Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical computer science and of practical interest in cryptography. This survey reviews notable research from the past four decades on the linear, quadratic and maximum-order complexities of pseudo-random sequences and their relations with Lempel-Ziv complexity, expansion complexity, 2-adic complexity, and correlation measures.
The proliferation of misinformation and harmful narratives in online discourse has underscored the critical need for effective Counter Narrative (CN) generation techniques. However, existing automatic evaluation methods often lack interpretability and fail to capture the nuanced relationship between generated CNs and human perception. Aiming to achieve a higher correlation with human judgments, this paper proposes a novel approach to asses generated CNs that consists on the use of a Large Language Model (LLM) as a evaluator. By comparing generated CNs pairwise in a tournament-style format, we establish a model ranking pipeline that achieves a correlation of $0.88$ with human preference. As an additional contribution, we leverage LLMs as zero-shot (ZS) CN generators and conduct a comparative analysis of chat, instruct, and base models, exploring their respective strengths and limitations. Through meticulous evaluation, including fine-tuning experiments, we elucidate the differences in performance and responsiveness to domain-specific data. We conclude that chat-aligned models in ZS are the best option for carrying out the task, provided they do not refuse to generate an answer due to security concerns.
The performance of large language models (LLMs) is acutely sensitive to the phrasing of prompts, which raises significant concerns about their reliability in real-world scenarios. Existing studies often divide prompts into task-level instructions and case-level inputs and primarily focus on evaluating and improving robustness against variations in tasks-level instructions. However, this setup fails to fully address the diversity of real-world user queries and assumes the existence of task-specific datasets. To address these limitations, we introduce RobustAlpacaEval, a new benchmark that consists of semantically equivalent case-level queries and emphasizes the importance of using the worst prompt performance to gauge the lower bound of model performance. Extensive experiments on RobustAlpacaEval with ChatGPT and six open-source LLMs from the Llama, Mistral, and Gemma families uncover substantial variability in model performance; for instance, a difference of 45.48% between the worst and best performance for the Llama-2-70B-chat model, with its worst performance dipping as low as 9.38%. We further illustrate the difficulty in identifying the worst prompt from both model-agnostic and model-dependent perspectives, emphasizing the absence of a shortcut to characterize the worst prompt. We also attempt to enhance the worst prompt performance using existing prompt engineering and prompt consistency methods, but find that their impact is limited. These findings underscore the need to create more resilient LLMs that can maintain high performance across diverse prompts. Data and code are available at //github.com/cbwbuaa/On-the-Worst-Prompt- Performance-of-LLMs.
We examine the continuous-time counterpart of mirror descent, namely mirror flow, on classification problems which are linearly separable. Such problems are minimised `at infinity' and have many possible solutions; we study which solution is preferred by the algorithm depending on the mirror potential. For exponential tailed losses and under mild assumptions on the potential, we show that the iterates converge in direction towards a $\phi_\infty$-maximum margin classifier. The function $\phi_\infty$ is the $\textit{horizon function}$ of the mirror potential and characterises its shape `at infinity'. When the potential is separable, a simple formula allows to compute this function. We analyse several examples of potentials and provide numerical experiments highlighting our results.
We introduce a simulation environment to facilitate research into emergent collective behaviour, with a focus on replicating the dynamics of ant colonies. By leveraging real-world data, the environment simulates a target ant trail that a controllable agent must learn to replicate, using sensory data observed by the target ant. This work aims to contribute to the neuroevolution of models for collective behaviour, focusing on evolving neural architectures that encode domain-specific behaviours in the network topology. By evolving models that can be modified and studied in a controlled environment, we can uncover the necessary conditions required for collective behaviours to emerge. We hope this environment will be useful to those studying the role of interactions in emergent behaviour within collective systems.
The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.
We present a new, inductive construction of the Vietoris-Rips complex, in which we take advantage of a small amount of unexploited combinatorial structure in the $k$-skeleton of the complex in order to avoid unnecessary comparisons when identifying its $(k+1)$-simplices. In doing so, we achieve a significant reduction in the number of comparisons required to construct the Vietoris-Rips compared to state-of-the-art algorithms, which is seen here by examining the computational complexity of the critical step in the algorithms. In experiments comparing a C/C++ implementation of our algorithm to the GUDHI v3.9.0 software package, this results in an observed $5$-$10$-fold improvement in speed of on sufficiently sparse Erd\H{o}s-R\'enyi graphs with the best advantages as the graphs become sparser, as well as for higher dimensional Vietoris-Rips complexes. We further clarify that the algorithm described in Boissonnat and Maria (//doi.org/10.1007/978-3-642-33090-2_63) for the construction of the Vietoris-Rips complex is exactly the Incremental Algorithm from Zomorodian (//doi.org/10.1016/j.cag.2010.03.007), albeit with the additional requirement that the result be stored in a tree structure, and we explain how these techniques are different from the algorithm presented here.
