Deep learning training involves a large number of operations, which are dominated by high dimensionality Matrix-Vector Multiplies (MVMs). This has motivated hardware accelerators to enhance compute efficiency, but where data movement and accessing are proving to be key bottlenecks. In-Memory Computing (IMC) is an approach with the potential to overcome this, whereby computations are performed in-place within dense 2-D memory. However, IMC fundamentally trades efficiency and throughput gains for dynamic-range limitations, raising distinct challenges for training, where compute precision requirements are seen to be substantially higher than for inferencing. This paper explores training on IMC hardware by leveraging two recent developments: (1) a training algorithm enabling aggressive quantization through a radix-4 number representation; (2) IMC leveraging compute based on precision capacitors, whereby analog noise effects can be made well below quantization effects. Energy modeling calibrated to a measured silicon prototype implemented in 16 nm CMOS shows that energy savings of over 400x can be achieved with full quantizer adaptability, where all training MVMs can be mapped to IMC, and 3x can be achieved for two-level quantizer adaptability, where two of the three training MVMs can be mapped to IMC.

In this paper, we present an approach for supervised training of a neural network operating on camera images to estimate the receive power of an automotive radar. The training requires the association of pixels from camera images and radar spectra via an image-warping layer. We evaluate the influence of forward and backward image warping, known from classical image processing, on the application of receive power estimation. It is found, that the implementation via backward image warping results in a biased estimation of the receive power whilst the forward image warp results in an unbiased estimation.

We present an approach to automatically generate semantic labels for real recordings of automotive range-Doppler (RD) radar spectra. Such labels are required when training a neural network for object recognition from radar data. The automatic labeling approach rests on the simultaneous recording of camera and lidar data in addition to the radar spectrum. By warping radar spectra into the camera image, state-of-the-art object recognition algorithms can be applied to label relevant objects, such as cars, in the camera image. The warping operation is designed to be fully differentiable, which allows backpropagating the gradient computed on the camera image through the warping operation to the neural network operating on the radar data. As the warping operation relies on accurate scene flow estimation, we further propose a novel scene flow estimation algorithm which exploits information from camera, lidar and radar sensors. The proposed scene flow estimation approach is compared against a state-of-the-art scene flow algorithm, and it outperforms it by approximately 30% w.r.t. mean average error. The feasibility of the overall framework for automatic label generation for RD spectra is verified by evaluating the performance of neural networks trained with the proposed framework for Direction-of-Arrival estimation.

Model-based reinforcement learning agents must make compromises about which aspects of the environment their models should capture. The value equivalence (VE) principle posits that these compromises should be made considering the model's eventual use in value-based planning. Given sets of functions and policies, a model is said to be order-k VE to the environment if k applications of the Bellman operators induced by the policies produce the correct result when applied to the functions. Prior work investigated the classes of models induced by VE when we vary k and the sets of policies and functions. This gives rise to a rich collection of topological relationships and conditions under which VE models are optimal for planning. Despite this effort, relatively little is known about the planning performance of models that fail to satisfy these conditions. This is due to the rigidity of the VE formalism, as classes of VE models are defined with respect to exact constraints on their Bellman operators. This limitation gets amplified by the fact that such constraints themselves may depend on functions that can only be approximated in practice. To address these problems we propose approximate value equivalence (AVE), which extends the VE formalism by replacing equalities with error tolerances. This extension allows us to show that AVE models with respect to one set of functions are also AVE with respect to any other set of functions if we tolerate a high enough error. We can then derive bounds on the performance of VE models with respect to arbitrary sets of functions. Moreover, AVE models more accurately reflect what can be learned by our agents in practice, allowing us to investigate previously unexplored tensions between model capacity and the choice of VE model class. In contrast to previous works, we show empirically that there are situations where agents with limited capacity should prefer to learn more accurate models with respect to smaller sets of functions over less accurate models with respect to larger sets of functions.

