Quantum extreme learning machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate—the quantum reservoir—and the efficient post-measurement training via linear regression. Here, we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. In particular, our result on the reservoir-induced concentration strongly indicates that quantum reservoirs drawn from a highly random ensemble make QELM models unscalable. Our analysis elucidates the potential and fundamental limitations of QELMs and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

Background: Mild cognitive impairment (MCI) is an early stage of cognitive decline which could develop into dementia. An early detection of MCI is a crucial step for timely prevention and intervention. Recent studies have developed deep learning models to detect MCI and dementia using a bedside task like the classic clock drawing test (CDT). However, it remains a challenge to predict the early stage of the disease using the CDT data alone. Moreover, the state-of-the-art deep learning techniques still face black box challenges, making it questionable to implement them in a clinical setting. Methods: We recruited 918 subjects from King Chulalongkorn Memorial Hospital (651 healthy subjects and 267 MCI patients). We propose a novel deep learning framework that incorporates data from the CDT, cube-copying, and trail-making tests. Soft label and self-attention were applied to improve the model performance and provide a visual explanation. The interpretability of the visualization of our model and the Grad-CAM approach were rated by experienced medical personnel and quantitatively evaluated using intersection over union (IoU) between the models’ heat maps and the regions of interest. Results: Rather than using a single CDT image in the baseline VGG16 model, using multiple drawing tasks as inputs into our proposed model with soft label significantly improves the classification performance between the healthy aging controls and the MCI patients. In particular, the classification accuracy increases from 0.75 (baseline model) to 0.81. The F1-score increases from 0.36 to 0.65, and the area under the receiver operating characteristic curve (AUC) increases from 0.74 to 0.84. Compared to the multi-input model that also offers interpretable visualization, i.e., Grad-CAM, our model receives higher interpretability scores given by experienced medical experts and higher IoUs. Conclusions: Our model achieves better classification performance at detecting MCI compared to the baseline model. In addition, the model provides visual explanations that are superior to those of the baseline model as quantitatively evaluated by experienced medical personnel. Thus, our work offers an interpretable machine learning model with high classification performance, both of which are crucial aspects of artificial intelligence in medical diagnosis.

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.

Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex degree and form very large numbers of simple polygons (triangles or squares). The models avoid the collapse phenomena that plague naive graph Hamiltonians based on triangle or square counts. More than that, statistically significant numbers of other geometric primitives (small pieces of regular lattices, cubes) emerge in our ensemble, even though they are not in any way explicitly pre-programmed into the formulation of the graph Hamiltonian, which only depends on properties of paths of length 2. While much of our motivation comes from hopes to construct a graph-based theory of random geometry (Euclidean quantum gravity), our presentation is completely self-contained within the context of exponential random graph theory, and the range of potential applications is considerably more broad.

Recurrent neural networks (RNNs) based on model neurons that communicate via continuous signals have been widely used to study how cortical neural circuits perform cognitive tasks. Training such networks to perform tasks that require information maintenance over a brief period (i.e., working memory tasks) remains a challenge. Inspired by the robust information maintenance observed in higher cortical areas such as the prefrontal cortex, despite substantial inherent noise, we investigated the effects of random noise on RNNs across different cognitive functions, including working memory. Our findings reveal that random noise not only speeds up training but also enhances the stability and performance of RNNs on working memory tasks. Importantly, this robust working memory performance induced by random noise during training is attributed to an increase in synaptic decay time constants of inhibitory units, resulting in slower decay of stimulus-specific activity critical for memory maintenance. Our study reveals the critical role of noise in shaping neural dynamics and cognitive functions, suggesting that inherent variability may be a fundamental feature driving the specialization of inhibitory neurons to support stable information processing in higher cortical regions.