Can a Large Language Model Learn Matrix Functions In Context?

Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of LLMs to solve non-linear numerical computations, with specific emphasis on functions of the Singular Value Decomposition. Our experiments show that while LLMs perform comparably to traditional models such as Stochastic Gradient Descent (SGD) based Linear Regression and Neural Networks (NN) for simpler tasks, they outperform these models on more complex tasks, particularly in the case of top-k Singular Values. Furthermore, LLMs demonstrate strong scalability, maintaining high accuracy even as the matrix size increases. Additionally, we found that LLMs can achieve high accuracy with minimal prior examples, converging quickly and avoiding the overfitting seen in classical models. These results suggest that LLMs could provide an efficient alternative to classical methods for solving high-dimensional problems. Future work will focus on extending these findings to larger matrices and more complex matrix operations while exploring the effect of using different numerical representations in ICL.

Automating Data Science Pipelines with Tensor Completion

Hyperparameter optimization is an essential component in many data science pipelines and typically entails exhaustive time and resource-consuming computations in order to explore the combinatorial search space. Similar to this problem, other key operations in data science pipelines exhibit the exact same properties. Important examples are: neural architecture search, where the goal is to identify the best design choices for a neural network, and query cardinality estimation, where given different predicate values for a SQL query the goal is to estimate the size of the output. In this paper, we abstract away those essential components of data science pipelines and we model them as instances of tensor completion, where each variable of the search space corresponds to one mode of the tensor, and the goal is to identify all missing entries of the tensor, corresponding to all combinations of variable values, starting from a very small sample of observed entries. In order to do so, we first conduct a thorough experimental evaluation of existing state-of-the-art tensor completion techniques and introduce domain-inspired adaptations (such as smoothness across the discretized variable space) and an ensemble technique which is able to achieve state-of-the-art performance. We extensively evaluate existing and proposed methods in a number of datasets generated corresponding to (a) hyperparameter optimization for non-neural network models, (b) neural architecture search, and (c) variants of query cardinality estimation, demonstrating the effectiveness of tensor completion as a tool for automating data science pipelines. Furthermore, we release our generated datasets and code in order to provide benchmarks for future work on this topic.

Your Diffusion Model is Secretly a Noise Classifier and Benefits from Contrastive Training

Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality degradation: the denoiser is poorly estimated in regions that are far Outside Of the training Distribution (OOD), and the sampling process inevitably evaluates in these OOD regions. This can become problematic for all sampling methods, especially when we move to parallel sampling which requires us to initialize and update the entire sample trajectory of dynamics in parallel, leading to many OOD evaluations. To address this problem, we introduce a new self-supervised training objective that differentiates the levels of noise added to a sample, leading to improved OOD denoising performance. The approach is based on our observation that diffusion models implicitly define a log-likelihood ratio that distinguishes distributions with different amounts of noise, and this expression depends on denoiser performance outside the standard training distribution. We show by diverse experiments that the proposed contrastive diffusion training is effective for both sequential and parallel settings, and it improves the performance and speed of parallel samplers significantly.

TRAWL: Tensor Reduced and Approximated Weights for Large Language Models

Large language models (LLMs) have fundamentally transformed artificial intelligence, catalyzing recent advancements while imposing substantial environmental and computational burdens. We introduce TRAWL (Tensor Reduced and Approximated Weights for Large Language Models), a novel methodology for optimizing LLMs through tensor decomposition. TRAWL leverages diverse strategies to exploit matrices within transformer-based architectures, realizing notable performance enhancements without necessitating retraining. The most significant improvements were observed through a layer-by-layer intervention strategy, particularly when applied to fully connected weights of the final layers, yielding up to 16% enhancement in accuracy without the need for additional data or fine-tuning. These results underscore the importance of targeted and adaptive techniques in increasing the efficiency and effectiveness of large language model optimization, thereby promoting the development of more sustainable and accessible AI systems.

GPT-generated Text Detection: Benchmark Dataset and Tensor-based Detection Method

As natural language models like ChatGPT become increasingly prevalent in applications and services, the need for robust and accurate methods to detect their output is of paramount importance. In this paper, we present GPT Reddit Dataset (GRiD), a novel Generative Pretrained Transformer (GPT)-generated text detection dataset designed to assess the performance of detection models in identifying generated responses from ChatGPT. The dataset consists of a diverse collection of context-prompt pairs based on Reddit, with human-generated and ChatGPT-generated responses. We provide an analysis of the dataset's characteristics, including linguistic diversity, context complexity, and response quality. To showcase the dataset's utility, we benchmark several detection methods on it, demonstrating their efficacy in distinguishing between human and ChatGPT-generated responses. This dataset serves as a resource for evaluating and advancing detection techniques in the context of ChatGPT and contributes to the ongoing efforts to ensure responsible and trustworthy AI-driven communication on the internet. Finally, we propose GpTen, a novel tensor-based GPT text detection method that is semi-supervised in nature since it only has access to human-generated text and performs on par with fully-supervised baselines.

