain code synthesis benchmarks while allowing us to expand to a much broader set of domains and tasks which was not previously possible without costly human annotations.

Efficient inference in high-dimensional models remains a central challenge in machine learning. This paper introduces the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, a fusion of the Ensemble Kalman filter and Gaussian belief propagation (GaBP) methods. GEnBP updates ensembles by passing low-rank local messages in a graphical model structure. This combination inherits favourable qualities from each method. Ensemble techniques allow GEnBP to handle high-dimensional states, parameters and intricate, noisy, black-box generation processes. The use of local messages in a graphical model structure ensures that the approach is suited to distributed computing and can efficiently handle complex dependence structures. GEnBP is particularly advantageous when the ensemble size is considerably smaller than the inference dimension. This scenario often arises in fields such as spatiotemporal modelling, image processing and physical model inversion. GEnBP can be applied to general problem structures, including jointly learning system parameters, observation parameters, and latent state variables.

This paper introduces the Quantified Boolean Bayesian Network (QBBN), which provides a unified view of logical and probabilistic reasoning. The QBBN is meant to address a central problem with the Large Language Model (LLM), which has become extremely popular in Information Retrieval, which is that the LLM hallucinates. A Bayesian Network, by construction, cannot hallucinate, because it can only return answers that it can explain. We show how a Bayesian Network over an unbounded number of boolean variables can be configured to represent the logical reasoning underlying human language. We do this by creating a key-value version of the First-Order Calculus, for which we can prove consistency and completeness. We show that the model is trivially trained over fully observed data, but that inference is non-trivial. Exact inference in a Bayesian Network is intractable (i.e. $\Omega(2^N)$ for $N$ variables). For inference, we investigate the use of Loopy Belief Propagation (LBP), which is not guaranteed to converge, but which has been shown to often converge in practice. Our experiments show that LBP indeed does converge very reliably, and our analysis shows that a round of LBP takes time $O(N2^n)$, where $N$ bounds the number of variables considered, and $n$ bounds the number of incoming connections to any factor, and further improvements may be possible. Our network is specifically designed to alternate between AND and OR gates in a Boolean Algebra, which connects more closely to logical reasoning, allowing a completeness proof for an expanded version of our network, and also allows inference to follow specific but adequate pathways, that turn out to be fast.

This paper presents a methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we consider is known as Boundary-Controlled Port-Hamiltonian Systems (BC-PHSs) and covers a wide class of Hyperbolic PDEs with a large type of boundary inputs and outputs. This is for instance the case of waves and beams with Neumann or Dirichlet boundary conditions at both sides and mixed boundary conditions. In addition, we recall the Loewner framework to reduce the discretized model. We show that if the initial PDE is {\it passive}, the discretized model is also. Moreover, if the initial PDE is {\it impedance energy preserving}, the discretized model is also. The {\it passive} structure is also preserved in the reduced-order if the selected frequency data has positive real part. We use the one-dimensional wave equation and the Timoshenko beam as examples to show the versatility of the proposed approach.

This paper describes the design and implementation of a virtual and remote laboratory based on Easy Java Simulations (EJS) and LabVIEW. The main application of this laboratory is to improve the study of sensors in Mobile Robotics, dealing with the problems that arise on the real world experiments. This laboratory allows the user to work from their homes, tele-operating a real robot that takes measurements from its sensors in order to obtain a map of its environment. In addition, the application allows interacting with a robot simulation (virtual laboratory) or with a real robot (remote laboratory), with the same simple and intuitive graphical user interface in EJS. Thus, students can develop signal processing and control algorithms for the robot in simulation and then deploy them on the real robot for testing purposes. Practical examples of application of the laboratory on the inter University Master of Systems Engineering and Automatic Control are presented.

