We investigate the complexity of training a two-layer ReLU neural network with weight decay regularization. Previous research has shown that the optimal solution of this problem can be found by solving a standard cone-constrained convex program. Using this convex formulation, we prove that the hardness of approximation of ReLU networks not only mirrors the complexity of the Max-Cut problem but also, in certain special cases, exactly corresponds to it. In particular, when $\epsilon\leq\sqrt{84/83}-1\approx 0.006$, we show that it is NP-hard to find an approximate global optimizer of the ReLU network objective with relative error $\epsilon$ with respect to the objective value. Moreover, we develop a randomized algorithm which mirrors the Goemans-Williamson rounding of semidefinite Max-Cut relaxations. To provide polynomial-time approximations, we classify training datasets into three categories: (i) For orthogonal separable datasets, a precise solution can be obtained in polynomial-time. (ii) When there is a negative correlation between samples of different classes, we give a polynomial-time approximation with relative error $\sqrt{\pi/2}-1\approx 0.253$. (iii) For general datasets, the degree to which the problem can be approximated in polynomial-time is governed by a geometric factor that controls the diameter of two zonotopes intrinsic to the dataset. To our knowledge, these results present the first polynomial-time approximation guarantees along with first hardness of approximation results for regularized ReLU networks.

The idea of a guaranteed income for all has been floating around for centuries, its popularity ebbing and flowing with the passing tide of current events. While it is still considered by many to be a radical concept, proponents of a universal basic income (UBI) no longer see it only as a solution to poverty but as the answer to some of the biggest threats faced by modern workers: wage inequality, job insecurity – and the looming possibility of AI-induced job losses. Elon Musk, at the recent Bletchley Park summit, said he believed "no job is needed" due to the development of AI, and that a job can be for "personal satisfaction". Economist and political theorist Karl Widerquist, professor of philosophy at Georgetown University-Qatar, sees it differently. "Even if AI takes your job away, you don't necessarily just become unemployed for the rest of your life," he says.

Lachlan Murdoch will become the sole chair of both companies in November. As Rupert Murdoch marked his final day as Executive Chairman of News Corp on Wednesday, the media icon saluted his son Lachlan as the right man to lead the company forward. "Lachlan is a principled leader, and a believer in the social purpose of journalism. I hope to continue an active role in the company," Rupert Murdoch said during the company's annual shareholders meeting. Rupert Murdoch, 92, will now be Chairman Emeritus of FOX Corporation and News Corp; he will mark his final day at the former on Friday.

Both those options risk being bogged down in Parliament, especially in the House of Lords, and again in the courts,

Understanding visually situated language requires recognizing text and visual elements, and interpreting complex layouts. State-of-the-art methods commonly use specialized pre-processing tools, such as optical character recognition (OCR) systems, that map document image inputs to extracted information in the space of textual tokens, and sometimes also employ large language models (LLMs) to reason in text token space. However, the gains from external tools and LLMs come at the cost of increased computational and engineering complexity. In this paper, we ask whether small pretrained image-to-text models can learn selective text or layout recognition and reasoning as an intermediate inference step in an end-to-end model for pixel-level visual language understanding. We incorporate the outputs of such OCR tools, LLMs, and larger multimodal models as intermediate ``rationales'' on training data, and train a small student model to predict both rationales and answers for input questions based on those training examples. A student model based on Pix2Struct (282M parameters) achieves consistent improvements on three visual document understanding benchmarks representing infographics, scanned documents, and figures, with improvements of more than 4\% absolute over a comparable Pix2Struct model that predicts answers directly.

Adapting pre-trained language models (PLMs) for time-series text classification amidst evolving domain shifts (EDS) is critical for maintaining accuracy in applications like stance detection. This study benchmarks the effectiveness of evolving domain adaptation (EDA) strategies, notably self-training, domain-adversarial training, and domain-adaptive pretraining, with a focus on an incremental self-training method. Our analysis across various datasets reveals that this incremental method excels at adapting PLMs to EDS, outperforming traditional domain adaptation techniques. These findings highlight the importance of continually updating PLMs to ensure their effectiveness in real-world applications, paving the way for future research into PLM robustness against the natural temporal evolution of language.

Recently, ChatGPT has emerged as a powerful NLP tool that can carry out several tasks. However, the range of languages ChatGPT can handle remains largely a mystery. In this work, we investigate ChatGPT's language identification abilities. For this purpose, we compile Babel-670, a benchmark comprising $670$ languages representing $23$ language families. Languages in Babel-670 run the gamut between the very high-resource to the very low-resource and are spoken in five continents. We then study ChatGPT's (both GPT-3.5 and GPT-4) ability to (i) identify both language names and language codes (ii) under both zero- and few-shot conditions (iii) with and without provision of label set. When compared to smaller finetuned language identification tools, we find that ChatGPT lags behind. Our empirical analysis shows the reality that ChatGPT still resides in a state of potential enhancement before it can sufficiently serve diverse communities.

Ensuring a neural network is not relying on protected attributes (e.g., race, sex, age) for predictions is crucial in advancing fair and trustworthy AI. While several promising methods for removing attribute bias in neural networks have been proposed, their limitations remain under-explored. In this work, we mathematically and empirically reveal an important limitation of attribute bias removal methods in presence of strong bias. Specifically, we derive a general non-vacuous information-theoretical upper bound on the performance of any attribute bias removal method in terms of the bias strength. We provide extensive experiments on synthetic, image, and census datasets to verify the theoretical bound and its consequences in practice. Our findings show that existing attribute bias removal methods are effective only when the inherent bias in the dataset is relatively weak, thus cautioning against the use of these methods in smaller datasets where strong attribute bias can occur, and advocating the need for methods that can overcome this limitation.

Hyperdimensional computing (HDC) is a novel computational paradigm that operates on long-dimensional vectors known as hypervectors. The hypervectors are constructed as long bit-streams and form the basic building blocks of HDC systems. In HDC, hypervectors are generated from scalar values without taking their bit significance into consideration. HDC has been shown to be efficient and robust in various data processing applications, including computer vision tasks. To construct HDC models for vision applications, the current state-of-the-art practice utilizes two parameters for data encoding: pixel intensity and pixel position. However, the intensity and position information embedded in high-dimensional vectors are generally not generated dynamically in the HDC models. Consequently, the optimal design of hypervectors with high model accuracy requires powerful computing platforms for training. A more efficient approach to generating hypervectors is to create them dynamically during the training phase, which results in accurate, low-cost, and highly performable vectors. To this aim, we use low-discrepancy sequences to generate intensity hypervectors only, while avoiding position hypervectors. By doing so, the multiplication step in vector encoding is eliminated, resulting in a power-efficient HDC system. For the first time in the literature, our proposed approach employs lightweight vector generators utilizing unary bit-streams for efficient encoding of data instead of using conventional comparator-based generators.

Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, and generalization outside of the training sample. The stronger the structural properties, the more effective these improvements become. Manifolds are a powerful nonlinear generalization of Euclidean space for modeling finite dimensions. Structural impositions in constrained systems increase when applying group structure, converting them into Lie manifolds. The range of their applications is very wide and includes the important case of robotic tasks. Canonical Correlation Analysis (CCA) can construct a hierarchical sequence of maximal correlations of up to two paired data sets in these Euclidean spaces. We present a method to generalize this concept to Lie Manifolds and demonstrate its efficacy through the substantial improvements it achieves in making structure-consistent predictions about changes in the state of a robotic hand.