Graph Neural Networks (GNNs) are the state-of-the-art model for machine learning on graph-structured data. The most popular class of GNNs operate by exchanging information between adjacent nodes, and are known as Message Passing Neural Networks (MPNNs). Given their widespread use, understanding the expressive power of MPNNs is a key question. However, existing results typically consider settings with uninformative node features. In this paper, we provide a rigorous analysis to determine which function classes of node features can be learned by an MPNN of a given capacity. We do so by measuring the level of pairwise interactions between nodes that MPNNs allow for. This measure provides a novel quantitative characterization of the so-called over-squashing effect, which is observed to occur when a large volume of messages is aggregated into fixed-size vectors. Using our measure, we prove that, to guarantee sufficient communication between pairs of nodes, the capacity of the MPNN must be large enough, depending on properties of the input graph structure, such as commute times. For many relevant scenarios, our analysis results in impossibility statements in practice, showing that over-squashing hinders the expressive power of MPNNs. We validate our theoretical findings through extensive controlled experiments and ablation studies.
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The number of local model-agnostic explanation techniques proposed has grown rapidly recently. One main reason is that the bar for developing new explainability techniques is low due to the lack of optimal evaluation measures. Without rigorous measures, it is hard to have concrete evidence of whether the new explanation techniques can significantly outperform their predecessors. Our study proposes a new taxonomy for evaluating local explanations: robustness, evaluation using ground truth from synthetic datasets and interpretable models, model randomization, and human-grounded evaluation. Using this proposed taxonomy, we highlight that all categories of evaluation methods, except those based on the ground truth from interpretable models, suffer from a problem we call the "blame problem." In our study, we argue that this category of evaluation measure is a more reasonable method for evaluating local model-agnostic explanations. However, we show that even this category of evaluation measures has further limitations. The evaluation of local explanations remains an open research problem.
Generative Artificial Intelligence (GAI) has high potential to help address a diversity of educational challenges. In principle, GAI could facilitate the implementation of interactive and empowering pedagogical activities to complement the standard teaching strategies and favor students active engagement, understanding and control over their learning processes. These dimensions are indeed fundamental for a better learning experience and longer-lasting cognitive outcomes. However, several characteristics of the interactions with GAI such as continuous confidence in the generated answers, and the lack of pedagogical stance in their behavior may lead students to poor states of control over learning (e.g. over-reliance on pre-generated content, over-estimation of one's own knowledge, loss of curious and critical-thinking sense, etc). The fine line between the two settings seems to lie in how this technology is used to carry out the pedagogical activities (e.g. types of interactions allowed, level of controllability by students, level of involvement of educators, etc) as well as to what extent students have the relevant skills (cognitive, metacognitive and GAI literacy) that allow them to correctly evaluate, analyze and interpret the system behaviors. In this context, this article proposes to identify some of the opportunities and challenges that could arise wrt students control over their learning when using GAI during formal pedagogical activities. In a second step, we also discuss the types of trainings that could be relevant to offer students in order to provide them with the appropriate set of skills that can help them use GAI in informed ways, when pursuing a given learning goal.
Large language models (LLMs) such as GPT-4 have exhibited remarkable performance in a variety of tasks, but this strong performance often comes with the high expense of using paid API services. In this paper, we are motivated to study building an LLM cascade to save the cost of using LLMs, particularly for performing reasoning (e.g., mathematical, causal) tasks. Our cascade pipeline follows the intuition that simpler questions can be addressed by a weaker but more affordable LLM, whereas only the challenging questions necessitate the stronger and more expensive LLM. To realize this decision-making, we consider the "answer consistency" of the weaker LLM as a signal of the question difficulty and propose several methods for the answer sampling and consistency checking, including one leveraging a mixture of two thought representations (i.e., Chain-of-Thought and Program-of-Thought). Through experiments on six reasoning benchmark datasets, with GPT-3.5-turbo and GPT-4 being the weaker and stronger LLMs, respectively, we demonstrate that our proposed LLM cascades can achieve performance comparable to using solely the stronger LLM but require only 40% of its cost.