This paper explores a modern predictive uncertainty estimation approach, called evidential deep learning (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their strong empirical performance, recent studies by Bengs et al. identify a fundamental pitfall of the existing methods: the learned epistemic uncertainty may not vanish even in the infinite-sample limit. We corroborate the observation by providing a unifying view of a class of widely used objectives from the literature. Our analysis reveals that the EDL methods essentially train a meta distribution by minimizing a certain divergence measure between the distribution and a sample-size-independent target distribution, resulting in spurious epistemic uncertainty. Grounded in theoretical principles, we propose learning a consistent target distribution by modeling it with a mixture of Dirichlet distributions and learning via variational inference. Afterward, a final meta distribution model distills the learned uncertainty from the target model. Experimental results across various uncertainty-based downstream tasks demonstrate the superiority of our proposed method, and illustrate the practical implications arising from the consistency and inconsistency of learned epistemic uncertainty.

This paper introduces a novel approach, Decision Theory-guided Deep Reinforcement Learning (DT-guided DRL), to address the inherent cold start problem in DRL. By integrating decision theory principles, DT-guided DRL enhances agents' initial performance and robustness in complex environments, enabling more efficient and reliable convergence during learning. Our investigation encompasses two primary problem contexts: the cart pole and maze navigation challenges. Experimental results demonstrate that the integration of decision theory not only facilitates effective initial guidance for DRL agents but also promotes a more structured and informed exploration strategy, particularly in environments characterized by large and intricate state spaces. The results of experiment demonstrate that DT-guided DRL can provide significantly higher rewards compared to regular DRL. Specifically, during the initial phase of training, the DT-guided DRL yields up to an 184% increase in accumulated reward. Moreover, even after reaching convergence, it maintains a superior performance, ending with up to 53% more reward than standard DRL in large maze problems. DT-guided DRL represents an advancement in mitigating a fundamental challenge of DRL by leveraging functions informed by human (designer) knowledge, setting a foundation for further research in this promising interdisciplinary domain.

Natural language (NL) to code suggestion systems assist developers in Integrated Development Environments (IDEs) by translating NL utterances into compilable code snippet. The current approaches mainly involve hard-coded, rule-based systems based on semantic parsing. These systems make heavy use of hand-crafted rules that map patterns in NL or elements in its syntax parse tree to various query constructs and can only work on a limited subset of NL with a restricted NL syntax. These systems are unable to extract semantic information from the coding intents of the developer, and often fail to infer types, names, and the context of the source code to get accurate system-level code suggestions. In this master thesis, we present sequence-to-sequence deep learning models and training paradigms to map NL to general-purpose programming languages that can assist users with suggestions of source code snippets, given a NL intent, and also extend auto-completion functionality of the source code to users while they are writing source code. The developed architecture incorporates contextual awareness into neural models which generate source code tokens directly instead of generating parse trees/abstract meaning representations from the source code and converting them back to source code. The proposed pretraining strategy and the data augmentation techniques improve the performance of the proposed architecture. The proposed architecture has been found to exceed the performance of a neural semantic parser, TranX, based on the BLEU-4 metric by 10.82%. Thereafter, a finer analysis for the parsable code translations from the NL intent for CoNaLA challenge was introduced. The proposed system is bidirectional as it can be also used to generate NL code documentation given source code. Lastly, a RoBERTa masked language model for Python was proposed to extend the developed system for code completion.

We study the problem of incorporating prior knowledge into a deep Transformer-based model,i.e.,Bidirectional Encoder Representations from Transformers (BERT), to enhance its performance on semantic textual matching tasks. By probing and analyzing what BERT has already known when solving this task, we obtain better understanding of what task-specific knowledge BERT needs the most and where it is most needed. The analysis further motivates us to take a different approach than most existing works. Instead of using prior knowledge to create a new training task for fine-tuning BERT, we directly inject knowledge into BERT's multi-head attention mechanism. This leads us to a simple yet effective approach that enjoys fast training stage as it saves the model from training on additional data or tasks other than the main task. Extensive experiments demonstrate that the proposed knowledge-enhanced BERT is able to consistently improve semantic textual matching performance over the original BERT model, and the performance benefit is most salient when training data is scarce.