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Eero P. Simoncelli

Publications and source records attributed to Eero P. Simoncelli.

At least 19 recordsLinked to original sources
arXiv2026

Learning a Maximum Entropy Model for Visual Textures using Diffusion

Visual textures -- spatially homogeneous image regions containing repeated elements (e.g. a field of grass, the bark of a tree) -- are ubiquitous in visual scenes and provide important cues for recognizing and analyzing materials and objects. A number of existing texture models extract essential statistics from a single texture image, and can then generate high-quality samples that are visually similar to the original by matching these statistics. However, their statistics are either hand-designed or based on a network pretrained for another purpose (e.g., object recognition). Here, we develop the first principled method for unsupervised learning of a set of statistics that are used to constrain a maximum entropy probability model. We leverage methods developed for generative diffusion models to derive training and sampling procedures, and compare these to the traditional method of sampling via matching the statistics. Despite the compactness of our trained model (512 statistics), it generates texture images whose quality is as good as or better than the current state-of-the-art model (~177k statistics). A more direct comparison of the two models, obtained by synthesizing images that are indistinguishable for one model but maximally different for the other, reveals their relative strengths and weaknesses. Finally, we show that unlike previous statistical texture models, a straight trajectory in the representation space of our model generates homogeneous texture samples that interpolate smoothly between the features of the two end points.

cs.CV↗
arXiv2026

GEOPHYS: The Geometry of Physical Plausibility

While humans can identify physically implausible events within milliseconds, machine learning approaches addressing the same problem are extremely slow and expensive. They either rely on external multimodal-LLM judges or require ad-hoc modifications to the training procedure. In this work, we argue that indicators of physical plausibility are implicitly captured by five geometric properties of the per-frame embeddings produced by frozen image encoders. In aggregate, we call them GEOPHYS. First, we show that these signals correlate with human EEG responses to two forms of object-permanence violations. Second, GEOPHYS robustly discriminates physically implausible videos from realistic ones, achieving state-of-the-art physics-violation detection: 98.3% on LikePhys and 93.3% on IntPhys2, whereas V-JEPA 2, GPT-4o, Gemini, and twelve modern video diffusion models perform near chance. Third, used as a best-of-N verifier for physical alignment during video generation, GEOPHYS lifts MAGI-1 24B from 50.01% to 64.50% on PhysicsIQ at 1.5x lower wall-clock and 4.65x lower memory than the V-JEPA 2 world-model verifier. Ultimately, GEOPHYS demonstrates that physical plausibility in videos can be assessed by leveraging the emergent geometric properties of temporal features extracted from image encoders.

cs.CV↗
arXiv2026

Learning a distance measure from the information-estimation geometry of data

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

eess.IV↗
arXiv2025

Disentangled representations via score-based variational autoencoders

We present the Score-based Autoencoder for Multiscale Inference (SAMI), a method for unsupervised representation learning that combines the theoretical frameworks of diffusion models and VAEs. By unifying their respective evidence lower bounds, SAMI formulates a principled objective that learns representations through score-based guidance of the underlying diffusion process. The resulting representations automatically capture meaningful structure in the data: it recovers ground truth generative factors in our synthetic dataset, learns factorized, semantic latent dimensions from complex natural images, and encodes video sequences into latent trajectories that are straighter than those of alternative encoders, despite training exclusively on static images. Furthermore, SAMI can extract useful representations from pre-trained diffusion models with minimal additional training. Finally, the explicitly probabilistic formulation provides new ways to identify semantically meaningful axes in the absence of supervised labels, and its mathematical exactness allows us to make formal statements about the nature of the learned representation. Overall, these results indicate that implicit structural information in diffusion models can be made explicit and interpretable through synergistic combination with a variational autoencoder.

stat.ML↗
arXiv2025

Generalized Compressed Sensing for Image Reconstruction with Diffusion Probabilistic Models

