While diffusion models have achieved promising performances in data synthesis, they might suffer error propagation because of their cascade structure, where the distributional mismatch spreads and magnifies through the chain of denoising modules. However, a strict analysis is expected since many sequential models such as Conditional Random Field (CRF) are free from error propagation. In this paper, we empirically and theoretically verify that diffusion models are indeed affected by error propagation and we then propose a regularization to address this problem. Our theoretical analysis reveals that the question can be reduced to whether every denoising module of the diffusion model is fault-tolerant. We derive insightful transition equations, indicating that the module can't recover from input errors and even propagates additional errors to the next module. Our analysis directly leads to a consistency regularization scheme for diffusion models, which explicitly reduces the distribution gap between forward and backward processes. We further introduce a bootstrapping algorithm to reduce the computation cost of the regularizer. Our experimental results on multiple image datasets show that our regularization effectively handles error propagation and significantly improves the performance of vanilla diffusion models.
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Control barrier functions (CBFs) provide a simple yet effective way for safe control synthesis. Recently, work has been done using differentiable optimization based methods to systematically construct CBFs for static obstacle avoidance tasks between geometric shapes. In this work, we extend the application of differentiable optimization based CBFs to perform dynamic obstacle avoidance tasks. We show that by using the time-varying CBF (TVCBF) formulation, we can perform obstacle avoidance for dynamic geometric obstacles. Additionally, we show how to alter the TVCBF constraint to consider measurement noise and actuation limits. To demonstrate the efficacy of our proposed approach, we first compare its performance with a model predictive control based method on a simulated dynamic obstacle avoidance task with non-ellipsoidal obstacles. Then, we demonstrate the performance of our proposed approach in experimental studies using a 7-degree-of-freedom Franka Research 3 robotic manipulator.
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a complexity comparable to linear vector autoregressive (VAR) models while still incorporating nonlinear interactions among different time-series variables. The modeling assumption is that the set of time series is generated in two steps: first, a linear VAR process in a latent space, and second, a set of invertible and Lipschitz continuous nonlinear mappings that are applied per sensor, that is, a component-wise mapping from each latent variable to a variable in the measurement space. The VAR coefficient identification provides a topology representation of the dependencies among the aforementioned variables. The proposed approach models each component-wise nonlinearity using an invertible neural network and imposes sparsity on the VAR coefficients to reflect the parsimonious dependencies usually found in real applications. To efficiently solve the formulated optimization problems, a custom algorithm is devised combining proximal gradient descent, stochastic primal-dual updates, and projection to enforce the corresponding constraints. Experimental results on both synthetic and real data sets show that the proposed algorithm improves the identification of the support of the VAR coefficients in a parsimonious manner while also improving the time-series prediction, as compared to the current state-of-the-art methods.
Random feature model with a nonlinear activation function has been shown to perform asymptotically equivalent to a Gaussian model in terms of training and generalization errors. Analysis of the equivalent model reveals an important yet not fully understood role played by the activation function. To address this issue, we study the "parameters" of the equivalent model to achieve improved generalization performance for a given supervised learning problem. We show that acquired parameters from the Gaussian model enable us to define a set of optimal nonlinearities. We provide two example classes from this set, e.g., second-order polynomial and piecewise linear functions. These functions are optimized to improve generalization performance regardless of the actual form. We experiment with regression and classification problems, including synthetic and real (e.g., CIFAR10) data. Our numerical results validate that the optimized nonlinearities achieve better generalization performance than widely-used nonlinear functions such as ReLU. Furthermore, we illustrate that the proposed nonlinearities also mitigate the so-called double descent phenomenon, which is known as the non-monotonic generalization performance regarding the sample size and the model size.
Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two frameworks: the sample size is deterministic, and the test statistics corresponding to different tests are independent. However, in many modern scientific avenues, these assumptions are often violated. There is little study that explores the multiple testing problem in a sequential framework where the test statistics corresponding to the various streams are dependent. This work fills this gap in a unified way by considering the classical means-testing problem in an equicorrelated Gaussian and sequential framework. We focus on sequential test procedures that control the type I and type II familywise error probabilities at pre-specified levels. We establish that our proposed test procedures achieve the optimal expected sample sizes under every possible signal configuration asymptotically, as the two error probabilities vanish at arbitrary rates. Towards this, we elucidate that the ratio of the expected sample size of our proposed rule and that of the classical SPRT goes to one asymptotically, thus illustrating their connection. Generalizing this, we show that our proposed procedures, with appropriately adjusted critical values, are asymptotically optimal for controlling any multiple testing error metric lying between multiples of FWER in a certain sense. This class of metrics includes FDR/FNR, pFDR/pFNR, the per-comparison and per-family error rates, and the false positive rate.
