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Satellite image time series (SITS) segmentation is crucial for many applications, like environmental monitoring, land cover mapping, and agricultural crop type classification. However, training models for SITS segmentation remains a challenging task due to the lack of abundant training data, which requires fine-grained annotation. We propose S4, a new self-supervised pretraining approach that significantly reduces the requirement for labeled training data by utilizing two key insights of satellite imagery: (a) Satellites capture images in different parts of the spectrum, such as radio frequencies and visible frequencies. (b) Satellite imagery is geo-registered, allowing for fine-grained spatial alignment. We use these insights to formulate pretraining tasks in S4. To the best of our knowledge, S4 is the first multimodal and temporal approach for SITS segmentation. S4’s novelty stems from leveraging multiple properties required for SITS self-supervision: (1) multiple modalities, (2) temporal information, and (3) pixel-level feature extraction. We also curate m2s2-SITS, a large-scale dataset of unlabeled, spatially aligned, multimodal, and geographic-specific SITS that serves as representative pretraining data for S4. Finally, we evaluate S4 on multiple SITS segmentation datasets and demonstrate its efficacy against competing baselines while using limited labeled data. Through a series of extensive comparisons and ablation studies, we demonstrate S4’s ability as an effective feature extractor for downstream semantic segmentation. 

Geometric image transformations that arise in the real world, such as scaling and rotation, have been shown to easily deceive deep neural networks (DNNs). Hence, training DNNs to be certifiably robust to these perturbations is critical. However, no prior work has been able to incorporate the objective of deterministic certified robustness against geometric transformations into the training procedure, as existing verifiers are exceedingly slow. To address these challenges, we propose the first provable defense for deterministic certified geometric robustness. Our framework leverages a novel GPU-optimized verifier that can certify images between 60× to 42,600× faster than existing geometric robustness verifiers, and thus unlike existing works, is fast enough for use in training. Across multiple datasets, our results show that networks trained via our framework consistently achieve state-of-the-art deterministic certified geometric robustness and clean accuracy. Furthermore, for the first time, we verify the geometric robustness of a neural network for the challenging, real-world setting of autonomous driving. 

We present a novel, general construction to abstractly interpret higher-order automatic differentiation (AD). Our construction allows one to instantiate an abstract interpreter for computing derivatives up to a chosen order. Furthermore, since our construction reduces the problem of abstractly reasoning about derivatives to abstractly reasoning about real-valued straight-line programs, it can be instantiated with almost any numerical abstract domain, both relational and non-relational. We formally establish the soundness of this construction. We implement our technique by instantiating our construction with both the non-relational interval domain and the relational zonotope domain to compute both first and higher-order derivatives. In the latter case, we are the first to apply a relational domain to automatic differentiation for abstracting higher-order derivatives, and hence we are also the first abstract interpretation work to track correlations across not only different variables, but different orders of derivatives. We evaluate these instantiations on multiple case studies, namely robustly explaining a neural network and more precisely computing a neural network’s Lipschitz constant. For robust interpretation, first and second derivatives computed via zonotope AD are up to 4.76× and 6.98× more precise, respectively, compared to interval AD. For Lipschitz certification, we obtain bounds that are up to 11,850× more precise with zonotopes, compared to the state-of-the-art interval-based tool. 

We present a novel abstraction for bounding the Clarke Jacobian of a Lipschitz continuous, but not necessarily differentiable function over a local input region. To do so, we leverage a novel abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed to compute the Clarke Jacobian. We formally prove that our novel forward-mode dual interval evaluation produces a sound, interval domain-based over-approximation of the true Clarke Jacobian for a given input region. Due to the generality of our formalism, we can compute and analyze interval Clarke Jacobians for a broader class of functions than previous works supported – specifically, arbitrary compositions of neural networks with Lipschitz, but non-differentiable perturbations. We implement our technique in a tool called DeepJ and evaluate it on multiple deep neural networks and non-differentiable input perturbations to showcase both the generality and scalability of our analysis. Concretely, we can obtain interval Clarke Jacobians to analyze Lipschitz robustness and local optimization landscapes of both fully-connected and convolutional neural networks for rotational, contrast variation, and haze perturbations, as well as their compositions.