We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to approximate directly a conditional distribution that encodes the null hypothesis, in a manner that maximizes power (the rate of true negatives). We show that such an approach requires only that density approximation be viable in order to ensure that we control type I error (the rate of false positives); in particular, no assumptions need to be made on the form of the distributions or feature dependencies. Using synthetic simulations with high-dimensional data we demonstrate significant gains in power over competing methods. In addition, we illustrate the use of our test to discover causal markers of disease in genetic data.

With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation.

Today's best language models still struggle with hallucinations: factually incorrect generations, which impede their ability to reliably retrieve information seen during training. The reversal curse, where models cannot recall information when probed in a different order than was encountered during training, exemplifies this in information retrieval. We reframe the reversal curse as a factorization curse -- a failure of models to learn the same joint distribution under different factorizations. Through a series of controlled experiments with increasing levels of realism including WikiReversal, a setting we introduce to closely simulate a knowledge intensive finetuning task, we find that the factorization curse is an inherent failure of the next-token prediction objective used in popular large language models. Moreover, we demonstrate reliable information retrieval cannot be solved with scale, reversed tokens, or even naive bidirectional-attention training. Consequently, various approaches to finetuning on specialized data would necessarily provide mixed results on downstream tasks, unless the model has already seen the right sequence of tokens. Across five tasks of varying levels of complexity, our results uncover a promising path forward: factorization-agnostic objectives can significantly mitigate the reversal curse and hint at improved knowledge storage and planning capabilities.

We propose to learn deep undirected graphical models (i.e., MRFs) with a non-ELBO objective for which we can calculate exact gradients.

We thank the reviewers for their insightful feedback; we address each review below. R1: "...it is known how to solve the BFE optimisation problem by double loop algorithms" Our understanding is "...what is meant by'they are run once..."' A Transformer or RNN is run over a sequence of embeddings corresponding "...meaningless for pairwise marginals..." Agreed. We included the pairwise marginals just for completeness. "Ising model...expect that the estimation quality will degrade with the (average) interaction strength." When sampling from N (0, 5) we obtain 0.358, 0.525, 0.619 for these 3 "The experiments have in my view a preliminary character" We agree our experiments are on small datasets.

Compiler backends are tasked with generating executable machine code for processors. With the proliferation of diverse processors, it is imperative for programmers to tailor specific compiler backends to accommodate each one. Meanwhile, compiler backend development is a laborious and time-consuming task, lacking effective automation methods. Although language models have demonstrated strong abilities in code related tasks, the lack of appropriate datasets for compiler backend development limits the application of language models in this field. In this paper, we introduce ComBack, the first public dataset designed for improving compiler backend development capabilities of language models. Com-Back includes 178 backends for mainstream compilers and three tasks including statement-level completion, next-statement suggestion and code generation, representing common development scenarios. We conducted experiments by fine-tuning six pre-trained language models with ComBack, demonstrating its effectiveness in enhancing model accuracy across the three tasks. We further evaluated the top-performing model (CodeT5+) across the three tasks for new targets, comparing its accuracy with conventional methods (Fork-Flow), ChatGPT-3.5-Turbo,

Recently, Gaussian Splatting, a method that represents a 3D scene as a collection of Gaussian distributions, has gained significant attention in addressing the task of novel view synthesis. In this paper, we highlight a fundamental limitation of Gaussian Splatting: its inability to accurately render discontinuities and boundaries in images due to the continuous nature of Gaussian distributions. To address this issue, we propose a novel framework enabling Gaussian Splatting to perform discontinuity-aware image rendering. Additionally, we introduce a Bézier-boundary gradient approximation strategy within our framework to keep the "differentiability" of the proposed discontinuity-aware rendering process. Extensive experiments demonstrate the efficacy of our framework.

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally. We show that the empirical estimate of the test power criterion converges with increasing sample size, ensuring the quality of the returned features. In real-world benchmarks on highdimensional text and image data, linear-time tests using the proposed semimetrics achieve comparable performance to the state-of-the-art quadratic-time maximum mean discrepancy test, while returning human-interpretable features that explain the test results.

We study finite sample expressivity, i.e., memorization power of ReLU networks. Recent results require N hidden nodes to memorize/interpolate arbitrary N data points. In contrast, by exploiting depth, we show that 3-layer ReLU networks with Ω( N) hidden nodes can perfectly memorize most datasets with N points. We also prove that width Θ( N) is necessary and sufficient for memorizing N data points, proving tight bounds on memorization capacity. The sufficiency result can be extended to deeper networks; we show that an L-layer network with W parameters in the hidden layers can memorize N data points if W = Ω(N). Combined with a recent upper bound O(W L log W) on VC dimension, our construction is nearly tight for any fixed L. Subsequently, we analyze memorization capacity of residual networks under a general position assumption; we prove results that substantially reduce the known requirement of N hidden nodes. Finally, we study the dynamics of stochastic gradient descent (SGD), and show that when initialized near a memorizing global minimum of the empirical risk, SGD quickly finds a nearby point with much smaller empirical risk.

How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its "width"-- namely, number of channels in convolutional layers, and number of nodes in fully-connected internal layers -- is allowed to increase to infinity? Such questions have come to the forefront in the quest to theoretically understand deep learning and its mysteries about optimization and generalization. They also connect deep learning to notions such as Gaussian processes and kernels. A recent paper [Jacot et al., 2018] introduced the Neural Tangent Kernel (NTK) which captures the behavior of fully-connected deep nets in the infinite width limit trained by gradient descent; this object was implicit in some other recent papers. An attraction of such ideas is that a pure kernel-based method is used to capture the power of a fully-trained deep net of infinite width. The current paper gives the first efficient exact algorithm for computing the extension of NTK to convolutional neural nets, which we call Convolutional NTK (CNTK), as well as an efficient GPU implementation of this algorithm. This results in a significant new benchmark for performance of a pure kernel-based method on CIFAR-10, being 10% higher than the methods reported in [Novak et al., 2019], and only 6% lower than the performance of the corresponding finite deep net architecture (once batch normalization etc. are turned off). Theoretically, we also give the first non-asymptotic proof showing that a fully-trained sufficiently wide net is indeed equivalent to the kernel regression predictor using NTK.