pwc-archive/papers-with-abstracts huggingface dataset:
Very Basics of Tensors with Graphical Notations: Unfolding, Calculations, and Decompositions
Authors: Tatsuya Yokota
Date: 2024-11-25 00:00:00

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described simply and intuitively, and it also helps to understand the essence of tensor products. In fact, most of matrix/tensor products including inner product, outer product, Hadamard product, Kronecker product, and Khatri-Rao product can be written in graphical notation. These matrix/tensor operations are essential building blocks for the use of matrix/tensor decompositions in signal processing and machine learning. The purpose of this lecture note is to learn the very basics of tensors and how to represent them in mathematical symbols and graphical notation. Many papers using tensors omit these detailed definitions and explanations, which can be difficult for the reader. I hope this note will be of help to such readers.
Exploring the Generalization Capabilities of AID-based Bi-level Optimization
Authors: Congliang Chen, Li Shen, Zhiqiang Xu, Wei Liu, Zhi-Quan Luo, Peilin Zhao
Date: 2024-11-25 00:00:00

Bi-level optimization has achieved considerable success in contemporary machine learning applications, especially for given proper hyperparameters. However, due to the two-level optimization structure, commonly, researchers focus on two types of bi-level optimization methods: approximate implicit differentiation (AID)-based and iterative differentiation (ITD)-based approaches. ITD-based methods can be readily transformed into single-level optimization problems, facilitating the study of their generalization capabilities. In contrast, AID-based methods cannot be easily transformed similarly but must stay in the two-level structure, leaving their generalization properties enigmatic. In this paper, although the outer-level function is nonconvex, we ascertain the uniform stability of AID-based methods, which achieves similar results to a single-level nonconvex problem. We conduct a convergence analysis for a carefully chosen step size to maintain stability. Combining the convergence and stability results, we give the generalization ability of AID-based bi-level optimization methods. Furthermore, we carry out an ablation study of the parameters and assess the performance of these methods on real-world tasks. Our experimental results corroborate the theoretical findings, demonstrating the effectiveness and potential applications of these methods.
VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
Authors: Yadi Cao, Yuxuan Liu, Liu Yang, Rose Yu, Hayden Schaeffer, Stanley Osher
Date: 2024-11-25 00:00:00
Tasks: Computational Efficiency, In-Context Learning, Operator learning

In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, existing ICONs process each spatial point as an individual token, severely limiting computational efficiency when handling dense data in higher spatial dimensions. We propose Vision In-Context Operator Networks (VICON), which integrates vision transformer architectures to efficiently process 2D data through patch-wise operations while preserving ICON's adaptability to multiphysics systems and varying timesteps. Evaluated across three fluid dynamics benchmarks, VICON significantly outperforms state-of-the-art baselines: DPOT and MPP, reducing the averaged last-step rollout error by 37.9% compared to DPOT and 44.7% compared to MPP, while requiring only 72.5% and 34.8% of their respective inference times. VICON naturally supports flexible rollout strategies with varying timestep strides, enabling immediate deployment in imperfect measurement systems where sampling frequencies may differ or frames might be dropped - common challenges in real-world settings - without requiring retraining or interpolation. In these realistic scenarios, VICON exhibits remarkable robustness, experiencing only 24.41% relative performance degradation compared to 71.37%-74.49% degradation in baseline methods, demonstrating its versatility for deploying in realistic applications. Our scripts for processing datasets and code are publicly available at https://github.com/Eydcao/VICON.
Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments
Authors: Koji Hashimoto, Koshiro Matsuo, Masaki Murata, Gakuto Ogiwara, Daichi Takeda
Date: 2024-11-25 00:00:00

