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Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of a multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite-difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme, and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains.

Recently, various parameter-efficient fine-tuning (PEFT) strategies for application to language models have been proposed and successfully implemented. However, this raises the question of whether PEFT, which only updates a limited set of model parameters, constitutes security vulnerabilities when confronted with weight-poisoning backdoor attacks. In this study, we show that PEFT is more susceptible to weight-poisoning backdoor attacks compared to the full-parameter fine-tuning method, with pre-defined triggers remaining exploitable and pre-defined targets maintaining high confidence, even after fine-tuning. Motivated by this insight, we developed a Poisoned Sample Identification Module (PSIM) leveraging PEFT, which identifies poisoned samples through confidence, providing robust defense against weight-poisoning backdoor attacks. Specifically, we leverage PEFT to train the PSIM with randomly reset sample labels. During the inference process, extreme confidence serves as an indicator for poisoned samples, while others are clean. We conduct experiments on text classification tasks, five fine-tuning strategies, and three weight-poisoning backdoor attack methods. Experiments show near 100% success rates for weight-poisoning backdoor attacks when utilizing PEFT. Furthermore, our defensive approach exhibits overall competitive performance in mitigating weight-poisoning backdoor attacks.

Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently remains a challenge: existing decoders often fall short of meeting requirements such as having low computational complexity (ideally linear in the code's blocklength), low decoding latency, and low power consumption. In this paper we propose a novel bit-flipping (BF) decoder tailored for toric and surface codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting a particular class of harmful degenerate errors. Our algorithm achieves linear complexity growth and it can be efficiently implemented as it only involves simple operations such as bit-wise additions, quasi-cyclic permutations and vector-matrix multiplications. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code and 7% for the rotated planar code over the binary symmetric channel.

We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown functions and allow evaluations only in regions that are safe with high probability. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. Moreover, the way in which they exploit regularity assumptions about the constraint introduces an additional critical hyperparameter. In this paper, we propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate. The combination of this exploration criterion with a well known Bayesian optimization acquisition function yields a novel safe Bayesian optimization selection criterion. Our approach is naturally applicable to continuous domains and does not require additional explicit hyperparameters. We theoretically analyze the method and show that we do not violate the safety constraint with high probability and that we learn about the value of the safe optimum up to arbitrary precision. Empirical evaluations demonstrate improved data-efficiency and scalability.

Whenever a binary classifier is used to provide decision support, it typically provides both a label prediction and a confidence value. Then, the decision maker is supposed to use the confidence value to calibrate how much to trust the prediction. In this context, it has been often argued that the confidence value should correspond to a well calibrated estimate of the probability that the predicted label matches the ground truth label. However, multiple lines of empirical evidence suggest that decision makers have difficulties at developing a good sense on when to trust a prediction using these confidence values. In this paper, our goal is first to understand why and then investigate how to construct more useful confidence values. We first argue that, for a broad class of utility functions, there exist data distributions for which a rational decision maker is, in general, unlikely to discover the optimal decision policy using the above confidence values -- an optimal decision maker would need to sometimes place more (less) trust on predictions with lower (higher) confidence values. However, we then show that, if the confidence values satisfy a natural alignment property with respect to the decision maker's confidence on her own predictions, there always exists an optimal decision policy under which the level of trust the decision maker would need to place on predictions is monotone on the confidence values, facilitating its discoverability. Further, we show that multicalibration with respect to the decision maker's confidence on her own predictions is a sufficient condition for alignment. Experiments on four different AI-assisted decision making tasks where a classifier provides decision support to real human experts validate our theoretical results and suggest that alignment may lead to better decisions.

Transformer-based models have significantly improved performance across a range of multimodal understanding tasks, such as visual question answering and action recognition. However, multimodal Transformers significantly suffer from a quadratic complexity of the multi-head attention with the input sequence length, especially as the number of modalities increases. To address this, we introduce Low-Cost Multimodal Transformer (LoCoMT), a novel multimodal attention mechanism that aims to reduce computational cost during training and inference with minimal performance loss. Specifically, by assigning different multimodal attention patterns to each attention head, LoCoMT can flexibly control multimodal signals and theoretically ensures a reduced computational cost compared to existing multimodal Transformer variants. Experimental results on two multimodal datasets, namely Audioset and MedVidCL demonstrate that LoCoMT not only reduces GFLOPs but also matches or even outperforms established models.

We propose a noble, comprehensive and robust agile requirements change management (ARCM) model that addresses the limitations of existing models and is tailored for agile software development in the global software development paradigm. To achieve this goal, we conducted an exhaustive literature review and an empirical study with RCM industry experts. Our study evaluated the effectiveness of the proposed RCM model in a real-world setting and identifies any limitations or areas for improvement. The results of our study provide valuable insights into how the proposed RCM model can be applied in agile global software development environments to improve software development practices and optimize project success rates.

Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.

Recently, various auxiliary tasks have been proposed to accelerate representation learning and improve sample efficiency in deep reinforcement learning (RL). However, existing auxiliary tasks do not take the characteristics of RL problems into consideration and are unsupervised. By leveraging returns, the most important feedback signals in RL, we propose a novel auxiliary task that forces the learnt representations to discriminate state-action pairs with different returns. Our auxiliary loss is theoretically justified to learn representations that capture the structure of a new form of state-action abstraction, under which state-action pairs with similar return distributions are aggregated together. In low data regime, our algorithm outperforms strong baselines on complex tasks in Atari games and DeepMind Control suite, and achieves even better performance when combined with existing auxiliary tasks.

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.