Significant pattern mining is a fundamental task in mining transactional data, requiring to identify patterns significantly associated with the value of a given feature, the target. In several applications, such as biomedicine, basket market analysis, and social networks, the goal is to discover patterns whose association with the target is defined with respect to an underlying population, or process, of which the dataset represents only a collection of observations, or samples. A natural way to capture the association of a pattern with the target is to consider its statistical significance, assessing its deviation from the (null) hypothesis of independence between the pattern and the target. While several algorithms have been proposed to find statistically significant patterns, it remains a computationally demanding task, and for complex patterns such as subgroups, no efficient solution exists. We present FSR, an efficient algorithm to identify statistically significant patterns with rigorous guarantees on the probability of false discoveries. FSR builds on a novel general framework for mining significant patterns that captures some of the most commonly considered patterns, including itemsets, sequential patterns, and subgroups. FSR uses a small number of resampled datasets, obtained by assigning i.i.d. labels to each transaction, to rigorously bound the supremum deviation of a quality statistic measuring the significance of patterns. FSR builds on novel tight bounds on the supremum deviation that require to mine a small number of resampled datasets, while providing a high effectiveness in discovering significant patterns. As a test case, we consider significant subgroup mining, and our evaluation on several real datasets shows that FSR is effective in discovering significant subgroups, while requiring a small number of resampled datasets.
Segmentation models for brain lesions in MRI are commonly developed for a specific disease and trained on data with a predefined set of MRI modalities. Each such model cannot segment the disease using data with a different set of MRI modalities, nor can it segment any other type of disease. Moreover, this training paradigm does not allow a model to benefit from learning from heterogeneous databases that may contain scans and segmentation labels for different types of brain pathologies and diverse sets of MRI modalities. Is it feasible to use Federated Learning (FL) for training a single model on client databases that contain scans and labels of different brain pathologies and diverse sets of MRI modalities? We demonstrate promising results by combining appropriate, simple, and practical modifications to the model and training strategy: Designing a model with input channels that cover the whole set of modalities available across clients, training with random modality drop, and exploring the effects of feature normalization methods. Evaluation on 7 brain MRI databases with 5 different diseases shows that such FL framework can train a single model that is shown to be very promising in segmenting all disease types seen during training. Importantly, it is able to segment these diseases in new databases that contain sets of modalities different from those in training clients. These results demonstrate, for the first time, feasibility and effectiveness of using FL to train a single segmentation model on decentralised data with diverse brain diseases and MRI modalities, a necessary step towards leveraging heterogeneous real-world databases. Code will be made available at: //github.com/FelixWag/FL-MultiDisease-MRI
Cooperative Multi-Agent Reinforcement Learning (MARL) algorithms, trained only to optimize task reward, can lead to a concentration of power where the failure or adversarial intent of a single agent could decimate the reward of every agent in the system. In the context of teams of people, it is often useful to explicitly consider how power is distributed to ensure no person becomes a single point of failure. Here, we argue that explicitly regularizing the concentration of power in cooperative RL systems can result in systems which are more robust to single agent failure, adversarial attacks, and incentive changes of co-players. To this end, we define a practical pairwise measure of power that captures the ability of any co-player to influence the ego agent's reward, and then propose a power-regularized objective which balances task reward and power concentration. Given this new objective, we show that there always exists an equilibrium where every agent is playing a power-regularized best-response balancing power and task reward. Moreover, we present two algorithms for training agents towards this power-regularized objective: Sample Based Power Regularization (SBPR), which injects adversarial data during training; and Power Regularization via Intrinsic Motivation (PRIM), which adds an intrinsic motivation to regulate power to the training objective. Our experiments demonstrate that both algorithms successfully balance task reward and power, leading to lower power behavior than the baseline of task-only reward and avoid catastrophic events in case an agent in the system goes off-policy.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.