In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however, uncertainty in the input data is a usual phenomenon, whereby this is normally not covered in optimization versions of NP problems. One concept to model the uncertainty in the input data, is recoverable robustness. The instance of the recoverable robust version of a combinatorial problem P is split into a base scenario $\sigma_0$ and an uncertainty scenario set $\textsf{S}$. The base scenario and all members of the uncertainty scenario set are instances of the original combinatorial problem P. The task is to calculate a solution $s_0$ for the base scenario $\sigma_0$ and solutions $s$ for all uncertainty scenarios $\sigma \in \textsf{S}$ such that $s_0$ and $s$ are not too far away from each other according to a distance measure, so $s_0$ can be easily adapted to $s$. This paper introduces Hamming Distance Recoverable Robustness, in which solutions $s_0$ and $s$ have to be calculated, such that $s_0$ and $s$ may only differ in at most $\kappa$ elements. We survey the complexity of Hamming distance recoverable robust versions of optimization problems, typically found in NP for different scenario encodings. The complexity is primarily situated in the lower levels of the polynomial hierarchy. The main contribution of the paper is a gadget reduction framework that shows that the recoverable robust versions of problems in a large class of combinatorial problems is $\Sigma^P_{3}$-complete. This class includes problems such as Vertex Cover, Coloring or Subset Sum. Additionally, we expand the results to $\Sigma^P_{2m+1}$-completeness for multi-stage recoverable robust problems with $m \in \mathbb{N}$ stages.
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Denoising diffusion models (DDMs) have attracted attention for their exceptional generation quality and diversity. This success is largely attributed to the use of class- or text-conditional diffusion guidance methods, such as classifier and classifier-free guidance. In this paper, we present a more comprehensive perspective that goes beyond the traditional guidance methods. From this generalized perspective, we introduce novel condition- and training-free strategies to enhance the quality of generated images. As a simple solution, blur guidance improves the suitability of intermediate samples for their fine-scale information and structures, enabling diffusion models to generate higher quality samples with a moderate guidance scale. Improving upon this, Self-Attention Guidance (SAG) uses the intermediate self-attention maps of diffusion models to enhance their stability and efficacy. Specifically, SAG adversarially blurs only the regions that diffusion models attend to at each iteration and guides them accordingly. Our experimental results show that our SAG improves the performance of various diffusion models, including ADM, IDDPM, Stable Diffusion, and DiT. Moreover, combining SAG with conventional guidance methods leads to further improvement.
The future of automated driving (AD) is rooted in the development of robust, fair and explainable artificial intelligence methods. Upon request, automated vehicles must be able to explain their decisions to the driver and the car passengers, to the pedestrians and other vulnerable road users and potentially to external auditors in case of accidents. However, nowadays, most explainable methods still rely on quantitative analysis of the AD scene representations captured by multiple sensors. This paper proposes a novel representation of AD scenes, called Qualitative eXplainable Graph (QXG), dedicated to qualitative spatiotemporal reasoning of long-term scenes. The construction of this graph exploits the recent Qualitative Constraint Acquisition paradigm. Our experimental results on NuScenes, an open real-world multi-modal dataset, show that the qualitative eXplainable graph of an AD scene composed of 40 frames can be computed in real-time and light in space storage which makes it a potentially interesting tool for improved and more trustworthy perception and control processes in AD.