We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS) based on random projections, all of which rely on axis- or subspace-aligned statistical characterization of the signal source. However, many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements for efficient image reconstruction, where the signal statistics are expressed by the prior implicit in a neural network trained to perform denoising (known as a "diffusion model"). We demonstrate that the optimal measurements derived for two natural image datasets differ from those of PCA, ICA, or CS, and result in substantially lower mean squared reconstruction error. Interestingly, the marginal distributions of the measurement values are asymmetrical (skewed), substantially more so than those of previous methods. We also find that optimizing with respect to perceptual loss, as quantified by structural similarity (SSIM), leads to measurements different from those obtained when optimizing for MSE. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.

cs.CV↗
arXiv2025

Discriminating image representations with principal distortions

Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a framework for comparing a set of image representations in terms of their local geometries. We quantify the local geometry of a representation using the Fisher information matrix, a standard statistical tool for characterizing the sensitivity to local stimulus distortions, and use this as a substrate for a metric on the local geometry in the vicinity of a base image. This metric may then be used to optimally differentiate a set of models, by finding a pair of "principal distortions" that maximize the variance of the models under this metric. As an example, we use this framework to compare a set of simple models of the early visual system, identifying a novel set of image distortions that allow immediate comparison of the models by visual inspection. In a second example, we apply our method to a set of deep neural network models and reveal differences in the local geometry that arise due to architecture and training types. These examples demonstrate how our framework can be used to probe for informative differences in local sensitivities between complex models, and suggest how it could be used to compare model representations with human perception.

q-bio.NC↗
arXiv2025

Detection of Moving Objects Using Self-motion Constraints on Optic Flow

As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints that self-motion imposes on retinal velocities. When an eye translates and rotates in a stationary 3D scene, the velocity at each retinal location is constrained to a line segment in the 2D space of retinal velocities. The slope and intercept of this segment is determined by the eye's translation and rotation, and the position along the segment is determined by the local scene depth. Since all possible velocities arising from a stationary scene must lie on this segment, velocities that are not must correspond to objects moving within the scene. We hypothesize that humans make use of these constraints by using deviations of local velocity from these constraint lines to detect moving objects. To test this, we used a virtual reality headset to present rich wide-field stimuli, simulating the visual experience of translating forward in several virtual environments with varied precision of depth information. Participants had to determine if a cued object moved relative to the scene. Consistent with the hypothesis, we found that performance depended on the deviation of the object velocity from the constraint segment, rather than a difference between retinal velocities of the object and its local surround. We also found that the endpoints of the constraint segment reflected the precision of depth information available in the different virtual environments.

q-bio.NC↗
arXiv2025

Learning predictable and robust neural representations by straightening image sequences

Prediction is a fundamental capability of all living organisms, and has been proposed as an objective for learning sensory representations. Recent work demonstrates that in primate visual systems, prediction is facilitated by neural representations that follow straighter temporal trajectories than their initial photoreceptor encoding, which allows for prediction by linear extrapolation. Inspired by these experimental findings, we develop a self-supervised learning (SSL) objective that explicitly quantifies and promotes straightening. We demonstrate the power of this objective in training deep feedforward neural networks on smoothly-rendered synthetic image sequences that mimic commonly-occurring properties of natural videos. The learned model contains neural embeddings that are predictive, but also factorize the geometric, photometric, and semantic attributes of objects. The representations also prove more robust to noise and adversarial attacks compared to previous SSL methods that optimize for invariance to random augmentations. Moreover, these beneficial properties can be transferred to other training procedures by using the straightening objective as a regularizer, suggesting a broader utility for straightening as a principle for robust unsupervised learning.

cs.CV↗
arXiv2025

Shaping the distribution of neural responses with interneurons in a recurrent circuit model

