A CORDIC-based configuration for the design of Activation Functions (AF) was previously suggested to accelerate ASIC hardware design for resource-constrained systems by providing functional reconfigurability. Since its introduction, this new approach for neural network acceleration has gained widespread popularity, influencing numerous designs for activation functions in both academic and commercial AI processors. In this retrospective analysis, we explore the foundational aspects of this initiative, summarize key developments over recent years, and introduce the DA-VINCI AF tailored for the evolving needs of AI applications. This new generation of dynamically configurable and precision-adjustable activation function cores promise greater adaptability for a range of activation functions in AI workloads, including Swish, SoftMax, SeLU, and GeLU, utilizing the Shift-and-Add CORDIC technique. The previously presented design has been optimized for MAC, Sigmoid, and Tanh functionalities and incorporated into ReLU AFs, culminating in an accumulative NEURIC compute unit. These enhancements position NEURIC as a fundamental component in the resource-efficient vector engine for the realization of AI accelerators that focus on DNNs, RNNs/LSTMs, and Transformers, achieving a quality of results (QoR) of 98.5%.

Recent works have characterized the function-space inductive bias of infinite-width bounded-norm single-hidden-layer neural networks as a kind of bounded-variation-type space. This novel neural network Banach space encompasses many classical multivariate function spaces including certain Sobolev spaces and the spectral Barron spaces. Notably, this Banach space also includes functions that exhibit less classical regularity such as those that only vary in a few directions. On bounded domains, it is well-established that the Gaussian reproducing kernel Hilbert space (RKHS) strictly embeds into this Banach space, demonstrating a clear gap between the Gaussian RKHS and the neural network Banach space. It turns out that when investigating these spaces on unbounded domains, e.g., all of $\mathbb{R}^d$, the story is fundamentally different. We establish the following fundamental result: Certain functions that lie in the Gaussian RKHS have infinite norm in the neural network Banach space. This provides a nontrivial gap between kernel methods and neural networks by the exhibition of functions in which kernel methods can do strictly better than neural networks.

In recent years, neural network-based models have achieved state-of-the-art performance across a wide array of tasks. These models effectively capture relevant features or concepts from samples, tailored to the specific prediction tasks they address (Yang and Hu, 2021b; Bordelon and Pehlevan, 2022a; Ba et al., 2022b). A fundamental challenge lies in understanding how these models learn such features and determining whether these features can be interpreted or even retrieved directly (Radhakrishnan et al., 2024). Recent advancements in mechanistic interpretability have opened multiple avenues for elucidating how transformerbased models, including Large Language Models (LLMs), acquire and represent features (Bricken et al., 2023; Doshi-Velez and Kim, 2017). These advances include uncovering neural circuits that encode specific concepts (Marks et al., 2024b; Olah et al., 2020), understanding feature composition across attention layers (Yang and Hu, 2021b), and revealing how models develop structured representations (Elhage et al., 2022). One line of research posits that features are encoded linearly within the latent representation space through sparse activations, a concept known as the linear representation hypothesis (LRH) (Mikolov et al., 2013; Arora et al., 2016). However, this hypothesis faces challenges in explaining how neural networks function, as models often need to represent more distinct features than their layer dimensions would theoretically allow under purely linear encoding. This phenomenon has been studied extensively in the context of large language models through the lens of superposition (Elhage et al., 2022), where multiple features share the same dimensional space in structured ways.

In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal guarantees on the query complexity required to learn smooth, but otherwise general, distance functions under two notions of approximation: $\omega$-additive approximation and $(1 + \omega)$-multiplicative approximation. For the additive approximation, we propose a global method whose query complexity is quadratic in the size of a finite cover of the sample space. For the (stronger) multiplicative approximation, we introduce a method that combines global and local approaches, utilizing multiple Mahalanobis distance functions to capture local geometry. This method has a query complexity that scales quadratically with both the size of the cover and the ambient space dimension of the sample space.

Recent advances in machine learning have led to increased interest in reproducing kernel Banach spaces (RKBS) as a more general framework that extends beyond reproducing kernel Hilbert spaces (RKHS). These works have resulted in the formulation of representer theorems under several regularized learning schemes. However, little is known about an optimization method that encompasses these results in this setting. This paper addresses a learning problem on Banach spaces endowed with a reproducing kernel, focusing on efficient optimization within RKBS. To tackle this challenge, we propose an algorithm based on mirror descent (MDA). Our approach involves an iterative method that employs gradient steps in the dual space of the Banach space using the reproducing kernel. We analyze the convergence properties of our algorithm under various assumptions and establish two types of results: first, we identify conditions under which a linear convergence rate is achievable, akin to optimization in the Euclidean setting, and provide a proof of the linear rate; second, we demonstrate a standard convergence rate in a constrained setting. Moreover, to instantiate this algorithm in practice, we introduce a novel family of RKBSs with $p$-norm ($p \neq 2$), characterized by both an explicit dual map and a kernel.

In order to vary the arithmetic resource consumption of neural network applications at runtime, this work proposes the flexible reuse of approximate multipliers for neural network layer computations. We introduce a search algorithm that chooses an appropriate subset of approximate multipliers of a user-defined size from a larger search space and enables retraining to maximize task performance. Unlike previous work, our approach can output more than a single, static assignment of approximate multiplier instances to layers. These different operating points allow a system to gradually adapt its Quality of Service (QoS) to changing environmental conditions by increasing or decreasing its accuracy and resource consumption. QoS-Nets achieves this by reassigning the selected approximate multiplier instances to layers at runtime. To combine multiple operating points with the use of retraining, we propose a fine-tuning scheme that shares the majority of parameters between operating points, with only a small amount of additional parameters required per operating point. In our evaluation on MobileNetV2, QoS-Nets is used to select four approximate multiplier instances for three different operating points. These operating points result in power savings for multiplications between 15.3% and 42.8% at a Top-5 accuracy loss between 0.3 and 2.33 percentage points. Through our fine-tuning scheme, all three operating points only increase the model's parameter count by only 2.75%.

