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Deep Learning · Other Representation Learning

Rui Li, Chaozhuo Li, Yanming Shen, Zeyu Zhang, Xu Chen

Recent advances in knowledge graph embedding (KGE) rely on Euclidean/hyperbolic orthogonal relation transformations to model intrinsic logical patterns and topological structures. However, existing approaches are confined to rigid relational orthogonalization with restricted dimension and homogeneous geometry, leading to deficient modeling capability. In this work, we move beyond these approaches in terms of both dimension and geometry by introducing a powerful framework named GoldE, which features a universal orthogonal parameterization based on a generalized form of Householder reflection. Such parameterization can naturally achieve dimensional extension and geometric unification with theoretical guarantees, enabling our framework to simultaneously capture crucial logical patterns and inherent topological heterogeneity of knowledge graphs. Empirically, GoldE achieves state-of-the-art performance on three standard benchmarks. Codes are available at https://github.com/xxrep/GoldE.

Social Aspects · Fairness, Equity, Justice and Safety

L. Elisa Celis, Amit Kumar, Nisheeth K. Vishnoi, Shangyu Andrew Xu

This paper considers the scenario in which there are multiple institutions, each with a limited capacity for candidates, and candidates, each with preferences over the institutions. A central entity evaluates the utility of each candidate to the institutions, and the goal is to select candidates for each institution in a way that maximizes utility while also considering the candidates' preferences. The paper focuses on the setting in which candidates are divided into multiple groups and the observed utilities of candidates in some groups are biased--systematically lower than their true utilities. The first result is that, in these biased settings, prior algorithms can lead to selections with sub-optimal true utility and significant discrepancies in the fraction of candidates from each group that get their preferred choices. Subsequently, an algorithm is presented along with proof that it produces selections that achieve near-optimal group fairness with respect to preferences while also nearly maximizing the true utility under distributional assumptions. Further, extensive empirical validation of these results in real-world and synthetic settings, in which the distributional assumptions may not hold, are presented.

Deep Learning · Large Language Models

Dyah Adila, Shuai Zhang, Boran Han, Yuyang Wang

The question-answering (QA) capabilities of foundation models are highly sensitive to prompt variations, rendering their performance susceptible to superficial, non-meaning-altering changes. This vulnerability often stems from the model's preference or bias towards specific input characteristics, such as option position or superficial image features in multi-modal settings. We propose to rectify this bias directly in the model's internal representation. Our approach, SteerFair, finds the bias direction in the model's representation space and steers activation values away from it during inference. Specifically, we exploit the observation that bias often adheres to simple association rules, such as the spurious association between the first option and correctness likelihood. Next, we construct demonstrations of these rules from unlabeled samples and use them to identify the bias directions. We empirically show that SteerFair significantly reduces instruction-tuned model performance variance across prompt modifications on three benchmark tasks. Remarkably, our approach surpasses a supervised baseline with 100 labels by an average of 10.86% accuracy points and 12.95 score points and matches the performance with 500 labels.

Deep Learning · Theory

Mohannad Elhamod, Anuj Karpatne

In recent years, there has been a growing interest in visualizing the loss landscape of neural networks. Linear landscape visualization methods, such as principal component analysis, have become widely used as they intuitively help researchers study neural networks and their training process. However, these linear methods suffer from limitations and drawbacks due to their lack of flexibility and low fidelity at representing the high dimensional landscape. In this paper, we present a novel auto-encoder-based non-linear landscape visualization method called Neuro-Visualizer that addresses these shortcoming and provides useful insights about neural network loss landscapes. To demonstrate its potential, we run experiments on a variety of problems in two separate applications of knowledge-guided machine learning (KGML). Our findings show that Neuro-Visualizer outperforms other linear and non-linear baselines and helps corroborate, and sometime challenge, claims proposed by machine learning community. All code and data used in the experiments of this paper can be found at the link below.

Probabilistic Methods · Bayesian Models and Methods

Sergio Calvo Ordoñez, Matthieu Meunier, Francesco Piatti, Yuantao Shi

In this paper, we present Partially Stochastic Infinitely Deep Bayesian Neural Networks, a novel family of architectures that integrates partial stochasticity into the framework of infinitely deep neural networks. Our new class of architectures is designed to improve the computational efficiency of existing architectures at training and inference time. To do this, we leverage the advantages of partial stochasticity in the infinite-depth limit which include the benefits of full stochasticity e.g. robustness, uncertainty quantification, and memory efficiency, whilst improving their limitations around computational complexity. We present a variety of architectural configurations, offering flexibility in network design including different methods for weight partition. We also provide mathematical guarantees on the expressivity of our models by establishing that our network family qualifies as Universal Conditional Distribution Approximators. Lastly, empirical evaluations across multiple tasks show that our proposed architectures achieve better downstream task performance and uncertainty quantification than their counterparts while being significantly more efficient. The code can be found at https://github.com/Sergio20f/part_stoch_inf_deep