We introduce a novel interpretable Neural Network (NN) model designed to perform precision bulk reconstruction under the AdS/CFT correspondence. According to the correspondence, a specific condensed matter system on a ring is holographically equivalent to a gravitational system on a bulk disk, through which tabletop quantum gravity experiments may be possible as reported in arXiv:2211.13863. The purpose of this paper is to reconstruct a higher-dimensional gravity metric from the condensed matter system data via machine learning using the NN. Our machine reads spatially and temporarily inhomogeneous linear response data of the condensed matter system, and incorporates a novel layer that implements the Runge-Kutta method to achieve better numerical control. We confirm that our machine can let a higher-dimensional gravity metric be automatically emergent as its interpretable weights, using a linear response of the condensed matter system as data, through supervised machine learning. The developed method could serve as a foundation for generic bulk reconstruction, i.e., a practical solution to the AdS/CFT correspondence, and would be implemented in future tabletop quantum gravity experiments.
Downlink MIMO Channel Estimation from Bits: Recoverability and Algorithm
Authors: Rajesh Shrestha, Mingjie Shao, Mingyi Hong, Wing-Kin Ma, Xiao Fu
Date: 2024-11-25 00:00:00
Tasks: Quantization

In frequency division duplex (FDD) massive MIMO systems, a major challenge lies in acquiring the downlink channel state information}\ (CSI) at the base station (BS) from limited feedback sent by the user equipment (UE). To tackle this fundamental task, our contribution is twofold: First, a simple feedback framework is proposed, where a compression and Gaussian dithering-based quantization strategy is adopted at the UE side, and then a maximum likelihood estimator (MLE) is formulated at the BS side. Recoverability of the MIMO channel under the widely used double directional model is established. Specifically, analyses are presented for two compression schemes -- showing one being more overhead-economical and the other computationally lighter at the UE side. Second, to realize the MLE, an alternating direction method of multipliers (ADMM) algorithm is proposed. The algorithm is carefully designed to integrate a sophisticated harmonic retrieval (HR) solver as subroutine, which turns out to be the key of effectively tackling this hard MLE problem.Extensive numerical experiments are conducted to validate the efficacy of our approach.
Predicting Emergent Capabilities by Finetuning
Authors: Charlie Snell, Eric Wallace, Dan Klein, Sergey Levine
Date: 2024-11-25 00:00:00
Tasks: CoLA, GSM8K, MMLU

A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable -- sometimes even exhibiting emergent jumps -- which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). We validate this approach using four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we can accurately predict whether models trained with up to 4x more compute have emerged. Finally, we present a case study of two realistic uses for emergence prediction.
Generative AI for Brane Configurations and Coamoeba
Authors: Rak-Kyeong Seong
Date: 2024-11-25 00:00:00

We introduce a generative AI model to obtain Type IIB brane configurations that realize toric phases of a family of 4d N=1 supersymmetric gauge theories. These 4d N=1 quiver gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold. The Type IIB brane configurations are given by the coamoeba projection of the mirror curve associated with the toric Calabi-Yau 3-fold. The shape of the mirror curve and its coamoeba projection, as well as the corresponding Type IIB brane configuration and the toric phase of the 4d N=1 theory, all depend on the complex structure moduli parameterizing the mirror curve. We train a generative AI model, a conditional variational autoencoder (CVAE), that takes a choice of complex structure moduli as input and generates the corresponding coamoeba. This enables us not only to obtain a high-resolution representation of the entire phase space for a family of 4d N=1 theories corresponding to the same toric Calabi-Yau 3-fold, but also to continuously track the movements of the mirror curve and the branes wrapping the curve in the corresponding Type IIB brane configurations during phase transitions associated with Seiberg duality.
Binary Search with Distributional Predictions
Authors: Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, Aidin Niaparast, Sergei Vassilvitskii
Date: 2024-11-25 00:00:00
Tasks: Prediction

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first distributionally-robust algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.
M3: Mamba-assisted Multi-Circuit Optimization via MBRL with Effective Scheduling
Authors: Youngmin Oh, Jinje Park, Seunggeun Kim, Taejin Paik, David Pan, Bosun Hwang
Date: 2024-11-25 00:00:00
Tasks: Mamba, Reinforcement Learning (RL), Scheduling

