The computational intensity of Large Language Models (LLMs) is a critical bottleneck, primarily due to the $O(n^2)$ complexity of the attention mechanism in transformer architectures. Addressing this, sparse attention emerges as a key innovation, aiming to reduce computational load while maintaining model performance. This study presents a rigorous theoretical analysis of the sparsity in attention scores within LLMs, particularly under the framework of Gaussian inputs. By establishing a set of foundational assumptions and employing a methodical theoretical approach, we unravel the intrinsic characteristics of attention score sparsity and its implications on computational efficiency. Our main contribution lies in providing a detailed theoretical examination of how sparsity manifests in attention mechanisms, offering insights into the potential trade-offs between computational savings and model effectiveness. This work not only advances our understanding of sparse attention but also provides a scaffold for future research in optimizing the computational frameworks of LLMs, paving the way for more scalable and efficient AI systems.

Large language models (LLMs) often generate content that contains factual errors when responding to fact-seeking prompts on open-ended topics. To benchmark a model's long-form factuality in open domains, we first use GPT-4 to generate LongFact, a prompt set comprising thousands of questions spanning 38 topics. We then propose that LLM agents can be used as automated evaluators for long-form factuality through a method which we call Search-Augmented Factuality Evaluator (SAFE). SAFE utilizes an LLM to break down a long-form response into a set of individual facts and to evaluate the accuracy of each fact using a multi-step reasoning process comprising sending search queries to Google Search and determining whether a fact is supported by the search results. Furthermore, we propose extending F1 score as an aggregated metric for long-form factuality. To do so, we balance the percentage of supported facts in a response (precision) with the percentage of provided facts relative to a hyperparameter representing a user's preferred response length (recall). Empirically, we demonstrate that LLM agents can outperform crowdsourced human annotators - on a set of ~16k individual facts, SAFE agrees with crowdsourced human annotators 72% of the time, and on a random subset of 100 disagreement cases, SAFE wins 76% of the time. At the same time, SAFE is more than 20 times cheaper than human annotators. We also benchmark thirteen language models on LongFact across four model families (Gemini, GPT, Claude, and PaLM-2), finding that larger language models generally achieve better long-form factuality. LongFact, SAFE, and all experimental code are available at https://github.com/google-deepmind/long-form-factuality.

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time Graph Neural Network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also utilizes a dedicated loss function that incorporates a mean squared error component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

Large language models (LLMs) have been applied to a wide range of data-to-text generation tasks, including tables, graphs, and time-series numerical data-to-text settings. While research on generating prompts for structured data such as tables and graphs is gaining momentum, in-depth investigations into prompting for time-series numerical data are lacking. Therefore, this study explores various input representations, including sequences of tokens and structured formats such as HTML, LaTeX, and Python-style codes. In our experiments, we focus on the task of Market Comment Generation, which involves taking a numerical sequence of stock prices as input and generating a corresponding market comment. Contrary to our expectations, the results show that prompts resembling programming languages yield better outcomes, whereas those similar to natural languages and longer formats, such as HTML and LaTeX, are less effective. Our findings offer insights into creating effective prompts for tasks that generate text from numerical sequences.

Vertebral fracture grading classifies the severity of vertebral fractures, which is a challenging task in medical imaging and has recently attracted Deep Learning (DL) models. Only a few works attempted to make such models human-interpretable despite the need for transparency and trustworthiness in critical use cases like DL-assisted medical diagnosis. Moreover, such models either rely on post-hoc methods or additional annotations. In this work, we propose a novel interpretable-by-design method, ProtoVerse, to find relevant sub-parts of vertebral fractures (prototypes) that reliably explain the model's decision in a human-understandable way. Specifically, we introduce a novel diversity-promoting loss to mitigate prototype repetitions in small datasets with intricate semantics. We have experimented with the VerSe'19 dataset and outperformed the existing prototype-based method. Further, our model provides superior interpretability against the post-hoc method.

Deep learning applications for assessing medical images are limited because the datasets are often small and imbalanced. The use of synthetic data has been proposed in the literature, but neither a robust comparison of the different methods nor generalizability has been reported. Our approach integrates a retinal image quality assessment model and StyleGAN2 architecture to enhance Age-related Macular Degeneration (AMD) detection capabilities and improve generalizability. This work compares ten different Generative Adversarial Network (GAN) architectures to generate synthetic eye-fundus images with and without AMD. We combined subsets of three public databases (iChallenge-AMD, ODIR-2019, and RIADD) to form a single training and test set. We employed the STARE dataset for external validation, ensuring a comprehensive assessment of the proposed approach. The results show that StyleGAN2 reached the lowest Frechet Inception Distance (166.17), and clinicians could not accurately differentiate between real and synthetic images. ResNet-18 architecture obtained the best performance with 85% accuracy and outperformed the two human experts (80% and 75%) in detecting AMD fundus images. The accuracy rates were 82.8% for the test set and 81.3% for the STARE dataset, demonstrating the model's generalizability. The proposed methodology for synthetic medical image generation has been validated for robustness and accuracy, with free access to its code for further research and development in this field.