Large Language Models (LLMs) have the ability to solve a variety of tasks, such as text summarization and mathematical questions, just out of the box, but they are often trained with a single task in mind. Due to high computational costs, the current trend is to use prompt instruction tuning to better adjust monolithic, pretrained LLMs for new -- but often individual -- downstream tasks. Thus, how one would expand prompt tuning to handle -- concomitantly -- heterogeneous tasks and data distributions is a widely open question. To address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs, associated with smart gating functionality: the latter -- whose design is one of the contributions of this paper -- can identify relevant skills embedded in different groups of prompts and dynamically assign combined experts (i.e., collection of prompts), based on the target task. Additionally, MoPs are empirically agnostic to any model compression technique applied -- for efficiency reasons -- as well as instruction data source and task composition. In practice, MoPs can simultaneously mitigate prompt training "interference" in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources), as well as possible implications from model approximations. As a highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to $\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim 3\%$ up to $\sim30\%$ in the centralized scenario.
This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our approach demonstrates that matching the quantisation scheme to the real data distribution can reduce computational overhead while maintaining acceptable precision. Moreover, our approach is robust when applied to real-world data and mixed-precision quantisation, where most objects are quantised to 4 bits. Our findings inform model quantisation and deployment decisions while providing a foundation for advancing quantisation techniques.
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial challenges, emphasizing their nature. We will traverse the class P, which comprises problems solvable in polynomial time using deterministic algorithms, contrasting it with the class NP, where finding efficient solutions remains an enigmatic endeavor, understanding the intricacies of algorithmic transitions and thresholds demarcating the boundary between tractable and intractable problems. We will discuss the implications of the P versus NP problem, representing one of the profoundest unsolved enigmas of computer science and mathematics, bearing a tantalizing reward for its resolution. Drawing parallels between combinatorics and statistical physics, we will uncover intriguing interconnections that shed light on the nature of challenging problems. Statistical physics unveils profound analogies with complexities witnessed in combinatorial landscapes. Throughout this chapter, we will discuss the interplay between computational complexity theory and statistical physics. By unveiling the mysteries surrounding challenging problems, we aim to deepen understanding of the very essence of computation and its boundaries. Through this interdisciplinary approach, we aspire to illuminate the intricate tapestry of complexity underpinning the mathematical and physical facets of hard problems.
In the evolving landscape of digital art, Non-Fungible Tokens (NFTs) have emerged as a groundbreaking platform, bridging the realms of art and technology. NFTs serve as the foundational framework that has revolutionized the market for digital art, enabling artists to showcase and monetize their creations in unprecedented ways. NFTs combine metadata stored on the blockchain with off-chain data, such as images, to create a novel form of digital ownership. It is not fully understood how these factors come together to determine NFT prices. In this study, we analyze both on-chain and off-chain data of NFT collections trading on OpenSea to understand what influences NFT pricing. Our results show that while text and image data of the NFTs can be used to explain price variations within collections, the extracted features do not generalize to new, unseen collections. Furthermore, we find that an NFT collection's trading volume often relates to its online presence, like social media followers and website traffic.
Visualization of dynamic processes in scientific high-performance computing is an immensely data intensive endeavor. Application codes have recently demonstrated scaling to full-size Exascale machines, and generating high-quality data for visualization is consequently on the machine-scale, easily spanning 100s of TBytes of input to generate a single video frame. In situ visualization, the technique to consume the many-node decomposed data in-memory, as exposed by applications, is the dominant workflow. Although in situ visualization has achieved tremendous progress in the last decade, scaling to system-size together with the application codes that produce its data, there is one important question that we cannot skip: is what we produce insightful and inspiring?
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.
Language model pre-training has proven to be useful in learning universal language representations. As a state-of-the-art language model pre-training model, BERT (Bidirectional Encoder Representations from Transformers) has achieved amazing results in many language understanding tasks. In this paper, we conduct exhaustive experiments to investigate different fine-tuning methods of BERT on text classification task and provide a general solution for BERT fine-tuning. Finally, the proposed solution obtains new state-of-the-art results on eight widely-studied text classification datasets.
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