Hassan Hamad

William Chang, Hassan Hamad, Keith M. Chugg

Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously proposed morphological perceptrons use max-sum, in place of sum-product, node processing and have promising properties for circuit implementations. In this paper we show that these max-sum ANNs do not have universal approximation capabilities. Furthermore, we consider proposed signed-max-sum and max-star-sum generalizations of morphological ANNs and show that these variants also do not have universal approximation capabilities. We contrast these variations to log-number system (LNS) implementations which also avoid multiplications, but do exhibit universal approximation capabilities.

Hassan Hamad, Yuou Qiu, Peter A. Beerel et al.

While advancements in quantization have significantly reduced the computational costs of inference in deep learning, training still predominantly relies on complex floating-point arithmetic. Low-precision fixed-point training presents a compelling alternative. This work introduces a novel enhancement in low-precision logarithmic fixed-point training, geared towards future hardware accelerator designs. We propose incorporating bitwidth in the design of approximations to arithmetic operations. To this end, we introduce a new hardware-friendly, piece-wise linear approximation for logarithmic addition. Using simulated annealing, we optimize this approximation at different precision levels. A C++ bit-true simulation demonstrates training of VGG-11 and VGG-16 models on CIFAR-100 and TinyImageNet, respectively, using 12-bit integer arithmetic with minimal accuracy degradation compared to 32-bit floating-point training. Our hardware study reveals up to 32.5% reduction in area and 53.5% reduction in energy consumption for the proposed LNS multiply-accumulate units compared to that of linear fixed-point equivalents.

Hassan Hamad, Yingru Xu, Liang Zhao et al.

Tool-augmented large language models (LLMs) are increasingly employed in real-world applications, but tool usage errors still hinder their reliability. We introduce ToolCritic, a diagnostic framework that evaluates and improves LLM behavior in multi-turn, tool-augmented dialogues. ToolCritic detects eight distinct error types specific to tool-calling (e.g., premature invocation, argument misalignment, and misinterpretation of tool outputs) and provides targeted feedback to the main LLM. The main LLM, assumed to have strong reasoning, task understanding and orchestration capabilities, then revises its response based on ToolCritic's feedback. We systematically define these error categories and construct a synthetic dataset to train ToolCritic. Experimental results on the Schema-Guided Dialogue (SGD) dataset demonstrate that ToolCritic improves tool-calling accuracy by up to 13% over baselines, including zero-shot prompting and self-correction techniques. This represents a promising step toward more robust LLM integration with external tools in real-world dialogue applications.