Optimization

William Powell, Hanbaek Lyu

For obtaining optimal first-order convergence guarantees for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling algorithms (e.g., i.i.d., MCMC, random reshuffling) are indeed recurrent under mild assumptions. In this work, we show that for a particular class of stochastic optimization algorithms, we do not need any further property (e.g., independence, exponential mixing, and reshuffling) beyond recurrence in data sampling to guarantee optimal rate of first-order convergence. Namely, using regularized versions of Minimization by Incremental Surrogate Optimization (MISO), we show that for non-convex and possibly non-smooth objective functions with constraints, the expected optimality gap converges at an optimal rate $O(n^{-1/2})$ under general recurrent sampling schemes. Furthermore, the implied constant depends explicitly on the 'speed of recurrence', measured by the expected amount of time to visit a data point, either averaged ('target time') or supremized ('hitting time') over the starting locations. We discuss applications of our general framework to decentralized optimization and distributed non-negative matrix factorization.

Deep Learning · Other Representation Learning

Jungeun Kim, Junwon You, Dongjin Lee, Ha Young Kim, Jae-Hun Jung

Knowledge distillation (KD) aims to transfer knowledge from larger (teacher) to smaller (student) networks. Previous studies focus on point-to-point or pairwise relationships in embedding features as knowledge and struggle to efficiently transfer relationships of complex latent spaces. To tackle this issue, we propose a novel KD method called TopKD, which considers the global topology of the latent spaces. We define *global topology knowledge* using the persistence diagram (PD) that captures comprehensive geometric structures such as shape of distribution, multiscale structure and connectivity, and the *topology distillation loss* for teaching this knowledge. To make the PD transferable within reasonable computational time, we employ approximated persistence images of PDs. Through experiments, we support the benefits of using global topology as knowledge and demonstrate the potential of TopKD. Code is available at https://github.com/jekim5418/TopKD

Social Aspects · Trustworthy Machine Learning

Kartik Patwari, Chen-Nee Chuah, Lingjuan Lyu, Vivek Sharma

Current image anonymization techniques, largely focus on localized pseudonymization, typically modify identifiable features like faces or full bodies and evaluate anonymity through metrics such as detection and re-identification rates. However, this approach often overlooks information present in the entire image post-anonymization that can compromise privacy, such as specific locations, objects/items, or unique attributes. Acknowledging the pivotal role of human judgment in anonymity, our study conducts a thorough analysis of perceptual anonymization, exploring its spectral nature and its critical implications for image privacy assessment, particularly in light of regulations such as the General Data Protection Regulation (GDPR). To facilitate this, we curated a dataset specifically tailored for assessing anonymized images. We introduce a learning-based metric, PerceptAnon, which is tuned to align with the human Perception of Anonymity. PerceptAnon evaluates both original-anonymized image pairs and solely anonymized images. Trained using human annotations, our metric encompasses both anonymized subjects and their contextual backgrounds, thus providing a comprehensive evaluation of privacy vulnerabilities. We envision this work as a milestone for understanding and assessing image anonymization, and establishing a foundation for future research. The codes and dataset are available in https://github.com/SonyResearch/gdpr_perceptanon.

Theory

Shivam Gupta, Ajil Jalal, Aditya Parulekar, Eric Price, Zhiyang Xun

Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid y)$. Posterior sampling is useful for tasks such as inpainting, super-resolution, and MRI reconstruction, so a number of recent works have given algorithms to heuristically approximate it; but none are known to converge to the correct distribution in polynomial time. In this paper we show that posterior sampling is *computationally intractable*: under the most basic assumption in cryptography---that one-way functions exist---there are instances for which *every* algorithm takes superpolynomial time, even though *unconditional* sampling is provably fast. We also show that the exponential-time rejection sampling algorithm is essentially optimal under the stronger plausible assumption that there are one-way functions that take exponential time to invert.

