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The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such group actions are translations or $90^\circ$ rotations on images. We describe such equivariant or invariant subvarieties as direct products of determinantal varieties, from which we deduce their dimension, degree, Euclidean distance degree, and their singularities. We fully characterize invariance for arbitrary permutation groups, and equivariance for cyclic groups. We draw conclusions for the parameterization and the design of equivariant and invariant linear networks in terms of sparsity and weight-sharing properties. We prove that all invariant linear functions can be parameterized by a single linear autoencoder with a weight-sharing property imposed by the cycle decomposition of the considered permutation. The space of rank-bounded equivariant functions has several irreducible components, so it can {\em not} be parameterized by a single network -- but each irreducible component can. Finally, we show that minimizing the squared-error loss on our invariant or equivariant networks reduces to minimizing the Euclidean distance from determinantal varieties via the Eckart--Young theorem.

Deep learning models are trained with certain assumptions about the data during the development stage and then used for prediction in the deployment stage. It is important to reason about the trustworthiness of the model's predictions with unseen data during deployment. Existing methods for specifying and verifying traditional software are insufficient for this task, as they cannot handle the complexity of DNN model architecture and expected outcomes. In this work, we propose a novel technique that uses rules derived from neural network computations to infer data preconditions for a DNN model to determine the trustworthiness of its predictions. Our approach, DeepInfer involves introducing a novel abstraction for a trained DNN model that enables weakest precondition reasoning using Dijkstra's Predicate Transformer Semantics. By deriving rules over the inductive type of neural network abstract representation, we can overcome the matrix dimensionality issues that arise from the backward non-linear computation from the output layer to the input layer. We utilize the weakest precondition computation using rules of each kind of activation function to compute layer-wise precondition from the given postcondition on the final output of a deep neural network. We extensively evaluated DeepInfer on 29 real-world DNN models using four different datasets collected from five different sources and demonstrated the utility, effectiveness, and performance improvement over closely related work. DeepInfer efficiently detects correct and incorrect predictions of high-accuracy models with high recall (0.98) and high F-1 score (0.84) and has significantly improved over prior technique, SelfChecker. The average runtime overhead of DeepInfer is low, 0.22 sec for all unseen datasets. We also compared runtime overhead using the same hardware settings and found that DeepInfer is 3.27 times faster than SelfChecker.

We present Flow-Guided Density Ratio Learning (FDRL), a simple and scalable approach to generative modeling which builds on the stale (time-independent) approximation of the gradient flow of entropy-regularized f-divergences introduced in DGflow. In DGflow, the intractable time-dependent density ratio is approximated by a stale estimator given by a GAN discriminator. This is sufficient in the case of sample refinement, where the source and target distributions of the flow are close to each other. However, this assumption is invalid for generation and a naive application of the stale estimator fails due to the large chasm between the two distributions. FDRL proposes to train a density ratio estimator such that it learns from progressively improving samples during the training process. We show that this simple method alleviates the density chasm problem, allowing FDRL to generate images of dimensions as high as $128\times128$, as well as outperform existing gradient flow baselines on quantitative benchmarks. We also show the flexibility of FDRL with two use cases. First, unconditional FDRL can be easily composed with external classifiers to perform class-conditional generation. Second, FDRL can be directly applied to unpaired image-to-image translation with no modifications needed to the framework. Code is publicly available at //github.com/ajrheng/FDRL.

