Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout

Optical readout in low-light imaging is fundamentally limited by measurement noise, including photon shot noise, detector noise, and quantization error. In this regime, downstream inference depends not only on the optical front end, but also on how noisy high-dimensional sensor measurements are represented before classification or decision-making. Here we show that eigentasks provide a measurement-adapted representation for optical sensor outputs by ordering readout features according to their resolvability under noise. Using experimental data from a lens-based optical imaging system and a reanalysis of published data from a single-photon-detection neural network, we find that eigentask representations frequently outperform standard baselines including principal component analysis and filtering-based compression. The advantage is most pronounced in photon-limited, few-shot, and higher-difficulty classification regimes. In few-shot MPEG-7 classification, for example, the advantage over other methods reaches about 10 percentage points as the number of classes increases. In these settings, eigentasks yield more informative low-dimensional features and improve sample-efficient downstream learning. These results identify measurement-adapted representation as a promising strategy for optical inference when photon budget, acquisition time, and task complexity are constrained.

Ultra-low-light computer vision using trained photon correlations

Illumination using correlated photon sources has been established as an approach to allowing high-fidelity images to be reconstructed from noisy camera frames by taking advantage of the knowledge that signal photons are spatially correlated whereas detector clicks due to noise are uncorrelated. However, in computer-vision tasks, the goal is often not ultimately to reconstruct an image, but to make inferences about a scene -- such as what object is present. Here we show how correlated-photon illumination can be used to gain an advantage in a hybrid optical-electronic computer-vision pipeline for object recognition. We demonstrate correlation-aware training (CAT): end-to-end optimization of a trainable correlated-photon illumination source and a Transformer backend in a way that the Transformer can learn to benefit from the correlations, using a small number (<= 100) of shots. We show a classification accuracy enhancement of up to 15 percentage points over conventional, uncorrelated-illumination-based computer vision in ultra-low-light and noisy imaging conditions, as well as an improvement over using untrained correlated-photon illumination. Our work illustrates how specializing to a computer-vision task -- object recognition -- and training the pattern of photon correlations in conjunction with a digital backend allows us to push the limits of accuracy in highly photon-budget-constrained scenarios beyond existing methods focused on image reconstruction.

Machine vision with small numbers of detected photons per inference

Machine vision, including object recognition and image reconstruction, is a central technology in many consumer devices and scientific instruments. The design of machine-vision systems has been revolutionized by the adoption of end-to-end optimization, in which the optical front end and the post-processing back end are jointly optimized. However, while machine vision currently works extremely well in moderate-light or bright-light situations -- where a camera may detect thousands of photons per pixel and billions of photons per frame -- it is far more challenging in very low-light situations. We introduce photon-aware neuromorphic sensing (PANS), an approach for end-to-end optimization in highly photon-starved scenarios. The training incorporates knowledge of the low photon budget and the stochastic nature of light detection when the average number of photons per pixel is near or less than 1. We report a proof-of-principle experimental demonstration in which we performed low-light image classification using PANS, achieving 73% (82%) accuracy on FashionMNIST with an average of only 4.9 (17) detected photons in total per inference, and 86% (97%) on MNIST with 8.6 (29) detected photons -- orders of magnitude more photon-efficient than conventional approaches. We also report simulation studies showing how PANS could be applied to other classification, event-detection, and image-reconstruction tasks. By taking into account the statistics of measurement results for non-classical states or alternative sensing hardware, PANS could in principle be adapted to enable high-accuracy results in quantum and other photon-starved setups.