Applications · Physics

Kai Weixian Lan, Elias Gueidon, Ayano Kaneda, Julian Panetta, Joseph Teran

We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems, but only when equipped with powerful preconditioners. Unfortunately, effective preconditioners like multigrid require costly setup phases that must be re-executed every time domain shapes or boundary conditions change, forming a severe bottleneck for problems with evolving boundaries. In contrast, we present a neural preconditioner trained to efficiently approximate the inverse of the discrete Laplacian in the presence of such changes. Our approach generalizes to domain shapes, boundary conditions, and grid sizes outside the training set. The key to our preconditioner's success is a novel, lightweight neural network architecture featuring spatially varying convolution kernels and supporting fast inference. We demonstrate that our solver outperforms state-of-the-art methods like algebraic multigrid as well as recently proposed neural preconditioners on challenging test cases arising from incompressible fluid simulations.

Probabilistic Methods · Bayesian Models and Methods

Yirui Liu, Xinghao Qiao, Yulong Pei, Liying Wang

This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF2M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF2M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF2M. Empirical results from four real-world datasets demonstrate that DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.

Theory · Deep Learning

Chuanhao Sun, Zhihang Yuan, Kai Xu, Luo Mai, Siddharth N, Shuo Chen, Mahesh Marina

Fourier features based positional encoding (PE) is commonly used in machine learning tasks that involve learning high-frequency features from low-dimensional inputs, such as 3D view synthesis and time series regression with neural tangent kernels. Despite their effectiveness, existing PEs require manual, empirical adjustment of crucial hyperparameters, specifically the Fourier features, tailored to each unique task. Further, PEs face challenges in efficiently learning high-frequency functions, particularly in tasks with limited data. In this paper, we introduce sinusoidal PE (SPE), designed to efficiently learn adaptive frequency features closely aligned with the true underlying function. Our experiments demonstrate that SPE, without hyperparameter tuning, consistently achieves enhanced fidelity and faster training across various tasks, including 3D view synthesis, Text-to-Speech generation, and 1D regression. SPE is implemented as a direct replacement for existing PEs. Its plug-and-play nature lets numerous tasks easily adopt and benefit from SPE.

Deep Learning · Generative Models and Autoencoders

Weili Nie, Sifei Liu, Morteza Mardani, Chao Liu, Benjamin Eckart, Arash Vahdat

Existing text-to-image models struggle to follow complex text prompts, raising the need for extra grounding inputs for better controllability. In this work, we propose to decompose a scene into visual primitives - denoted as dense blob representations - that contain fine-grained details of the scene while being modular, human-interpretable, and easy-to-construct. Based on blob representations, we develop a blob-grounded text-to-image diffusion model, termed BlobGEN, for compositional generation. Particularly, we introduce a new masked cross-attention module to disentangle the fusion between blob representations and visual features. To leverage the compositionality of large language models (LLMs), we introduce a new in-context learning approach to generate blob representations from text prompts. Our extensive experiments show that BlobGEN achieves superior zero-shot generation quality and better layout-guided controllability on MS-COCO. When augmented by LLMs, our method exhibits superior numerical and spatial correctness on compositional image generation benchmarks.

Social Aspects · Fairness, Equity, Justice and Safety

Shomik Jain, Kathleen A. Creel, Ashia Wilson

Contrary to traditional deterministic notions of algorithmic fairness, this paper argues that fairly allocating scarce resources using machine learning often requires randomness. We address why, when, and how to randomize by offering a set of stochastic procedures that more adequately account for all of the claims individuals have to allocations of social goods or opportunities and effectively balances their interests.

Hoang Phan, Andrew Wilson, Qi Lei

Models trained on data composed of different groups or domains can suffer from severe performance degradation under distribution shifts. While recent methods have largely focused on optimizing the worst-group objective, this often comes at the expense of good performance on other groups. To address this problem, we introduce an optimization scheme to achieve good performance across groups and find a good solution for all without severely sacrificing performance on any of them. However, directly applying such optimization involves updating the parameters of the entire network, making it both computationally expensive and challenging. Thus, we introduce Controllable Prompt Tuning (CPT), which couples our approach with prompt-tuning techniques. On spurious correlation benchmarks, our procedures achieve state-of-the-art results across both transformer and non-transformer architectures, as well as unimodal and multimodal data, while requiring only $0.4\%$ tunable parameters.

Applications · Health

Xiangjian Jiang, Andrei Margeloiu, Nikola Simidjievski, Mateja Jamnik

Tabular biomedical data poses challenges in machine learning because it is often high-dimensional and typically low-sample-size (HDLSS). Previous research has attempted to address these challenges via local feature selection, but existing approaches often fail to achieve optimal performance due to their limitation in identifying globally important features and their susceptibility to the co-adaptation problem. In this paper, we propose ProtoGate, a prototype-based neural model for feature selection on HDLSS data. ProtoGate first selects instance-wise features via adaptively balancing global and local feature selection. Furthermore, ProtoGate employs a non-parametric prototype-based prediction mechanism to tackle the co-adaptation problem, ensuring the feature selection results and predictions are consistent with underlying data clusters. We conduct comprehensive experiments to evaluate the performance and interpretability of ProtoGate on synthetic and real-world datasets. The results show that ProtoGate generally outperforms state-of-the-art methods in prediction accuracy by a clear margin while providing high-fidelity feature selection and explainable predictions. Code is available at https://github.com/SilenceX12138/ProtoGate.