Driven by the appealing properties of neural fields for storing and communicating 3D data, the problem of directly processing them to address tasks such as classification and part segmentation has emerged and has been investigated in recent works. Early approaches employ neural fields parameterized by shared networks trained on the whole dataset, achieving good task performance but sacrificing reconstruction quality. To improve the latter, later methods focus on individual neural fields parameterized as large Multi-Layer Perceptrons (MLPs), which are, however, challenging to process due to the high dimensionality of the weight space, intrinsic weight space symmetries, and sensitivity to random initialization. Hence, results turn out significantly inferior to those achieved by processing explicit representations, e.g., point clouds or meshes. In the meantime, hybrid representations, in particular based on tri-planes, have emerged as a more effective and efficient alternative to realize neural fields, but their direct processing has not been investigated yet. In this paper, we show that the tri-plane discrete data structure encodes rich information, which can be effectively processed by standard deep-learning machinery. We define an extensive benchmark covering a diverse set of fields such as occupancy, signed/unsigned distance, and, for the first time, radiance fields. While processing a field with the same reconstruction quality, we achieve task performance far superior to frameworks that process large MLPs and, for the first time, almost on par with architectures handling explicit representations.

Recent empirical and theoretical studies have established the generalization capabilities of large machine learning models that are trained to (approximately or exactly) fit noisy data. In this work, we prove a surprising result that even if the ground truth itself is robust to adversarial examples, and the benignly overfitted model is benign in terms of the ``standard'' out-of-sample risk objective, this benign overfitting process can be harmful when out-of-sample data are subject to adversarial manipulation. More specifically, our main results contain two parts: (i) the min-norm estimator in overparameterized linear model always leads to adversarial vulnerability in the ``benign overfitting'' setting; (ii) we verify an asymptotic trade-off result between the standard risk and the ``adversarial'' risk of every ridge regression estimator, implying that under suitable conditions these two items cannot both be small at the same time by any single choice of the ridge regularization parameter. Furthermore, under the lazy training regime, we demonstrate parallel results on two-layer neural tangent kernel (NTK) model, which align with empirical observations in deep neural networks. Our finding provides theoretical insights into the puzzling phenomenon observed in practice, where the true target function (e.g., human) is robust against adverasrial attack, while beginly overfitted neural networks lead to models that are not robust.

In causal inference with panel data under staggered adoption, the goal is to estimate and derive confidence intervals for potential outcomes and treatment effects. We propose a computationally efficient procedure, involving only simple matrix algebra and singular value decomposition. We derive non-asymptotic bounds on the entrywise error, establishing its proximity to a suitably scaled Gaussian variable. Despite its simplicity, our procedure turns out to be instance-optimal, in that our theoretical scaling matches a local instance-wise lower bound derived via a Bayesian Cram\'{e}r-Rao argument. Using our insights, we develop a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage guarantees. Our analysis is based on a general inferential toolbox for the SVD algorithm applied to the matrix denoising model, which might be of independent interest.

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This limitation poses a substantial obstacle when dealing with long documents or high-resolution images. In this work, we study the self-attention mechanism by analyzing the distribution of the attention matrix and its concentration ability. Furthermore, we propose instruments to measure these quantities and introduce a novel self-attention mechanism, Linear Log-Normal Attention, designed to emulate the distribution and concentration behavior of the original self-attention. Our experimental results on popular natural language benchmarks reveal that our proposed Linear Log-Normal Attention outperforms other linearized attention alternatives, offering a promising avenue for enhancing the scalability of transformer models. Our code is available in supplementary materials.

Agent-based modeling and simulation has evolved as a powerful tool for modeling complex systems, offering insights into emergent behaviors and interactions among diverse agents. Integrating large language models into agent-based modeling and simulation presents a promising avenue for enhancing simulation capabilities. This paper surveys the landscape of utilizing large language models in agent-based modeling and simulation, examining their challenges and promising future directions. In this survey, since this is an interdisciplinary field, we first introduce the background of agent-based modeling and simulation and large language model-empowered agents. We then discuss the motivation for applying large language models to agent-based simulation and systematically analyze the challenges in environment perception, human alignment, action generation, and evaluation. Most importantly, we provide a comprehensive overview of the recent works of large language model-empowered agent-based modeling and simulation in multiple scenarios, which can be divided into four domains: cyber, physical, social, and hybrid, covering simulation of both real-world and virtual environments. Finally, since this area is new and quickly evolving, we discuss the open problems and promising future directions.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.