Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In this paper we characterize the geometric structure of flows using principal manifolds and understand the relationship between latent variables and samples using contours. We introduce a novel class of normalizing flows, called principal component flows (PCF), whose contours are its principal manifolds, and a variant for injective flows (iPCF) that is more efficient to train than regular injective flows. PCFs can be constructed using any flow architecture, are trained with a regularized maximum likelihood objective and can perform density estimation on all of their principal manifolds. In our experiments we show that PCFs and iPCFs are able to learn the principal manifolds over a variation of datasets. Additionally, we show that PCFs can perform density estimation on data that lie on a manifold with variable dimensionality, which is not possible with existing normalizing flows.
ML algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, recently researchers have demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause mis-classification). Existence of adversarial examples has hindered deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is "pulled back" into the data manifold before classifying. These defenses rely on the manifold assumption (data lie in a manifold of lower dimension than the input space). These defenses use a generative model to approximate the input distribution. This paper asks the following question- do the generative models used in manifold-based defenses need to be topology-aware? Our paper suggests the answer is yes. We provide theoretical and empirical evidence to support our claim.
In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed.
The functions of an autonomous system can generally be partitioned into those concerned with perception and those concerned with action. Perception builds and maintains an internal model of the world (i.e., the system’s environment) that is used to plan and execute actions to accomplish a goal established by human supervisors. Accordingly, assurance decomposes into two parts- a) ensuring that the model is an accurate representation of the world as it changes through time and b) ensuring that the actions are safe (and effective), given the model. Both perception and action may employ AI, including machine learning (ML), and these present challenges to assurance. However, it is usually feasible to guard the actions with traditionally engineered and assured monitors, and thereby ensure safety, given the model. Thus, the model becomes the central focus for assurance. We propose an architecture and methods to ensure the accuracy of models derived from sensors whose interpretation uses AI and ML. Rather than derive the model from sensors bottom-up, we reverse the process and use the model to predict sensor interpretation. Small prediction errors indicate the world is evolving as expected and the model is updated accordingly. Large prediction errors indicate surprise, which may be due to errors in sensing or interpretation, or unexpected changes in the world (e.g., a pedestrian steps into the road). The former initiate error masking or recovery, while the latter requires revision to the model. Higher-level AI functions assist in diagnosis and execution of these tasks. Although this two-level architecture where the lower level does “predictive processing” and the upper performs more reflective tasks, both focused on maintenance of a world model, is derived by engineering considerations, it also matches a widely accepted theory of human cognition.
ML algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, recently researchers have demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause mis-classification). Existence of adversarial examples has hindered deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is "pulled back" into the data manifold before classifying. These defenses rely on the manifold assumption (data lie in a manifold of lower dimension than the input space). These defenses use a generative model to approximate the input distribution. This paper asks the following question- do the generative models used in manifold-based defenses need to be topology-aware? Our paper suggests the answer is yes. We provide theoretical and empirical evidence to support our claim.
Deep neural networks (DNNs) are known to produce incorrect predictions with very high confidence on out-of-distribution inputs (OODs). This limitation is one of the key challenges in the adoption of DNNs in high-assurance systems such as autonomous driving, air traffic management, and medical diagnosis. This challenge has received significant attention recently, and several techniques have been developed to detect inputs where the model's prediction cannot be trusted. These techniques detect OODs as datapoints with either high epistemic uncertainty or high aleatoric uncertainty. We demonstrate the difference in the detection ability of these techniques and propose an ensemble approach for detection of OODs as datapoints with high uncertainty (epistemic or aleatoric). We perform experiments on vision datasets with multiple DNN architectures, achieving state-of-the-art results in most cases.
