Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and model scale. Additionally, we discuss length generalization challenges. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction objective for rapidly eliciting arithmetic capabilities.
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In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more generally, parameterized approximation algorithms. In this work, we generalize those results to the weighted setting. More formally, we consider monotone subset minimization problems over a weighted universe of size $n$ (e.g., Vertex Cover, $d$-Hitting Set and Feedback Vertex Set). We consider a model where the algorithm is only given access to a subroutine that finds a solution of weight at most $\alpha \cdot W$ (and of arbitrary cardinality) in time $c^k \cdot n^{O(1)}$ where $W$ is the minimum weight of a solution of cardinality at most $k$. In the unweighted setting, Esmer et al. determine the smallest value $d$ for which a $\beta$-approximation algorithm running in time $d^n \cdot n^{O(1)}$ can be obtained in this model. We show that the same dependencies also hold in a weighted setting in this model: for every fixed $\varepsilon>0$ we obtain a $\beta$-approximation algorithm running in time $O\left((d+\varepsilon)^{n}\right)$, for the same $d$ as in the unweighted setting. Similarly, we also extend a $\beta$-approximate brute-force search (in a model which only provides access to a membership oracle) to the weighted setting. Using existing approximation algorithms and exact parameterized algorithms for weighted problems, we obtain the first exponential-time $\beta$-approximation algorithms that are better than brute force for a variety of problems including Weighted Vertex Cover, Weighted $d$-Hitting Set, Weighted Feedback Vertex Set and Weighted Multicut.
Large Language Models (LLMs) have shown promise in multiple software engineering tasks including code generation, code summarisation, test generation and code repair. Fault localisation is essential for facilitating automatic program debugging and repair, and is demonstrated as a highlight at ChatGPT-4's launch event. Nevertheless, there has been little work understanding LLMs' capabilities for fault localisation in large-scale open-source programs. To fill this gap, this paper presents an in-depth investigation into the capability of ChatGPT-3.5 and ChatGPT-4, the two state-of-the-art LLMs, on fault localisation. Using the widely-adopted Defects4J dataset, we compare the two LLMs with the existing fault localisation techniques. We also investigate the stability and explanation of LLMs in fault localisation, as well as how prompt engineering and the length of code context affect the fault localisation effectiveness. Our findings demonstrate that within a limited code context, ChatGPT-4 outperforms all the existing fault localisation methods. Additional error logs can further improve ChatGPT models' localisation accuracy and stability, with an average 46.9% higher accuracy over the state-of-the-art baseline SmartFL in terms of TOP-1 metric. However, performance declines dramatically when the code context expands to the class-level, with ChatGPT models' effectiveness becoming inferior to the existing methods overall. Additionally, we observe that ChatGPT's explainability is unsatisfactory, with an accuracy rate of only approximately 30%. These observations demonstrate that while ChatGPT can achieve effective fault localisation performance under certain conditions, evident limitations exist. Further research is imperative to fully harness the potential of LLMs like ChatGPT for practical fault localisation applications.
Transformers have emerged as the cornerstone of state-of-the-art natural language processing models, showcasing exceptional performance across a wide range of AI applications. However, the memory demands posed by the self-attention mechanism and the large feedforward network in Transformers limit their ability to handle long sequences, thereby creating challenges for tasks involving multiple long sequences or long-term dependencies. We present a distinct approach, Blockwise Parallel Transformer (BPT), that leverages blockwise computation of self-attention and feedforward network fusion to minimize memory costs. By processing longer input sequences while maintaining memory efficiency, BPT enables training sequences 32 times longer than vanilla Transformers and up to 4 times longer than previous memory-efficient methods. Extensive experiments on language modeling and reinforcement learning tasks demonstrate the effectiveness of BPT in reducing memory requirements and improving performance.