Large Language Models (LLMs) present strong general capabilities, and a current compelling challenge is stimulating their specialized capabilities, such as machine translation, through low-cost instruction tuning. The standard instruction-following data is sequentially organized as the concatenation of an instruction, an input, and a response. As the attention mechanism of LLMs has limitations on local focus, LLMs tend to focus more on the words or sentences nearby at each position. This leads to a high risk of instruction forgetting during decoding. To alleviate the above issues, We propose SWIE (Segment-Weighted Instruction Embedding) and an instruction-following dataset OVERMISS. SWIE improves the model instruction understanding by adding a global instruction representation on the following input and response representations. OVERMISS improves model faithfulness by comparing over-translation and miss-translation results with the correct translation. We apply our methods to two main-stream open-source LLMs, BLOOM and LLaMA. The experimental results demonstrate significant improvements in translation performance with SWIE based on BLOOMZ-3b, particularly in zero-shot and long text translations due to reduced instruction forgetting risk. Additionally, OVERMISS outperforms the baseline in translation performance (e.g. an increase in BLEU scores from 0.69 to 3.12 and an average improvement of 0.48 percentage comet scores for LLaMA-7b) with further enhancements seen in models combining OVERMISS and SWIE (e.g. the BLUE scores increase up to 0.56 from English to German across three different backbones), and both exhibit improvements in the faithfulness metric based on word alignment.
Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering and manufacturing, transportation, and health care. Optimization models are mathematical abstractions of the problem of making the best decision while satisfying a set of requirements or constraints. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, also known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent strides have been taken to apply this computational framework in tackling and resolving various issues related to text processing. The resultant solutions demonstrate marked advantages over their classical counterparts. This study employs quantum computation to efficaciously surmount text processing challenges, particularly those involving string comparison. The focus is on the alignment of fixed-length substrings within two input strings. Specifically, given two input strings, $x$ and $y$, both of length $n$, and a value $d \leq n$, we want to verify the following conditions: the existence of a common prefix of length $d$, the presence of a common substring of length $d$ beginning at position $j$ (with $0 \leq j < n$) and, the presence of any common substring of length $d$ beginning in both strings at the same position. Such problems find applications as sub-procedures in a variety of problems concerning text processing and sequence analysis. Notably, our approach furnishes polylogarithmic solutions, a stark contrast to the linear complexity inherent in the best classical alternatives.
We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate polynomial is evaluated over its corresponding dataset and propose a generalization of the Lagrange Coded Computing framework (Yu et al. 2019) to perform all computations simultaneously while providing robustness against stragglers who do not respond in time, adversarial workers who respond with wrong computation and information-theoretic security of dataset against colluding workers. Our scheme introduces a small computation overhead which results in a reduction in download cost and also offers comparable resistance to stragglers over existing solutions. On top of it, we also propose two verification schemes to detect the presence of adversaries, which leads to incorrect results, without involving additional nodes.
Measures of algorithmic fairness are usually discussed in the context of binary decisions. We extend the approach to continuous scores. So far, ROC-based measures have mainly been suggested for this purpose. Other existing methods depend heavily on the distribution of scores, are unsuitable for ranking tasks, or their effect sizes are not interpretable. Here, we propose a distributionally invariant version of fairness measures for continuous scores with a reasonable interpretation based on the Wasserstein distance. Our measures are easily computable and well suited for quantifying and interpreting the strength of group disparities as well as for comparing biases across different models, datasets, or time points. We derive a link between the different families of existing fairness measures for scores and show that the proposed distributionally invariant fairness measures outperform ROC-based fairness measures because they are more explicit and can quantify significant biases that ROC-based fairness measures miss. Finally, we demonstrate their effectiveness through experiments on the most commonly used fairness benchmark datasets.
Formal methods were frequently shown to be effective and, perhaps because of that, practitioners are interested in using them more often. Still, these methods are far less applied than expected, particularly, in critical domains where they are strongly recommended and where they have the greatest potential. Our hypothesis is that formal methods still seem not to be applicable enough or ready for their intended use. In critical software engineering, what do we mean when we speak of a formal method? And what does it mean for such a method to be applicable both from a scientific and practical viewpoint? Based on what the literature tells about the first question, with this manifesto, we lay out a set of principles that when followed by a formal method give rise to its mature applicability in a given scope. Rather than exercising criticism of past developments, this manifesto strives to foster an increased use of formal methods to the maximum benefit.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
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.
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