Toward a mechanistic understanding of inference in visual cortex and diffusion models
Authors: Zeyu Yun, Alexander Belsten, Dasheng Bi, Zahra Kadkhodaie, Yubei Chen, Bruno A. Olshausen
Organizations: Dept. of Electrical Engineering and Computer Science, UC Berkeley · Redwood Center for Theoretical Neuroscience, UC Berkeley · Herbert Wertheim School of Optometry and Vision Science, UC Berkeley · Flatiron Institute · Dept. of Electrical and Computer Engineering, UC Davis · Helen Wills Neuroscience Institute, UC Berkeley
Abstract
We describe a model of perceptual inference in primary visual cortex (V1) equivalent to a minimal diffusion model whose function can be readily understood from its parameters. The model is based on sparse coding with a non-factorial prior over latent variables in the form of an unconstrained, pairwise interaction matrix, extending standard sparse coding inference to a general recurrent dynamical system. We efficiently train these recurrent dynamics using a denoising score-matching objective and implicit differentiation. After training on natural images, the learned interaction matrix mirrors the structure of horizontal connections in superficial layers of V1 that link neurons of similar orientation tuning. This model exhibits exceptionally good denoising performance, restoring image features such as extended contours amid extreme visual ambiguity, nearly matching the behavior of standard, black-box diffusion architectures in generalization regime. Owing to the model's simplicity, the network's Jacobian can be decomposed directly in terms of the interaction matrix between latent variables, revealing mechanistically how the recurrent dynamics assign high probability over a continuous family of natural structural deformations. Intriguingly, within this circuit, a large fraction of latent variables learn to disconnect from visual input altogether, essentially forming a hierarchical representation that appears to enforce global consistency among image features. Together, the model and results bridge two distinct domains: for neuroscience, it generates concrete, testable hypotheses regarding functional connectivity in recurrent neural circuits during perceptual inference tasks; for machine learning, it elucidates the internal mechanisms learned by diffusion models that allow them to generate infinitely many novel images from a finite training set.
Deep neural networks trained on natural images are shown to produce outputs consistent with human observers for brightness illusions. While this phenomenon has been documented across architectures, all evidence, to date, is measured at the output level: restored pixels, decoded trajectories, or classification decisions. Whether these models actually represent illusions internally, and if so where and how, remains unknown. We show that denoising models develop illusion-sensitive representations at specific internal layers, across varied architectures. Specifically, we identify the layers and channels that discriminate illusory from physically matched control regions. We show that the denoising objective is a more important driver of the effect than the architecture. On domain-appropriate stimuli, these activations track a validated psychophysical model of human brightness perception (FLODOG; Spearman ρ≥0.70) and scale monotonically with parametric illusion strength. Leveraging these findings, we provide causal evidence via channel ablation showing that illusion-sensitive channels specifically and substantially affect the internal signal. Yet injecting these representations into the generation pipeline produces no measurable pixel shift across all tested architectures; we term such representations perceptual phantoms: active in internal processing yet invisible to any output-based evaluation. While related internal-output dissociations have been characterized in language models, this is the first such characterization for perceptual representations in denoising vision models.
Understanding the neural mechanisms underlying visual computation has long been a central challenge in neuroscience. Recent alignment based approaches have improved the accuracy of decoding visual stimuli from brain activity, yet they provide limited insight into the neural computations that give rise to these improvements. To address this gap, we propose Dual-Tower Image-Neural Alignment (DINA), an interpretable contrastive framework for analyzing population level visual computations in primary visual cortex (V1). DINA jointly trains a biologically motivated dual-tower architecture that aligns visual stimuli and corresponding V1 population responses in a shared latent space at the level of intermediate feature maps, enabling both accurate decoding and direct access to interpretable feature maps. Evaluated on large-scale two-photon calcium imaging data from mouse V1, DINA achieves accurate neural-based decoding while revealing that decoding performance is primarily supported by coarse, low-level visual structure, rather than semantic category information or fine-grained details. Further analysis reveals that alignable feature maps emerge from multiple spatially distributed image regions, capturing both shape and texture cues, and are predominantly reconstructed by sparse subsets of strongly responsive neurons and their functional interactions. Together, these results confirm that, beyond enabling accurate decoding, DINA provides a principled framework for probing the computational mechanisms underlying visual processing in V1.
Hierarchical predictive coding provides an interpretable framework for perception as error-driven inference in multi-layer generative models, while sparse coding imposes parsimonious latent representations through explicit sparsity constraints. Their combination yields hierarchical sparse predictive coding models with appealing computational and neuroscientific properties, but practical use is often limited by the cost of iterative latent inference. In such models, each input may require many recurrent refinement steps before a useful sparse representation is obtained, and this burden becomes more severe as the hierarchy deepens. We study this bottleneck by holding the hierarchical sparse energy fixed and varying the inference procedure. The comparison includes four schemes: classical iterative inference based on ISTA, an accelerated MFISTA reference, structurally informed amortized inference using a LISTA-style bottom-up encoder adapted to the hierarchical model, and a hybrid method in which this fast amortized initialization is followed by a small number of corrective energy-based refinement steps. Under this shared objective, we measure reconstruction quality, sparsity, latency, and stability on static image benchmarks. The results show that a shallow LISTA-style initializer plus short corrective recurrence improves over pure amortization while remaining much faster than long iterative inference.