Deep Learning · Theory

Libin Zhu, Chaoyue Liu, Adityanarayanan Radhakrishnan, Misha Belkin

In this paper, we first present an explanation regarding the common occurrence of spikes in the training loss when neural networks are trained with stochastic gradient descent (SGD). We provide evidence that the spikes in the training loss of SGD are "catapults", an optimization phenomenon originally observed in GD with large learning rates in Lewkowycz et al. (2020). We empirically show that these catapults occur in a low-dimensional subspace spanned by the top eigenvectors of the tangent kernel, for both GD and SGD. Second, we posit an explanation for how catapults lead to better generalization by demonstrating that catapults increase feature learning by increasing alignment with the Average Gradient Outer Product (AGOP) of the true predictor. Furthermore, we demonstrate that a smaller batch size in SGD induces a larger number of catapults, thereby improving AGOP alignment and test performance.

Deep Learning · Attention Mechanisms

Hongkang Li, Meng Wang, Songtao Lu, Xiaodong Cui, Pin-Yu Chen

Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that task. Despite the empirical success, the mechanics of how to train a Transformer to achieve ICL and the corresponding ICL capacity is mostly elusive due to the technical challenges of analyzing the nonconvex training problems resulting from the nonlinear self-attention and nonlinear activation in Transformers. To the best of our knowledge, this paper provides the first theoretical analysis of the training dynamics of Transformers with nonlinear self-attention and nonlinear MLP, together with the ICL generalization capability of the resulting model. Focusing on a group of binary classification tasks, we train Transformers using data from a subset of these tasks and quantify the impact of various factors on the ICL generalization performance on the remaining unseen tasks with and without data distribution shifts. We also analyze how different components in the learned Transformers contribute to the ICL performance. Furthermore, we provide the first theoretical analysis of how model pruning affects ICL performance and prove that proper magnitude-based pruning can have a minimal impact on ICL while reducing inference costs. These theoretical findings are justified through numerical experiments.

Deep Learning · Graph Neural Networks

Hongkang Li, Meng Wang, Tengfei Ma, Sijia Liu, Zaixi Zhang, Pin-Yu Chen

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions across layers and the recursive graph structure have made it challenging to establish a theoretical foundation for learning and generalization. This study introduces the first theoretical investigation of a shallow Graph Transformer for semi-supervised node classification, comprising a self-attention layer with relative positional encoding and a two-layer perception. Focusing on a graph data model with discriminative nodes that determine node labels and non-discriminative nodes that are class-irrelevant, we characterize the sample complexity required to achieve a desirable generalization error by training with stochastic gradient descent (SGD). This paper provides the quantitative characterization of the sample complexity and number of iterations for convergence dependent on the fraction of discriminative nodes, the dominant patterns, and the initial model errors. Furthermore, we demonstrate that self-attention and positional encoding enhance generalization by making the attention map sparse and promoting the core neighborhood during training, which explains the superior feature representation of Graph Transformers. Our theoretical results are supported by empirical experiments on synthetic and real-world benchmarks.

Deep Learning

Bonan Zhang, Chia-Yu Chen, Naveen Verma

In-memory computing (IMC) has emerged as a promising solution to address both computation and data-movement challenges, by performing computation on data in-place directly in the memory array. IMC typically relies on analog operation, which makes analog-to-digital converters (ADCs) necessary, for converting results back to the digital domain. However, ADCs maintain computational efficiency by having limited precision, leading to substantial quantization errors in compute outputs. This work proposes RAOQ (Reshape and Adapt for Output Quantization) to overcome this issue, which comprises two classes of mechanisms including: 1) mitigating ADC quantization error by adjusting the statistics of activations and weights, through an activation-shifting approach (A-shift) and a weight reshaping technique (W-reshape); 2) adapting AI models to better tolerate ADC quantization through a bit augmentation method (BitAug), complemented by the introduction of ADC-LoRA, a low-rank approximation technique, to reduce the training overhead. RAOQ demonstrates consistently high performance across different scales and domains of neural network models for computer vision and natural language processing (NLP) tasks at various bit precisions, achieving state-of-the-art results with practical IMC implementations.