Radar sensors offer power-efficient solutions for always-on smart devices, but processing the data streams on resource-constrained embedded platforms remains challenging. This paper presents novel techniques that leverage the temporal correlation present in streaming radar data to enhance the efficiency of Early Exit Neural Networks for Deep Learning inference on embedded devices. These networks add additional classifier branches between the architecture's hidden layers that allow for an early termination of the inference if their result is deemed sufficient enough by an at-runtime decision mechanism. Our methods enable more informed decisions on when to terminate the inference, reducing computational costs while maintaining a minimal loss of accuracy. Our results demonstrate that our techniques save up to 26% of operations per inference over a Single Exit Network and 12% over a confidence-based Early Exit version. Our proposed techniques work on commodity hardware and can be combined with traditional optimizations, making them accessible for resource-constrained embedded platforms commonly used in smart devices. Such efficiency gains enable real-time radar data processing on resource-constrained platforms, allowing for new applications in the context of smart homes, Internet-of-Things, and human-computer interaction.

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper learning rules fall far from answering the need. In this work we study the fundamental paradigm of (robust) $\textit{empirical risk minimization}$ (RERM), a simple process in which the learner outputs any hypothesis minimizing its training error. RERM famously fails to robustly learn VC classes (Montasser et al., 2019a), a bound we show extends even to `nice' settings such as (bounded) halfspaces. As such, we study a recent relaxation of the robust model called $\textit{tolerant}$ robust learning (Ashtiani et al., 2022) where the output classifier is compared to the best achievable error over slightly larger perturbation sets. We show that under geometric niceness conditions, a natural tolerant variant of RERM is indeed sufficient for $\gamma$-tolerant robust learning VC classes over $\mathbb{R}^d$, and requires only $\tilde{O}\left( \frac{VC(H)d\log \frac{D}{\gamma\delta}}{\epsilon^2}\right)$ samples for robustness regions of (maximum) diameter $D$.

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural network computations as a surrogate model for behavioral simulation of approximate multipliers. The continuous and differentiable properties of the solution space spanned by the additive Gaussian noise model are used as a heuristic that generates meaningful estimates of layer robustness without the need for combinatorial optimization techniques. Instead, the amount of noise injected into the accurate computations is learned during network training using backpropagation. A probabilistic model of the multiplier error is presented to bridge the gap between the domains; the model estimates the standard deviation of the approximate multiplier error, connecting solutions in the additive Gaussian noise space to actual hardware instances. Our experiments show that the combination of heterogeneous approximation and neural network retraining reduces the energy consumption for multiplications by 70% to 79% for different ResNet variants on the CIFAR-10 dataset with a Top-1 accuracy loss below one percentage point. For the more complex Tiny ImageNet task, our VGG16 model achieves a 53 % reduction in energy consumption with a drop in Top-5 accuracy of 0.5 percentage points. We further demonstrate that our error model can predict the parameters of an approximate multiplier in the context of the commonly used additive Gaussian noise (AGN) model with high accuracy. Our software implementation is available under https://github.com/etrommer/agn-approx.

The recent advances in machine learning, in general, and Artificial Neural Networks (ANN), in particular, has made smart embedded systems an attractive option for a larger number of application areas. However, the high computational complexity, memory footprints, and energy requirements of machine learning models hinder their deployment on resource-constrained embedded systems. Most state-of-the-art works have considered this problem by proposing various low bit-width data representation schemes, optimized arithmetic operators' implementations, and different complexity reduction techniques such as network pruning. To further elevate the implementation gains offered by these individual techniques, there is a need to cross-examine and combine these techniques' unique features. This paper presents ExPAN(N)D, a framework to analyze and ingather the efficacy of the Posit number representation scheme and the efficiency of fixed-point arithmetic implementations for ANNs. The Posit scheme offers a better dynamic range and higher precision for various applications than IEEE $754$ single-precision floating-point format. However, due to the dynamic nature of the various fields of the Posit scheme, the corresponding arithmetic circuits have higher critical path delay and resource requirements than the single-precision-based arithmetic units. Towards this end, we propose a novel Posit to fixed-point converter for enabling high-performance and energy-efficient hardware implementations for ANNs with minimal drop in the output accuracy. We also propose a modified Posit-based representation to store the trained parameters of a network. Compared to an $8$-bit fixed-point-based inference accelerator, our proposed implementation offers $\approx46\%$ and $\approx18\%$ reductions in the storage requirements of the parameters and energy consumption of the MAC units, respectively.

Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension, for kernelized perceptrons for different families of feature maps. As a warm-up, we show that the teaching complexity is $\Theta(d)$ for the exact teaching of linear perceptrons in $\mathbb{R}^d$, and $\Theta(d^k)$ for kernel perceptron with a polynomial kernel of order $k$. Furthermore, under certain smooth assumptions on the data distribution, we establish a rigorous bound on the complexity for approximately teaching a Gaussian kernel perceptron. We provide numerical examples of the optimal (approximate) teaching set under several canonical settings for linear, polynomial and Gaussian kernel perceptrons.

We examine the task of locating a target region among those induced by intersections of $n$ halfspaces in $\mathbb{R}^d$. This generic task connects to fundamental machine learning problems, such as training a perceptron and learning a $\phi$-separable dichotomy. We investigate the average teaching complexity of the task, i.e., the minimal number of samples (halfspace queries) required by a teacher to help a version-space learner in locating a randomly selected target. As our main result, we show that the average-case teaching complexity is $\Theta(d)$, which is in sharp contrast to the worst-case teaching complexity of $\Theta(n)$. If instead, we consider the average-case learning complexity, the bounds have a dependency on $n$ as $\Theta(n)$ for \tt{i.i.d.} queries and $\Theta(d \log(n))$ for actively chosen queries by the learner. Our proof techniques are based on novel insights from computational geometry, which allow us to count the number of convex polytopes and faces in a Euclidean space depending on the arrangement of halfspaces. Our insights allow us to establish a tight bound on the average-case complexity for $\phi$-separable dichotomies, which generalizes the known $\mathcal{O}(d)$ bound on the average number of "extreme patterns" in the classical computational geometry literature (Cover, 1965).