Unsupervised End-to-End Training with a Self-Defined Bio-Inspired Target

Current unsupervised learning methods depend on end-to-end training via deep learning techniques such as self-supervised learning, with high computational requirements, or employ layer-by-layer training using bio-inspired approaches like Hebbian learning, using local learning rules incompatible with supervised learning. Both approaches are problematic for edge AI hardware that relies on sparse computational resources and would strongly benefit from alternating between unsupervised and supervised learning phases - thus leveraging widely available unlabeled data from the environment as well as labeled training datasets. To solve this challenge, in this work, we introduce a 'self-defined target' that uses Winner-Take-All (WTA) selectivity at the network's final layer, complemented by regularization through biologically inspired homeostasis mechanism. This approach, framework-agnostic and compatible with both global (Backpropagation) and local (Equilibrium propagation) learning rules, achieves a 97.6% test accuracy on the MNIST dataset. Furthermore, we demonstrate that incorporating a hidden layer enhances classification accuracy and the quality of learned features across all training methods, showcasing the advantages of end-to-end unsupervised training. Extending to semi-supervised learning, our method dynamically adjusts the target according to data availability, reaching a 96.6% accuracy with just 600 labeled MNIST samples. This result highlights our 'unsupervised target' strategy's efficacy and flexibility in scenarios ranging from abundant to no labeled data availability.

Quantum-noise-limited optical neural networks operating at a few quanta per activation

Analog physical neural networks, which hold promise for improved energy efficiency and speed compared to digital electronic neural networks, are nevertheless typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10). What happens if an analog system is instead operated in an ultra-low-power regime, in which the behavior of the system becomes highly stochastic and the noise is no longer a small perturbation on the signal? In this paper, we study this question in the setting of optical neural networks operated in the limit where some layers use only a single photon to cause a neuron activation. Neuron activations in this limit are dominated by quantum noise from the fundamentally probabilistic nature of single-photon detection of weak optical signals. We show that it is possible to train stochastic optical neural networks to perform deterministic image-classification tasks with high accuracy in spite of the extremely high noise (SNR ~ 1) by using a training procedure that directly models the stochastic behavior of photodetection. We experimentally demonstrated MNIST classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to 0.008 photons per multiply-accumulate (MAC) operation, which is equivalent to 0.003 attojoules of optical energy per MAC. Our experiment used >40x fewer photons per inference than previous state-of-the-art low-optical-energy demonstrations, to achieve the same accuracy of >90%. Our work shows that some extremely stochastic analog systems, including those operating in the limit where quantum noise dominates, can nevertheless be used as layers in neural networks that deterministically perform classification tasks with high accuracy if they are appropriately trained.

Training Dynamical Binary Neural Networks with Equilibrium Propagation

Equilibrium Propagation (EP) is an algorithm intrinsically adapted to the training of physical networks, in particular thanks to the local updates of weights given by the internal dynamics of the system. However, the construction of such a hardware requires to make the algorithm compatible with the existing neuromorphic CMOS technology, which generally exploits digital communication between neurons and offers a limited amount of local memory. In this work, we demonstrate that EP can train dynamical networks with binary activations and weights. We first train systems with binary weights and full-precision activations, achieving an accuracy equivalent to that of full-precision models trained by standard EP on MNIST, and losing only 1.9% accuracy on CIFAR-10 with equal architecture. We then extend our method to the training of models with binary activations and weights on MNIST, achieving an accuracy within 1% of the full-precision reference for fully connected architectures and reaching the full-precision reference accuracy for the convolutional architecture. Our extension of EP training to binary networks is consistent with the requirements of today's dynamic, brain-inspired hardware platforms and paves the way for very low-power end-to-end learning.

EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementations

Neuromorphic systems achieve high energy efficiency by computing with spikes, in a brain-inspired way. However, finding spike-based learning algorithms that can be implemented within the local constraints of neuromorphic systems, while achieving high accuracy, remains a formidable challenge. Equilibrium Propagation is a hardware-friendly counterpart of backpropagation which only involves spatially local computations and applies to recurrent neural networks with static inputs. So far, hardware-oriented studies of Equilibrium Propagation focused on rate-based networks. In this work, we develop a spiking neural network algorithm called EqSpike, compatible with neuromorphic systems, which learns by Equilibrium Propagation. Through simulations, we obtain a test recognition accuracy of 96.9% on MNIST, similar to rate-based Equilibrium Propagation, and comparing favourably to alternative learning techniques for spiking neural networks. We show that EqSpike implemented in silicon neuromorphic technology could reduce the energy consumption of inference and training by up to three orders of magnitude compared to GPUs. Finally, we also show that during learning, EqSpike weight updates exhibit a form of Spike Timing Dependent Plasticity, highlighting a possible connection with biology.