Testing with randomly generated inputs (fuzzing) has gained significant traction due to its capacity to expose program vulnerabilities automatically. Fuzz testing campaigns generate large amounts of data, making them ideal for the application of machine learning (ML). Neural program smoothing (NPS), a specific family of ML-guided fuzzers, aims to use a neural network as a smooth approximation of the program target for new test case generation. In this paper, we conduct the most extensive evaluation of NPS fuzzers against standard gray-box fuzzers (>11 CPU years and >5.5 GPU years), and make the following contributions: (1) We find that the original performance claims for NPS fuzzers do not hold; a gap we relate to fundamental, implementation, and experimental limitations of prior works. (2) We contribute the first in-depth analysis of the contribution of machine learning and gradient-based mutations in NPS. (3) We implement Neuzz++, which shows that addressing the practical limitations of NPS fuzzers improves performance, but that standard gray-box fuzzers almost always surpass NPS-based fuzzers. (4) As a consequence, we propose new guidelines targeted at benchmarking fuzzing based on machine learning, and present MLFuzz, a platform with GPU access for easy and reproducible evaluation of ML-based fuzzers. Neuzz++, MLFuzz, and all our data are public.
The generation of adversarial inputs has become a crucial issue in establishing the robustness and trustworthiness of deep neural nets, especially when they are used in safety-critical application domains such as autonomous vehicles and precision medicine. However, the problem poses multiple practical challenges, including scalability issues owing to large-sized networks, and the generation of adversarial inputs that lack important qualities such as naturalness and output-impartiality. This problem shares its end goal with the task of patching neural nets where small changes in some of the network's weights need to be discovered so that upon applying these changes, the modified net produces the desirable output for a given set of inputs. We exploit this connection by proposing to obtain an adversarial input from a patch, with the underlying observation that the effect of changing the weights can also be brought about by changing the inputs instead. Thus, this paper presents a novel way to generate input perturbations that are adversarial for a given network by using an efficient network patching technique. We note that the proposed method is significantly more effective than the prior state-of-the-art techniques.
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms. In this paper, we propose a novel neural-ODE based method that uses spectral expansions in space to learn spatiotemporal DEs. The major advantage of our spectral neural DE learning approach is that it does not rely on spatial discretization, thus allowing the target spatiotemporal equations to contain long range, nonlocal spatial interactions that act on unbounded spatial domains. Our spectral approach is shown to be as accurate as some of the latest machine learning approaches for learning PDEs operating on bounded domains. By developing a spectral framework for learning both PDEs and integro-differential equations, we extend machine learning methods to apply to unbounded DEs and a larger class of problems.
The individualized treatment rule (ITR), which recommends an optimal treatment based on individual characteristics, has drawn considerable interest from many areas such as precision medicine, personalized education, and personalized marketing. Existing ITR estimation methods mainly adopt one of two or more treatments. However, a combination of multiple treatments could be more powerful in various areas. In this paper, we propose a novel Double Encoder Model (DEM) to estimate the individualized treatment rule for combination treatments. The proposed double encoder model is a nonparametric model which not only flexibly incorporates complex treatment effects and interaction effects among treatments, but also improves estimation efficiency via the parameter-sharing feature. In addition, we tailor the estimated ITR to budget constraints through a multi-choice knapsack formulation, which enhances our proposed method under restricted-resource scenarios. In theory, we provide the value reduction bound with or without budget constraints, and an improved convergence rate with respect to the number of treatments under the DEM. Our simulation studies show that the proposed method outperforms the existing ITR estimation in various settings. We also demonstrate the superior performance of the proposed method in PDX data that recommends optimal combination treatments to shrink the tumor size of the colorectal cancer.
Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
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