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Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call "example difficulty scores", are typically used to rank or categorize examples, but the consistency of rankings between different training runs, scoring methods, and model architectures is generally unknown. To determine how example rankings vary due to these random and controlled effects, we systematically compare different formulations of scores over a range of runs and model architectures. We find that scores largely share the following traits: they are noisy over individual runs of a model, strongly correlated with a single notion of difficulty, and reveal examples that range from being highly sensitive to insensitive to the inductive biases of certain model architectures. Drawing from statistical genetics, we develop a simple method for fingerprinting model architectures using a few sensitive examples. These findings guide practitioners in maximizing the consistency of their scores (e.g. by choosing appropriate scoring methods, number of runs, and subsets of examples), and establishes comprehensive baselines for evaluating scores in the future.

Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a tensor of transition costs between nodes in the grid. This captures many classical problems which are solved using DP such as the knapsack problem, the airplane refueling problem, and the minimal-weight polygon triangulation problem. We observe that for many of these problems, the tensor naturally has low tensor rank or low slice rank. We then give new algorithms and a web of fine-grained reductions to tightly determine the complexity of these problems. For instance, we show that a polynomial speedup over the DP algorithm is possible when the tensor rank is a constant or the slice rank is 1, but that such a speedup is impossible if the tensor rank is slightly super-constant (assuming SETH) or the slice rank is at least 3 (assuming the APSP conjecture). We find that this characterizes the known complexities for many of these problems, and in some cases leads to new faster algorithms.

In the arena of privacy-preserving machine learning, differentially private stochastic gradient descent (DP-SGD) has outstripped the objective perturbation mechanism in popularity and interest. Though unrivaled in versatility, DP-SGD requires a non-trivial privacy overhead (for privately tuning the model's hyperparameters) and a computational complexity which might be extravagant for simple models such as linear and logistic regression. This paper revamps the objective perturbation mechanism with tighter privacy analyses and new computational tools that boost it to perform competitively with DP-SGD on unconstrained convex generalized linear problems.

Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an exponentially long sequence of polynomially long proofs such that every adjacent pair of the proofs differs in at most one bit, and every proof can be probabilistically checked by reading a constant number of bits. Using the new characterization, we prove PSPACE-completeness of approximate versions of many reconfiguration problems, such as the Maxmin $3$-SAT Reconfiguration problem. This resolves the open problem posed by Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (ISAAC 2008; Theor. Comput. Sci. 2011) as well as the Reconfiguration Inapproximability Hypothesis by Ohsaka (STACS 2023) affirmatively. We also present PSPACE-completeness of approximating the Maxmin Clique Reconfiguration problem to within a factor of $n^\epsilon$ for some constant $\epsilon > 0$.

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral patterns. They rely on algorithms with a global view, significantly differing from biological neural networks, in which, to simulate information storage and retrieval processes, the limitations of centralized algorithms must be overcome. This study introduces a directed graph model that equips each node with adaptive learning and decision-making capabilities, thereby facilitating decentralized dynamic information storage and modeling and simulation of the brain's memory process. We abstract different storage instances as directed graph paths, transforming the storage of information into the assignment, discrimination, and extraction of different paths. To address writing and reading challenges, each node has a personalized adaptive learning ability. A storage algorithm without a God's eye view is developed, where each node uses its limited neighborhood information to facilitate the extension, formation, solidification, and awakening of directed graph paths, achieving competitive, reciprocal, and sustainable utilization of limited resources. Storage behavior occurs in each node, with adaptive learning behaviors of nodes concretized in a microcircuit centered around a variable resistor, simulating the electrophysiological behavior of neurons. Under the constraints of neurobiology on the anatomy and electrophysiology of biological neural networks, this model offers a plausible explanation for the mechanism of memory realization, providing a comprehensive, system-level experimental validation of the memory trace theory.

In this paper, we reflect on the educational challenges and research opportunities in running data visualization design activities in the context of large courses. With the increasing number and sizes of data visualization course, we need to better understand approaches to scaling our teaching efforts. We draw on experiences organizing and facilitating activities primarily based on one instance of a master's course given to about 130 students. We provide a detailed account of the course with particular focus on the purpose, structure, and outcome of six two-hour design activities. Based on this, we reflect on three aspects of the course: First, how the course scale led us to thoroughly plan, evaluate, and revise communication between students, teaching assistants, and lecturers. Second, how we designed learning scaffolds through the design activities, and the reflections we received from students on this matter. Finally, we reflect on the diversity of the students that followed the course, the visualization exercises we used, the projects they worked on, and when to key in on simple boring problems and data sets. Thus, our paper contributes with discussions about balancing topical diversity, scaling courses to many students, and problem-based learning.

There is an emerging line of research on multimodal instruction tuning, and a line of benchmarks has been proposed for evaluating these models recently. Instead of evaluating the models directly, in this paper, we try to evaluate the Vision-Language Instruction-Tuning (VLIT) datasets. Also, we seek the way of building a dataset for developing an all-powerful VLIT model, which we believe could also be of utility for establishing a grounded protocol for benchmarking VLIT models. For effective evaluation of VLIT datasets that remains an open question, we propose a tune-cross-evaluation paradigm: tuning on one dataset and evaluating on the others in turn. For each single tune-evaluation experiment set, we define the Meta Quality (MQ) as the mean score obtained by a set of caption metrics including BLEU, METEOR, and ROUGE-L to quantify the quality of a certain dataset or a sample. On this basis, to evaluate the comprehensiveness of a dataset, we develop the Dataset Quality (DQ) covering all tune-evaluation sets. To lay the foundation for building a comprehensive dataset and developing an all-powerful model for practical applications, we define the Sample Quality (SQ) to quantify the all-sided quality of each sample. Extensive experiments validate the rationality of the proposed evaluation paradigm. Based on the holistic evaluation, we build a new dataset, REVO-LION (REfining VisiOn-Language InstructiOn tuNing), by collecting samples with higher SQ from each dataset. Remarkably, even with only half of the complete data, the model trained on REVO-LION can achieve the performance comparable to simply adding all VLIT datasets up. Furthermore, REVO-LION not only facilitates the development of a powerful model but also incorporates an evaluation set, which is designed to serve as a convenient benchmark for future research in the field.

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the proposed stochastic method exhibits a linear convergence rate for solving sharp instances with a high probability. In addition, we propose an efficient coordinate-based stochastic oracle for unconstrained bilinear problems, which has $\mathcal O(1)$ per iteration cost and improves the complexity of the existing deterministic and stochastic algorithms. Finally, we show that the obtained linear convergence rate is nearly optimal (upto $\log$ terms) for a wide class of stochastic primal dual methods.

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.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.