Efficient coding theory posits that sensory circuits transform natural signals into neural representations that maximize information transmission subject to resource constraints. Local interneurons are thought to play an important role in these transformations, dynamically shaping patterns of local circuit activity to facilitate and direct information flow. However, the relationship between these coordinated, nonlinear, circuit-level transformations and the properties of interneurons (e.g., connectivity, activation functions, response dynamics) remains unknown. Here, we propose a normative computational model that establishes such a relationship. Our model is derived from an optimal transport objective that conceptualizes the circuit's input-response function as transforming the inputs to achieve an efficient target response distribution. The circuit, which is comprised of primary neurons that are recurrently connected to a set of local interneurons, continuously optimizes this objective by dynamically adjusting both the synaptic connections between neurons as well as the interneuron activation functions. In an example application motivated by redundancy reduction, we construct a circuit that learns a dynamical nonlinear transformation that maps natural image data to a spherical Gaussian, significantly reducing statistical dependencies in neural responses. Overall, our results provide a framework in which the distribution of circuit responses is systematically and nonlinearly controlled by adjustment of interneuron connectivity and activation functions.

q-bio.NC↗
arXiv2024

Video prediction using score-based conditional density estimation

Temporal prediction is inherently uncertain, but representing the ambiguity in natural image sequences is a challenging high-dimensional probabilistic inference problem. For natural scenes, the curse of dimensionality renders explicit density estimation statistically and computationally intractable. Here, we describe an implicit regression-based framework for learning and sampling the conditional density of the next frame in a video given previous observed frames. We show that sequence-to-image deep networks trained on a simple resilience-to-noise objective function extract adaptive representations for temporal prediction. Synthetic experiments demonstrate that this score-based framework can handle occlusion boundaries: unlike classical methods that average over bifurcating temporal trajectories, it chooses among likely trajectories, selecting more probable options with higher frequency. Furthermore, analysis of networks trained on natural image sequences reveals that the representation automatically weights predictive evidence by its reliability, which is a hallmark of statistical inference

cs.CV↗
arXiv2024

Feature-guided score diffusion for sampling conditional densities

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target density. Variants for conditional densities have been developed, but correct estimation of the corresponding scores is difficult. We avoid these difficulties by introducing an algorithm that guides the diffusion with a projected score. The projection pushes the image feature vector towards the feature vector centroid of the target class. The projected score and the feature vectors are learned by the same network. Specifically, the image feature vector is defined as the spatial averages of the channels activations in select layers of the network. Optimizing the projected score for denoising loss encourages image feature vectors of each class to cluster around their centroids. It also leads to the separations of the centroids. We show that these centroids provide a low-dimensional Euclidean embedding of the class conditional densities. We demonstrate that the algorithm can generate high quality and diverse samples from the conditioning class. Conditional generation can be performed using feature vectors interpolated between those of the training set, demonstrating out-of-distribution generalization.

cs.CV↗
arXiv2024

Layerwise complexity-matched learning yields an improved model of cortical area V2

Human ability to recognize complex visual patterns arises through transformations performed by successive areas in the ventral visual cortex. Deep neural networks trained end-to-end for object recognition approach human capabilities, and offer the best descriptions to date of neural responses in the late stages of the hierarchy. But these networks provide a poor account of the early stages, compared to traditional hand-engineered models, or models optimized for coding efficiency or prediction. Moreover, the gradient backpropagation used in end-to-end learning is generally considered to be biologically implausible. Here, we overcome both of these limitations by developing a bottom-up self-supervised training methodology that operates independently on successive layers. Specifically, we maximize feature similarity between pairs of locally-deformed natural image patches, while decorrelating features across patches sampled from other images. Crucially, the deformation amplitudes are adjusted proportionally to receptive field sizes in each layer, thus matching the task complexity to the capacity at each stage of processing. In comparison with architecture-matched versions of previous models, we demonstrate that our layerwise complexity-matched learning (LCL) formulation produces a two-stage model (LCL-V2) that is better aligned with selectivity properties and neural activity in primate area V2. We demonstrate that the complexity-matched learning paradigm is responsible for much of the emergence of the improved biological alignment. Finally, when the two-stage model is used as a fixed front-end for a deep network trained to perform object recognition, the resultant model (LCL-V2Net) is significantly better than standard end-to-end self-supervised, supervised, and adversarially-trained models in terms of generalization to out-of-distribution tasks and alignment with human behavior.

q-bio.NC↗
arXiv2024

Generalization in diffusion models arises from geometry-adaptive harmonic representations