We present Sherlock a tool for verification of deep neural networks along with some recent applications of the tool to verification and control problems for autonomous systems. Deep Neural Networks have emerged as an ubiquitous choice of concept representation in machine learning, and are commonly used as function approximators in many learning tasks. Learning methods using deep neural networks are often referred to as deep learning, and they have reached human-level accuracy on benchmark data-sets for several tasks such as image classification and speech recognition. This has inspired the adoption and integration of deep learning methods into safety-critical systems. For example, deep learning is often used in perception and several decision-making modules in automated vehicles. This has created a challenge in verifying and certifying these systems using traditional approaches developed for software and hardware verification. Further, these models are known to be brittle and prone to adversarial examples. Establishing robustness of these models is, thus, an important challenge. For safe integration of learning into critical systems, we must be able to encapsulate these models into assumption-guarantee contracts by verifying guarantees on the outputs of the model given the assumptions on its inputs. We discuss some of our recent work on this topic of verifying deep neural networks that is currently available as an open-source tool, Sherlock.
We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs- a set of observed traces and a template STL formula. The unknown parameters in the template can include time-bounds of the temporal operators, as well as the thresholds in the inequality predicates. TeLEx finds the value of the unknown parameters such that the synthesized STL property is satisfied by all the provided traces and it is tight. This requirement of tightness is essential to generating interesting properties when only positive examples are provided and there is no option to actively query the dynamical system to discover the boundaries of legal behavior. We propose a novel quantitative semantics for satisfaction of STL properties which enables TeLEx to learn tight STL properties without multidimensional optimization. The proposed new metric is also smooth. This is critical to enable the use of gradient-based numerical optimization engines and it produces a 30x to 100x speed-up with respect to the state-of-art gradient-free optimization. Second, we present a novel technique for automatically learning the structure of the STL formula by incrementally constructing more complex formula guided by the robustness metric of subformula. We demonstrate the effectiveness of the overall approach for learning STL formulas from only positive examples on a set of synthetic and real-world benchmarks.
This paper investigates data-efficient methods for learning robust control policies. Reinforcement learning has emerged as an effective approach to learn control policies by interacting directly with the plant, but it requires a significant number of example trajectories to converge to the optimal policy. Combining model-free reinforcement learning with model-based control methods achieves better data-efficiency via simultaneous system identification and controller synthesis. We study a novel approach that exploits the existence of approximate physics models to accelerate the learning of control policies. The proposed approach consists of iterating through three key steps- evaluating a selected policy on the real-world plant and recording trajectories, building a Gaussian process model to predict the reality-gap of a parametric physics model in the neighborhood of the selected policy, and synthesizing a new policy using reinforcement learning on the refined physics model that most likely approximates the real plant. The approach converges to an optimal policy as well as an approximate physics model. The real world experiments are limited to evaluating only promising candidate policies, and the use of Gaussian processes minimizes the number of required real world trajectories. We demonstrate the effectiveness of our techniques on a set of simulation case-studies using OpenAI gym environments.
Models produced by machine learning, particularly deep neural networks, are state-of-the-art for many machine learning tasks and demonstrate very high prediction accuracy. Unfortunately, these models are also very brittle and vulnerable to specially crafted adversarial examples. Recent results have shown that accuracy of these models can be reduced from close to hundred percent to below 5% using adversarial examples. This brittleness of deep neural networks makes it challenging to deploy these learning models in security-critical areas where adversarial activity is expected, and cannot be ignored. A number of methods have been recently proposed to craft more effective and generalizable attacks on neural networks along with competing efforts to improve robustness of these learning models. But the current approaches to make machine learning techniques more resilient fall short of their goal. Further, the succession of new adversarial attacks against proposed methods to increase neural network robustness raises doubts about a foolproof approach to robustify machine learning models against all possible adversarial attacks. In this paper, we consider the problem of detecting adversarial examples. This would help identify when the learning models cannot be trusted without attempting to repair the models or make them robust to adversarial attacks. This goal of finding limitations of the learning model presents a more tractable approach to protecting against adversarial attacks. Our approach is based on identifying a low dimensional manifold in which the training samples lie, and then using the distance of a new observation from this manifold to identify whether this data point is adversarial or not. Our empirical study demonstrates that adversarial examples not only lie farther away from the data manifold, but this distance from manifold of the adversarial examples increases with the attack confidence.