Abstract: By integrating survival analysis, machine learning algorithms, and economic interpretation, this research examines the temporal dynamics associated with attaining a 5 percent rise in purchasing power parity-adjusted GDP per capita over a period of 120 months (2013-2022). A comparative investigation reveals that DeepSurv is proficient at capturing non-linear interactions, although standard models exhibit comparable performance under certain circumstances. The weight matrix evaluates the economic ramifications of vulnerabilities, risks, and capacities. In order to meet the GDPpc objective, the findings emphasize the need of a balanced approach to risk-taking, strategic vulnerability reduction, and investment in governmental capacities and social cohesiveness. Policy guidelines promote individualized approaches that take into account the complex dynamics at play while making decisions. JEL: 04, C8, C5, O1 1. Introduction In contemporary economic research, the exploration of temporal dynamics in a nation's journey to achieve a specific level of GDP per capita gains paramount importance. This empirical investigation, conducted across 33 American countries, adopts a nuanced approach by incorporating a comprehensive dataset that includes countries with right-censored data (9 countries) and those reaching a 5% increase in GDP per capita at purchasing power parity (PIBpcPPP) within 120 months (24 countries). In addressing the central query, this research aims to unravel the intricate relationship of variables and risks influencing the time required for a country to achieve the specified 5% increase in GDP per capita. Leveraging advanced statistical techniques, particularly survival analysis, the study incorporates key variables such as Vul_Inherent, Vul_Fragility_Democracy, and Vul_Human Rights, offering a robust understanding of multifaceted vulnerabilities. This academic pursuit emphasizes rigorous methodologies, empirical analyses, and data-driven insights.

Continual learning, an important aspect of artificial intelligence and machine learning research, focuses on developing models that learn and adapt to new tasks while retaining previously acquired knowledge. Existing continual learning algorithms usually involve a small number of tasks with uniform sizes and may not accurately represent real-world learning scenarios. In this paper, we investigate the performance of continual learning algorithms with a large number of tasks drawn from a task distribution that is long-tail in terms of task sizes. We design one synthetic dataset and two real-world continual learning datasets to evaluate the performance of existing algorithms in such a setting. Moreover, we study an overlooked factor in continual learning, the optimizer states, e.g. first and second moments in the Adam optimizer, and investigate how it can be used to improve continual learning performance. We propose a method that reuses the optimizer states in Adam by maintaining a weighted average of the second moments from previous tasks. We demonstrate that our method, compatible with most existing continual learning algorithms, effectively reduces forgetting with only a small amount of additional computational or memory costs, and provides further improvements on existing continual learning algorithms, particularly in a long-tail task sequence.

Facts are subject to contingencies and can be true or false in different circumstances. One such contingency is time, wherein some facts mutate over a given period, e.g., the president of a country or the winner of a championship. Trustworthy language models ideally identify mutable facts as such and process them accordingly. We create MuLan, a benchmark for evaluating the ability of English language models to anticipate time-contingency, covering both 1:1 and 1:N relations. We hypothesize that mutable facts are encoded differently than immutable ones, hence being easier to update. In a detailed evaluation of six popular large language models, we consistently find differences in the LLMs' confidence, representations, and update behavior, depending on the mutability of a fact. Our findings should inform future work on the injection of and induction of time-contingent knowledge to/from LLMs.

This paper investigates whether recent advances in Large Language Models (LLMs) can assist in translating human explanations into a format that can robustly support learning Linear Temporal Logic (LTL) from demonstrations. Both LLMs and optimization-based methods can extract LTL specifications from demonstrations; however, they have distinct limitations. LLMs can quickly generate solutions and incorporate human explanations, but their lack of consistency and reliability hampers their applicability in safety-critical domains. On the other hand, optimization-based methods do provide formal guarantees but cannot process natural language explanations and face scalability challenges. We present a principled approach to combining LLMs and optimization-based methods to faithfully translate human explanations and demonstrations into LTL specifications. We have implemented a tool called Janaka based on our approach. Our experiments demonstrate the effectiveness of combining explanations with demonstrations in learning LTL specifications through several case studies.