Early Exit Neural Networks (EENNs) present a solution to enhance the efficiency of neural network deployments. However, creating EENNs is challenging and requires specialized domain knowledge, due to the large amount of additional design choices. To address this issue, we propose an automated augmentation flow that focuses on converting an existing model into an EENN. It performs all required design decisions for the deployment to heterogeneous or distributed hardware targets: Our framework constructs the EENN architecture, maps its subgraphs to the hardware targets, and configures its decision mechanism. To the best of our knowledge, it is the first framework that is able to perform all of these steps. We evaluated our approach on a collection of Internet-of-Things and standard image classification use cases. For a speech command detection task, our solution was able to reduce the mean operations per inference by 59.67%. For an ECG classification task, it was able to terminate all samples early, reducing the mean inference energy by 74.9% and computations by 78.3%. On CIFAR-10, our solution was able to achieve up to a 58.75% reduction in computations. The search on a ResNet-152 base model for CIFAR-10 took less than nine hours on a laptop CPU. Our proposed approach enables the creation of EENN optimized for IoT environments and can reduce the inference cost of Deep Learning applications on embedded and fog platforms, while also significantly reducing the search cost - making it more accessible for scientists and engineers in industry and research. The low search cost improves the accessibility of EENNs, with the potential to improve the efficiency of neural networks in a wide range of practical applications.

Deep Learning is becoming increasingly relevant in Embedded and Internet-of-things applications. However, deploying models on embedded devices poses a challenge due to their resource limitations. This can impact the model's inference accuracy and latency. One potential solution are Early Exit Neural Networks, which adjust model depth dynamically through additional classifiers attached between their hidden layers. However, the real-time termination decision mechanism is critical for the system's efficiency, latency, and sustained accuracy. This paper introduces Difference Detection and Temporal Patience as decision mechanisms for Early Exit Neural Networks. They leverage the temporal correlation present in sensor data streams to efficiently terminate the inference. We evaluate their effectiveness in health monitoring, image classification, and wake-word detection tasks. Our novel contributions were able to reduce the computational footprint compared to established decision mechanisms significantly while maintaining higher accuracy scores. We achieved a reduction of mean operations per inference by up to 80% while maintaining accuracy levels within 5% of the original model. These findings highlight the importance of considering temporal correlation in sensor data to improve the termination decision.

With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation, such as approximate and stochastic computing, that leverage the inherent error-resilience of such algorithms are being actively explored for implementing ML inference on resource-constrained systems. Approximate computing (AxC) aims to provide disproportionate gains in the power, performance, and area (PPA) of an application by allowing some level of reduction in its behavioral accuracy (BEHAV). Using approximate operators (AxOs) for computer arithmetic forms one of the more prevalent methods of implementing AxC. AxOs provide the additional scope for finer granularity of optimization, compared to only precision scaling of computer arithmetic. To this end, designing platform-specific and cost-efficient approximate operators forms an important research goal. Recently, multiple works have reported using AI/ML-based approaches for synthesizing novel FPGA-based AxOs. However, most of such works limit usage of AI/ML to designing ML-based surrogate functions used during iterative optimization processes. To this end, we propose a novel data analysis-driven mathematical programming-based approach to synthesizing approximate operators for FPGAs. Specifically, we formulate mixed integer quadratically constrained programs based on the results of correlation analysis of the characterization data and use the solutions to enable a more directed search approach for evolutionary optimization algorithms. Compared to traditional evolutionary algorithms-based optimization, we report up to 21% improvement in the hypervolume, for joint optimization of PPA and BEHAV, in the design of signed 8-bit multipliers.

The rising usage of AI and ML-based processing across application domains has exacerbated the need for low-cost ML implementation, specifically for resource-constrained embedded systems. To this end, approximate computing, an approach that explores the power, performance, area (PPA), and behavioral accuracy (BEHAV) trade-offs, has emerged as a possible solution for implementing embedded machine learning. Due to the predominance of MAC operations in ML, designing platform-specific approximate arithmetic operators forms one of the major research problems in approximate computing. Recently there has been a rising usage of AI/ML-based design space exploration techniques for implementing approximate operators. However, most of these approaches are limited to using ML-based surrogate functions for predicting the PPA and BEHAV impact of a set of related design decisions. While this approach leverages the regression capabilities of ML methods, it does not exploit the more advanced approaches in ML. To this end, we propose AxOCS, a methodology for designing approximate arithmetic operators through ML-based supersampling. Specifically, we present a method to leverage the correlation of PPA and BEHAV metrics across operators of varying bit-widths for generating larger bit-width operators. The proposed approach involves traversing the relatively smaller design space of smaller bit-width operators and employing its associated Design-PPA-BEHAV relationship to generate initial solutions for metaheuristics-based optimization for larger operators. The experimental evaluation of AxOCS for FPGA-optimized approximate operators shows that the proposed approach significantly improves the quality-resulting hypervolume for multi-objective optimization-of 8x8 signed approximate multipliers.