Deep learning is a state-of-the-art methodology in numerous domains, including image recognition, natural language processing, and data generation [1]. The discovery of scaling laws in deep learning models [2, 3] has motivated the development of increasingly larger models, commonly referred to as foundation models [4, 5, 6]. Recent studies have shown that reasoning tasks can be improved through iterative computations during the inference phase [7]. While computational power continues to be a major driver of artificial intelligence (AI) advancements, the associated costs remain a significant barrier to broader adoption across diverse industries [8, 9]. This issue is especially critical in edge AI systems, where energy consumption is constrained by the limited capacity of batteries, making the need for more efficient computation paramount [10]. One promising strategy to enhance energy efficiency is fabricating dedicated hardware. Since matrixvector multiplication is the computational core in deep learning, parallelization greatly enhances computational efficiency [11]. Moreover, in data-driven applications such as deep learning, a substantial portion of power consumption is due to data movement between the processor and memory, commonly referred to as the von Neumann bottleneck [12].

Many neural areas, notably, the hippocampus, show structured, dynamical, population behavior such as coordinated oscillations. It has long been observed that such oscillations provide a substrate for representing analog information in the firing phases of neurons relative to the underlying population rhythm. However, it has become increasingly clear that it is essential for neural populations to represent uncertainty about the information they capture, and the substantial recent work on neural codes for uncertainty has omitted any analysis of oscillatory systems. Here, we observe that, since neurons in an oscillatory network need not only fire once in each cycle (or even at all), uncertainty about the analog quantities each neuron represents by its firing phase might naturally be reported through the degree of concentration of the spikes that it fires. We apply this theory to memory in a model of oscillatory associative recall in hippocampal area CA3. Although it is not well treated in the literature, representing and manipulating uncertainty is fundamental to competent memory; our theory enables us to view CA3 as an effective uncertainty-aware, retrieval system.

Many neural areas, notably, the hippocampus, show structured, dynamical, population behavior such as coordinated oscillations. It has long been observed that such oscillations provide a substrate for representing analog information in the firing phases of neurons relative to the underlying population rhythm. However, it has become increasingly clear that it is essential for neural populations to represent uncertainty about the information they capture, and the substantial recent work on neural codes for uncertainty has omitted any analysis of oscillatory systems. Here, we observe that, since neurons in an oscillatory network need not only fire once in each cycle (or even at all), uncertainty about the analog quantities each neuron represents by its firing phase might naturally be reported through the degree of concentration of the spikes that it fires. We apply this theory to memory in a model of oscillatory associative recall in hippocampal area CA3. Although it is not well treated in the literature, representing and manipulating uncertainty is fundamental to competent memory; our theory enables us to view CA3 as an effective uncertainty-aware, retrieval system.

Many neural areas, notably, the hippocampus, show structured, dynamical, population behavior such as coordinated oscillations.