Recent advancements in reinforcement learning (RL) for analog circuit optimization have demonstrated significant potential for improving sample efficiency and generalization across diverse circuit topologies and target specifications. However, there are challenges such as high computational overhead, the need for bespoke models for each circuit. To address them, we propose M3, a novel Model-based RL (MBRL) method employing the Mamba architecture and effective scheduling. The Mamba architecture, known as a strong alternative to the transformer architecture, enables multi-circuit optimization with distinct parameters and target specifications. The effective scheduling strategy enhances sample efficiency by adjusting crucial MBRL training parameters. To the best of our knowledge, M3 is the first method for multi-circuit optimization by leveraging both the Mamba architecture and a MBRL with effective scheduling. As a result, it significantly improves sample efficiency compared to existing RL methods.
Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem
Authors: Hesameddin Mohammadi, Mohammad Tinati, Stephen Tu, Mahdi Soltanolkotabi, Mihailo R. Jovanović
Date: 2024-11-24 00:00:00

The symmetric low-rank matrix factorization serves as a building block in many learning tasks, including matrix recovery and training of neural networks. However, despite a flurry of recent research, the dynamics of its training via non-convex factorized gradient-descent-type methods is not fully understood especially in the over-parameterized regime where the fitted rank is higher than the true rank of the target matrix. To overcome this challenge, we characterize equilibrium points of the gradient flow dynamics and examine their local and global stability properties. To facilitate a precise global analysis, we introduce a nonlinear change of variables that brings the dynamics into a cascade connection of three subsystems whose structure is simpler than the structure of the original system. We demonstrate that the Schur complement to a principal eigenspace of the target matrix is governed by an autonomous system that is decoupled from the rest of the dynamics. In the over-parameterized regime, we show that this Schur complement vanishes at an $O(1/t)$ rate, thereby capturing the slow dynamics that arises from excess parameters. We utilize a Lyapunov-based approach to establish exponential convergence of the other two subsystems. By decoupling the fast and slow parts of the dynamics, we offer new insight into the shape of the trajectories associated with local search algorithms and provide a complete characterization of the equilibrium points and their global stability properties. Such an analysis via nonlinear control techniques may prove useful in several related over-parameterized problems.
Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise
Authors: Enea Monzio Compagnoni, Tianlin Liu, Rustem Islamov, Frank Norbert Proske, Antonio Orvieto, Aurelien Lucchi
Date: 2024-11-24 00:00:00

Despite the vast empirical evidence supporting the efficacy of adaptive optimization methods in deep learning, their theoretical understanding is far from complete. This work introduces novel SDEs for commonly used adaptive optimizers: SignSGD, RMSprop(W), and Adam(W). These SDEs offer a quantitatively accurate description of these optimizers and help illuminate an intricate relationship between adaptivity, gradient noise, and curvature. Our novel analysis of SignSGD highlights a noteworthy and precise contrast to SGD in terms of convergence speed, stationary distribution, and robustness to heavy-tail noise. We extend this analysis to AdamW and RMSpropW, for which we observe that the role of noise is much more complex. Crucially, we support our theoretical analysis with experimental evidence by verifying our insights: this includes numerically integrating our SDEs using Euler-Maruyama discretization on various neural network architectures such as MLPs, CNNs, ResNets, and Transformers. Our SDEs accurately track the behavior of the respective optimizers, especially when compared to previous SDEs derived for Adam and RMSprop. We believe our approach can provide valuable insights into best training practices and novel scaling rules.
Understanding Machine Learning Paradigms through the Lens of Statistical Thermodynamics: A tutorial
Authors: Star, Liu
Date: 2024-11-24 00:00:00
Tasks: Learning Theory, Variational Inference

This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial delves into advanced techniques like entropy, free energy, and variational inference which are utilized in machine learning, illustrating their significant contributions to model efficiency and robustness. By bridging these scientific disciplines, we aspire to inspire newer methodologies in researches, demonstrating how an in-depth comprehension of physical systems' behavior can yield more effective and dependable machine learning models, particularly in contexts characterized by uncertainty.
Customer Lifetime Value Prediction with Uncertainty Estimation Using Monte Carlo Dropout
Authors: Xinzhe Cao, Yadong Xu, Xiaofeng Yang
Date: 2024-11-24 00:00:00
Tasks: Value prediction