Symbolic knowledge graphs (KGs) play a pivotal role in knowledge-centric applications such as search, question answering and recommendation. As contemporary language models (LMs) trained on extensive textual data have gained prominence, researchers have extensively explored whether the parametric knowledge within these models can match up to that present in knowledge graphs. Various methodologies have indicated that enhancing the size of the model or the volume of training data enhances its capacity to retrieve symbolic knowledge, often with minimal or no human supervision. Despite these advancements, there is a void in comprehensively evaluating whether LMs can encompass the intricate topological and semantic attributes of KGs, attributes crucial for reasoning processes. In this work, we provide an exhaustive evaluation of language models of varying sizes and capabilities. We construct nine qualitative benchmarks that encompass a spectrum of attributes including symmetry, asymmetry, hierarchy, bidirectionality, compositionality, paths, entity-centricity, bias and ambiguity. Additionally, we propose novel evaluation metrics tailored for each of these attributes. Our extensive evaluation of various LMs shows that while these models exhibit considerable potential in recalling factual information, their ability to capture intricate topological and semantic traits of KGs remains significantly constrained. We note that our proposed evaluation metrics are more reliable in evaluating these abilities than the existing metrics. Lastly, some of our benchmarks challenge the common notion that larger LMs (e.g., GPT-4) universally outshine their smaller counterparts (e.g., BERT).
Contextual language models have been trained on Classical languages, including Ancient Greek and Latin, for tasks such as lemmatization, morphological tagging, part of speech tagging, authorship attribution, and detection of scribal errors. However, high-quality sentence embedding models for these historical languages are significantly more difficult to achieve due to the lack of training data. In this work, we use a multilingual knowledge distillation approach to train BERT models to produce sentence embeddings for Ancient Greek text. The state-of-the-art sentence embedding approaches for high-resource languages use massive datasets, but our distillation approach allows our Ancient Greek models to inherit the properties of these models while using a relatively small amount of translated sentence data. We build a parallel sentence dataset using a sentence-embedding alignment method to align Ancient Greek documents with English translations, and use this dataset to train our models. We evaluate our models on translation search, semantic similarity, and semantic retrieval tasks and investigate translation bias. We make our training and evaluation datasets freely available at //github.com/kevinkrahn/ancient-greek-datasets .
Deep neural networks (DNNs) have succeeded in many different perception tasks, e.g., computer vision, natural language processing, reinforcement learning, etc. The high-performed DNNs heavily rely on intensive resource consumption. For example, training a DNN requires high dynamic memory, a large-scale dataset, and a large number of computations (a long training time); even inference with a DNN also demands a large amount of static storage, computations (a long inference time), and energy. Therefore, state-of-the-art DNNs are often deployed on a cloud server with a large number of super-computers, a high-bandwidth communication bus, a shared storage infrastructure, and a high power supplement. Recently, some new emerging intelligent applications, e.g., AR/VR, mobile assistants, Internet of Things, require us to deploy DNNs on resource-constrained edge devices. Compare to a cloud server, edge devices often have a rather small amount of resources. To deploy DNNs on edge devices, we need to reduce the size of DNNs, i.e., we target a better trade-off between resource consumption and model accuracy. In this dissertation, we studied four edge intelligence scenarios, i.e., Inference on Edge Devices, Adaptation on Edge Devices, Learning on Edge Devices, and Edge-Server Systems, and developed different methodologies to enable deep learning in each scenario. Since current DNNs are often over-parameterized, our goal is to find and reduce the redundancy of the DNNs in each scenario.
With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Transformers have become one of the most important architectural innovations in deep learning and have enabled many breakthroughs over the past few years. Here we propose a simple attention-free network architecture, gMLP, based solely on MLPs with gating, and show that it can perform as well as Transformers in key language and vision applications. Our comparisons show that self-attention is not critical for Vision Transformers, as gMLP can achieve the same accuracy. For BERT, our model achieves parity with Transformers on pretraining perplexity and is better on some downstream tasks. On finetuning tasks where gMLP performs worse, making the gMLP model substantially larger can close the gap with Transformers. In general, our experiments show that gMLP can scale as well as Transformers over increased data and compute.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
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