Towards Aligned Canonical Correlation Analysis: Preliminary Formulation and Proof-of-Concept Results

Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional approaches, is unclear in many practical cases. In this work we propose a new framework Aligned Canonical Correlation Analysis (ACCA), to address this challenge by iteratively solving the alignment and multi-view embedding.

CARL-G: Clustering-Accelerated Representation Learning on Graphs

Self-supervised learning on graphs has made large strides in achieving great performance in various downstream tasks. However, many state-of-the-art methods suffer from a number of impediments, which prevent them from realizing their full potential. For instance, contrastive methods typically require negative sampling, which is often computationally costly. While non-contrastive methods avoid this expensive step, most existing methods either rely on overly complex architectures or dataset-specific augmentations. In this paper, we ask: Can we borrow from classical unsupervised machine learning literature in order to overcome those obstacles? Guided by our key insight that the goal of distance-based clustering closely resembles that of contrastive learning: both attempt to pull representations of similar items together and dissimilar items apart. As a result, we propose CARL-G - a novel clustering-based framework for graph representation learning that uses a loss inspired by Cluster Validation Indices (CVIs), i.e., internal measures of cluster quality (no ground truth required). CARL-G is adaptable to different clustering methods and CVIs, and we show that with the right choice of clustering method and CVI, CARL-G outperforms node classification baselines on 4/5 datasets with up to a 79x training speedup compared to the best-performing baseline. CARL-G also performs at par or better than baselines in node clustering and similarity search tasks, training up to 1,500x faster than the best-performing baseline. Finally, we also provide theoretical foundations for the use of CVI-inspired losses in graph representation learning.

Link Prediction with Non-Contrastive Learning

A recent focal area in the space of graph neural networks (GNNs) is graph self-supervised learning (SSL), which aims to derive useful node representations without labeled data. Notably, many state-of-the-art graph SSL methods are contrastive methods, which use a combination of positive and negative samples to learn node representations. Owing to challenges in negative sampling (slowness and model sensitivity), recent literature introduced non-contrastive methods, which instead only use positive samples. Though such methods have shown promising performance in node-level tasks, their suitability for link prediction tasks, which are concerned with predicting link existence between pairs of nodes (and have broad applicability to recommendation systems contexts) is yet unexplored. In this work, we extensively evaluate the performance of existing non-contrastive methods for link prediction in both transductive and inductive settings. While most existing non-contrastive methods perform poorly overall, we find that, surprisingly, BGRL generally performs well in transductive settings. However, it performs poorly in the more realistic inductive settings where the model has to generalize to links to/from unseen nodes. We find that non-contrastive models tend to overfit to the training graph and use this analysis to propose T-BGRL, a novel non-contrastive framework that incorporates cheap corruptions to improve the generalization ability of the model. This simple modification strongly improves inductive performance in 5/6 of our datasets, with up to a 120% improvement in Hits@50--all with comparable speed to other non-contrastive baselines and up to 14x faster than the best-performing contrastive baseline. Our work imparts interesting findings about non-contrastive learning for link prediction and paves the way for future researchers to further expand upon this area.

FRAPPE: $\underline{\text{F}}$ast $\underline{\text{Ra}}$nk $\underline{\text{App}}$roximation with $\underline{\text{E}}$xplainable Features for Tensors

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC decomposition (CPD), this value is known as the canonical rank and greatly affects the quality of the results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose FRAPPE and Self-FRAPPE: a cheaply supervised and a self-supervised method to estimate the canonical rank of a tensor without ever having to compute the CPD. We call FRAPPE cheaply supervised because it uses a fully synthetic training set without requiring real-world examples. We evaluate these methods on synthetic tensors, real tensors of known rank, and the weight tensor of a convolutional neural network. We show that FRAPPE and Self-FRAPPE offer large improvements in both effectiveness and speed, with a respective $15\%$ and $10\%$ improvement in MAPE and an $4000\times$ and $13\times$ improvement in evaluation speed over the best-performing baseline.

MAVIPER: Learning Decision Tree Policies for Interpretable Multi-Agent Reinforcement Learning

Many recent breakthroughs in multi-agent reinforcement learning (MARL) require the use of deep neural networks, which are challenging for human experts to interpret and understand. On the other hand, existing work on interpretable RL has shown promise in extracting more interpretable decision tree-based policies, but only in the single-agent setting. To fill this gap, we propose the first set of interpretable MARL algorithms that extract decision-tree policies from neural networks trained with MARL. The first algorithm, IVIPER, extends VIPER, a recent method for single-agent interpretable RL, to the multi-agent setting. We demonstrate that IVIPER can learn high-quality decision-tree policies for each agent. To better capture coordination between agents, we propose a novel centralized decision-tree training algorithm, MAVIPER. MAVIPER jointly grows the trees of each agent by predicting the behavior of the other agents using their anticipated trees, and uses resampling to focus on states that are critical for its interactions with other agents. We show that both algorithms generally outperform the baselines and that MAVIPER-trained agents achieve better-coordinated performance than IVIPER-trained agents on three different multi-agent particle-world environments.