One of the main challenges in model-based reinforcement learning (RL) is to decide which aspects of the environment should be modeled. The value-equivalence (VE) principle proposes a simple answer to this question: a model should capture the aspects of the environment that are relevant for value-based planning. Technically, VE distinguishes models based on a set of policies and a set of functions: a model is said to be VE to the environment if the Bellman operators it induces for the policies yield the correct result when applied to the functions. As the number of policies and functions increase, the set of VE models shrinks, eventually collapsing to a single point corresponding to a perfect model. A fundamental question underlying the VE principle is thus how to select the smallest sets of policies and functions that are sufficient for planning. In this paper we take an important step towards answering this question. We start by generalizing the concept of VE to order-$k$ counterparts defined with respect to $k$ applications of the Bellman operator. This leads to a family of VE classes that increase in size as $k \rightarrow \infty$. In the limit, all functions become value functions, and we have a special instantiation of VE which we call proper VE or simply PVE. Unlike VE, the PVE class may contain multiple models even in the limit when all value functions are used. Crucially, all these models are sufficient for planning, meaning that they will yield an optimal policy despite the fact that they may ignore many aspects of the environment. We construct a loss function for learning PVE models and argue that popular algorithms such as MuZero can be understood as minimizing an upper bound for this loss. We leverage this connection to propose a modification to MuZero and show that it can lead to improved performance in practice.

In this paper, a computationally efficient approach called block Kronecker compressed sensing (BKCS) algorithm is proposed to mitigate the mutual interference between two automotive radar systems in a 2-dimensional (2D) compressed sensing framework. Within the 2D framework, the receive signals of radar are jointly considered along both fast time and slow time dimensions, so that the signal sparsity can be better conserved than the one in 1-dimension (1D) case. Compared with the conventional Kronecker compressed sensing, BKCS requires much less resource, i.e. storage and computation power. Its performance has been verified with simulation and real measurement. The numerical assessment has shown that BKCS overcomes the shortcoming in 1D CS methods, and significantly outperforms classical signal reconstruction algorithms such as linear predictive coding as well.

Biological intelligence can learn to solve many diverse tasks in a data efficient manner by re-using basic knowledge and skills from one task to another. Furthermore, many of such skills are acquired without explicit supervision in an intrinsically driven fashion. This is in contrast to the state-of-the-art reinforcement learning agents, which typically start learning each new task from scratch and struggle with knowledge transfer. In this paper we propose a principled way to learn a basis set of policies, which, when recombined through generalised policy improvement, come with guarantees on the coverage of the final task space. In particular, we concentrate on solving goal-based downstream tasks where the execution order of actions is not important. We demonstrate both theoretically and empirically that learning a small number of policies that reach intrinsically specified goal regions in a disentangled latent space can be re-used to quickly achieve a high level of performance on an exponentially larger number of externally specified, often significantly more complex downstream tasks. Our learning pipeline consists of two stages. First, the agent learns to perform intrinsically generated, goal-based tasks in the total absence of environmental rewards. Second, the agent leverages this experience to quickly achieve a high level of performance on numerous diverse externally specified tasks.

Learning models of the environment from data is often viewed as an essential component to building intelligent reinforcement learning (RL) agents. The common practice is to separate the learning of the model from its use, by constructing a model of the environment's dynamics that correctly predicts the observed state transitions. In this paper we argue that the limited representational resources of model-based RL agents are better used to build models that are directly useful for value-based planning. As our main contribution, we introduce the principle of value equivalence: two models are value equivalent with respect to a set of functions and policies if they yield the same Bellman updates. We propose a formulation of the model learning problem based on the value equivalence principle and analyze how the set of feasible solutions is impacted by the choice of policies and functions. Specifically, we show that, as we augment the set of policies and functions considered, the class of value equivalent models shrinks, until eventually collapsing to a single point corresponding to a model that perfectly describes the environment. In many problems, directly modelling state-to-state transitions may be both difficult and unnecessary. By leveraging the value-equivalence principle one may find simpler models without compromising performance, saving computation and memory. We illustrate the benefits of value-equivalent model learning with experiments comparing it against more traditional counterparts like maximum likelihood estimation. More generally, we argue that the principle of value equivalence underlies a number of recent empirical successes in RL, such as Value Iteration Networks, the Predictron, Value Prediction Networks, TreeQN, and MuZero, and provides a first theoretical underpinning of those results.

We present a novel method for learning a set of disentangled reward functions that sum to the original environment reward and are constrained to be independently obtainable. We define independent obtainability in terms of value functions with respect to obtaining one learned reward while pursuing another learned reward. Empirically, we illustrate that our method can learn meaningful reward decompositions in a variety of domains and that these decompositions exhibit some form of generalization performance when the environment's reward is modified. Theoretically, we derive results about the effect of maximizing our method's objective on the resulting reward functions and their corresponding optimal policies.