Accurately predicting customer Lifetime Value (LTV) is crucial for companies to optimize their revenue strategies. Traditional deep learning models for LTV prediction are effective but typically provide only point estimates and fail to capture model uncertainty in modeling user behaviors. To address this limitation, we propose a novel approach that enhances the architecture of purely neural network models by incorporating the Monte Carlo Dropout (MCD) framework. We benchmarked the proposed method using data from one of the most downloaded mobile games in the world, and demonstrated a substantial improvement in predictive Top 5\% Mean Absolute Percentage Error compared to existing state-of-the-art methods. Additionally, our approach provides confidence metric as an extra dimension for performance evaluation across various neural network models, facilitating more informed business decisions.
Improving Pre-trained Self-Supervised Embeddings Through Effective Entropy Maximization
Authors: Deep Chakraborty, Yann Lecun, Tim G. J. Rudner, Erik Learned-Miller
Date: 2024-11-24 00:00:00
Tasks: Self-Supervised Learning

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends -- whether explicitly or implicitly -- upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.
Enhancing Symbolic Regression and Universal Physics-Informed Neural Networks with Dimensional Analysis
Authors: Lena Podina, Diba Darooneh, Joshveer Grewal, Mohammad Kohandel
Date: 2024-11-24 00:00:00
Tasks: regression, Symbolic Regression

We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically Ipsen's and Buckingham pi methods. Since symbolic regression often suffers from high computational costs and overfitting, non-dimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As our main contribution, we integrate Ipsen's method of dimensional analysis with Universal Physics-Informed Neural Networks. We also combine dimensional analysis with the AI Feynman symbolic regression algorithm to show that dimensional analysis significantly improves the accuracy of the recovered equation. The results demonstrate that transforming data into a dimensionless form significantly decreases computation time and improves accuracy of the recovered hidden term. For algebraic equations, using the Buckingham pi theorem reduced complexity, allowing the AI Feynman model to converge faster with fewer data points and lower error rates. For differential equations, Ipsen's method was combined with Universal Physics-Informed Neural Networks (UPINNs) to identify hidden terms more effectively. These findings suggest that integrating dimensional analysis with symbolic regression can significantly lower computational costs, enhance model interpretability, and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.
From Laws to Motivation: Guiding Exploration through Law-Based Reasoning and Rewards
Authors: Ziyu Chen, Zhiqing Xiao, Xinbei Jiang, Junbo Zhao
Date: 2024-11-24 00:00:00
Tasks: Reinforcement Learning (RL)

Large Language Models (LLMs) and Reinforcement Learning (RL) are two powerful approaches for building autonomous agents. However, due to limited understanding of the game environment, agents often resort to inefficient exploration and trial-and-error, struggling to develop long-term strategies or make decisions. We propose a method that extracts experience from interaction records to model the underlying laws of the game environment, using these experience as internal motivation to guide agents. These experience, expressed in language, are highly flexible and can either assist agents in reasoning directly or be transformed into rewards for guiding training. Our evaluation results in Crafter demonstrate that both RL and LLM agents benefit from these experience, leading to improved overall performance.
ExAL: An Exploration Enhanced Adversarial Learning Algorithm
Authors: A Vinil, Aneesh Sreevallabh Chivukula, Pranav Chintareddy
Date: 2024-11-24 00:00:00

Adversarial learning is critical for enhancing model robustness, aiming to defend against adversarial attacks that jeopardize machine learning systems. Traditional methods often lack efficient mechanisms to explore diverse adversarial perturbations, leading to limited model resilience. Inspired by game-theoretic principles, where adversarial dynamics are analyzed through frameworks like Nash equilibrium, exploration mechanisms in such setups allow for the discovery of diverse strategies, enhancing system robustness. However, existing adversarial learning methods often fail to incorporate structured exploration effectively, reducing their ability to improve model defense comprehensively. To address these challenges, we propose a novel Exploration-enhanced Adversarial Learning Algorithm (ExAL), leveraging the Exponentially Weighted Momentum Particle Swarm Optimizer (EMPSO) to generate optimized adversarial perturbations. ExAL integrates exploration-driven mechanisms to discover perturbations that maximize impact on the model's decision boundary while preserving structural coherence in the data. We evaluate the performance of ExAL on the MNIST Handwritten Digits and Blended Malware datasets. Experimental results demonstrate that ExAL significantly enhances model resilience to adversarial attacks by improving robustness through adversarial learning.