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but recent reports of memorization of the training set raise the question of whether these networks are learning the "true" continuous density of the data. Here, we show that two DNNs trained on non-overlapping subsets of a dataset learn nearly the same score function, and thus the same density, when the number of training images is large enough. In this regime of strong generalization, diffusion-generated images are distinct from the training set, and are of high visual quality, suggesting that the inductive biases of the DNNs are well-aligned with the data density. We analyze the learned denoising functions and show that the inductive biases give rise to a shrinkage operation in a basis adapted to the underlying image. Examination of these bases reveals oscillating harmonic structures along contours and in homogeneous regions. We demonstrate that trained denoisers are inductively biased towards these geometry-adaptive harmonic bases since they arise not only when the network is trained on photographic images, but also when it is trained on image classes supported on low-dimensional manifolds for which the harmonic basis is suboptimal. Finally, we show that when trained on regular image classes for which the optimal basis is known to be geometry-adaptive and harmonic, the denoising performance of the networks is near-optimal.

cs.CV↗
arXiv2023

A polar prediction model for learning to represent visual transformations

All organisms make temporal predictions, and their evolutionary fitness level depends on the accuracy of these predictions. In the context of visual perception, the motions of both the observer and objects in the scene structure the dynamics of sensory signals, allowing for partial prediction of future signals based on past ones. Here, we propose a self-supervised representation-learning framework that extracts and exploits the regularities of natural videos to compute accurate predictions. We motivate the polar architecture by appealing to the Fourier shift theorem and its group-theoretic generalization, and we optimize its parameters on next-frame prediction. Through controlled experiments, we demonstrate that this approach can discover the representation of simple transformation groups acting in data. When trained on natural video datasets, our framework achieves better prediction performance than traditional motion compensation and rivals conventional deep networks, while maintaining interpretability and speed. Furthermore, the polar computations can be restructured into components resembling normalized simple and direction-selective complex cell models of primate V1 neurons. Thus, polar prediction offers a principled framework for understanding how the visual system represents sensory inputs in a form that simplifies temporal prediction.

stat.ML↗
arXiv2023

Adaptive whitening with fast gain modulation and slow synaptic plasticity

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

q-bio.NC↗
arXiv2023

Adaptive whitening in neural populations with gain-modulating interneurons

Statistical whitening transformations play a fundamental role in many computational systems, and may also play an important role in biological sensory systems. Existing neural circuit models of adaptive whitening operate by modifying synaptic interactions; however, such modifications would seem both too slow and insufficiently reversible. Motivated by the extensive neuroscience literature on gain modulation, we propose an alternative model that adaptively whitens its responses by modulating the gains of individual neurons. Starting from a novel whitening objective, we derive an online algorithm that whitens its outputs by adjusting the marginal variances of an overcomplete set of projections. We map the algorithm onto a recurrent neural network with fixed synaptic weights and gain-modulating interneurons. We demonstrate numerically that sign-constraining the gains improves robustness of the network to ill-conditioned inputs, and a generalization of the circuit achieves a form of local whitening in convolutional populations, such as those found throughout the visual or auditory systems.

q-bio.NC↗
arXiv2023

Adaptive coding efficiency in recurrent cortical circuits via gain control

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

q-bio.NC↗
arXiv2021

Unsupervised Deep Video Denoising

Deep convolutional neural networks (CNNs) for video denoising are typically trained with supervision, assuming the availability of clean videos. However, in many applications, such as microscopy, noiseless videos are not available. To address this, we propose an Unsupervised Deep Video Denoiser (UDVD), a CNN architecture designed to be trained exclusively with noisy data. The performance of UDVD is comparable to the supervised state-of-the-art, even when trained only on a single short noisy video. We demonstrate the promise of our approach in real-world imaging applications by denoising raw video, fluorescence-microscopy and electron-microscopy data. In contrast to many current approaches to video denoising, UDVD does not require explicit motion compensation. This is advantageous because motion compensation is computationally expensive, and can be unreliable when the input data are noisy. A gradient-based analysis reveals that UDVD automatically adapts to local motion in the input noisy videos. Thus, the network learns to perform implicit motion compensation, even though it is only trained for denoising.

eess.IV↗