Understanding how sensory neurons exhibit selectivity to certain features and invariance to others is central to uncovering the computational principles underlying robustness and generalization in visual perception. Most existing methods for characterizing selectivity and invariance identify single or finite discrete sets of stimuli. Since these are only isolated measurements from an underlying continuous manifold, characterizing invariance properties accurately and comparing them across neurons with varying receptive field size, position, and orientation, becomes challenging. Consequently, a systematic analysis of invariance types at the population level remains under-explored. Building on recent advances in learning continuous invariance manifolds, we introduce a novel method to accurately identify and align invariance manifolds of visual sensory neurons, overcoming these challenges. Our approach first learns the continuous invariance manifold of stimuli that maximally excite a neuron modeled by a response-predicting deep neural network. It then learns an affine transformation on the pixel coordinates such that the same manifold activates another neuron as strongly as possible, effectively aligning their invariance manifolds spatially. This alignment provides a principled way to quantify and compare neuronal invariances irrespective of receptive field differences. Using simulated neurons, we demonstrate that our method accurately learns and aligns known invariance manifolds, robustly identifying functional clusters. When applied to macaque V1 neurons, it reveals functional clusters of neurons, including simple and complex cells. Overall, our method enables systematic, quantitative exploration of the neural invariance landscape, to gain new insights into the functional properties of visual sensory neurons.

Decoding visual stimuli from neural population activity is crucial for understanding the brain and for applications in brain-machine interfaces. However, such biological data is often scarce, particularly in primates or humans, where high-throughput recording techniques, such as two-photon imaging, remain challenging or impossible to apply. This, in turn, poses a challenge for deep learning decoding techniques. To overcome this, we introduce MEIcoder, a biologically informed decoding method that leverages neuron-specific most exciting inputs (MEIs), a structural similarity index measure loss, and adversarial training. MEIcoder achieves state-of-the-art performance in reconstructing visual stimuli from single-cell activity in primary visual cortex (V1), especially excelling on small datasets with fewer recorded neurons. Using ablation studies, we demonstrate that MEIs are the main drivers of the performance, and in scaling experiments, we show that MEIcoder can reconstruct high-fidelity natural-looking images from as few as 1,000-2,500 neurons and less than 1,000 training data points. We also propose a unified benchmark with over 160,000 samples to foster future research. Our results demonstrate the feasibility of reliable decoding in early visual system and provide practical insights for neuroscience and neuroengineering applications.