An agent with an inaccurate model of its environment faces a difficult choice: it can ignore the errors in its model and act in the real world in whatever way it determines is optimal with respect to its model. Alternatively, it can take a more conservative stance and eschew its model in favor of optimizing its behavior solely via real-world interaction. This latter approach can be exceedingly slow to learn from experience, while the former can lead to "planner overfitting" - aspects of the agent's behavior are optimized to exploit errors in its model. This paper explores an intermediate position in which the planner seeks to avoid overfitting through a kind of regularization of the plans it considers. We present three different approaches that demonstrably mitigate planner overfitting in reinforcement-learning environments.

In this paper, we present a neural network based classification algorithm for the discrimination of moving from stationary targets in the sight of an automotive radar sensor. Compared to existing algorithms, the proposed algorithm can take into account multiple local radar targets instead of performing classification inference on each target individually resulting in superior discrimination accuracy, especially suitable for non rigid objects, like pedestrians, which in general have a wide velocity spread when multiple targets are detected.

We examine the problem of learning and planning on high-dimensional domains with long horizons and sparse rewards. Recent approaches have shown great successes in many Atari 2600 domains. However, domains with long horizons and sparse rewards, such as Montezuma's Revenge and Venture, remain challenging for existing methods. Methods using abstraction (Dietterich 2000; Sutton, Precup, and Singh 1999) have shown to be useful in tackling long-horizon problems. We combine recent techniques of deep reinforcement learning with existing model-based approaches using an expert-provided state abstraction. We construct toy domains that elucidate the problem of long horizons, sparse rewards and high-dimensional inputs, and show that our algorithm significantly outperforms previous methods on these domains. Our abstraction-based approach outperforms Deep Q-Networks (Mnih et al. 2015) on Montezuma's Revenge and Venture, and exhibits backtracking behavior that is absent from previous methods.

Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned mechanisms that contribute to such effective behaviors and more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network's inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed "attention masks" support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision and natural language processing. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network's underlying decision-making process irrespective of the data modality.

In this paper, we present a hypothesis test for the classification of moving targets in the sight of an automotive radar sensor. For this purpose, a statistical model of the relative velocity between a stationary target and the radar sensor has been developed. With respect to the statistical properties a confidence interval is calculated and targets with relative velocity lying outside this interval are classified as moving targets. Compared to existing algorithms our approach is able to give robust classification independent of the number of observed moving targets and is characterized by an instantaneous classification, a simple parameterization of the model and an automatic calculation of the discriminating threshold.

In this paper we study the brachistochrone problem in an inverse-square gravitational field on the unit disk.We show that the time optimal solutions consist of either smooth strong solutions to the Euler-Lagrange equation or weak solutions formed by appropriately patched together strong solutions.This combination of weak and strong solutions completely foliates the unit disk.We also consider the problem on annular domains and show that the time optimal paths foliate the annulus.These foliations on the annular domains converge to the foliation on the unit disk in the limit of vanishing inner radius.

We examine the problem of learning mappings from state to state, suitable for use in a model-based reinforcement-learning setting, that simultaneously generalize to novel states and can capture stochastic transitions. We show that currently popular generative adversarial networks struggle to learn these stochastic transition models but a modification to their loss functions results in a powerful learning algorithm for this class of problems.

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilistic source. This paper looks particularly at this matching capability in the context of problems with one-dimensional outputs. We identify a class of function decompositions with properties that make them well suited to the critic role in a leading approach to GANs known as Wasserstein GANs. We show that Taylor and Fourier series decompositions belong to our class, provide examples of these critics outperforming standard GAN approaches, and suggest how they can be scaled to higher dimensional problems in the future.

In this paper we present an algorithm for the detection of moving targets in sight of an automotive radar sensor which can handle distorted ego-velocity information. In situations where biased or none velocity information is provided from the ego-vehicle, the algorithm is able to estimate the ego-velocity based on previously detected stationary targets with high accuracy, subsequently used for the target classification. Compared to existing ego-velocity algorithms our approach provides fast and efficient inference without sacrificing the practical classification accuracy. Other than that the algorithm is characterized by simple parameterization and little but appropriate model assumptions for high accurate production automotive radar sensors.

In this paper, we apply a high-resolution approach, i.e. the matrix pencil method (MPM), to the FMCW automotive radar system to separate the neighboring targets, which share similar parameters, i.e. range, relative speed and azimuth angle, and cause overlapping in the radar spectrum. In order to adapt the 1D model of MPM to the 2D range-velocity spectrum and simultaneously limit the computational cost, some preprocessing steps are proposed to construct a novel separation algorithm. Finally, this algorithm is evaluated in both simulation and real data, and the results indicate a promising performance.