Abstract The development of causal prediction models is challenged by the fact that the outcome is only observable for the applied (factual) intervention and not for its alternatives (the so-called counterfactuals); in medicine we only know patients’ survival for the administered drug and not for other therapeutic options. Machine learning approaches for counterfactual reasoning have to deal with both unobserved outcomes and distributional differences due to non-random treatment administration. Unsupervised domain adaptation (UDA) addresses similar issues; one has to deal with unobserved outcomes—the labels of the target domain—and distributional differences between source and target domain. We propose Adversarial Distribution Balancing for Counterfactual Reasoning (ADBCR), which directly uses potential outcome estimates of the counterfactuals to remove spurious causal relations. We show that ADBCR outcompetes state-of-the-art methods on three benchmark datasets, and demonstrate that ADBCR’s performance can be further improved if unlabeled validation data are included in the training procedure to better adapt the model to the validation domain.

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.

The neural activity in the visual processing is influenced by both external stimuli and internal brain states. Ideally, a neural predictive model should account for both of them. Currently, there are no dynamic encoding models that explicitly model a latent state and the entire neuronal response distribution. We address this gap by proposing a probabilistic model that predicts the joint distribution of the neuronal responses from video stimuli and stimulus-independent latent factors. After training and testing our model on mouse V1 neuronal responses, we find that it outperforms video-only models in terms of log-likelihood and achieves improvements in likelihood and correlation when conditioned on responses from other neurons. Furthermore, we find that the learned latent factors strongly correlate with mouse behavior and that they exhibit patterns related to the neurons’ position on the visual cortex, although the model was trained without behavior and cortical coordinates. Our findings demonstrate that unsupervised learning of latent factors from population responses can reveal biologically meaningful structure that bridges sensory processing and behavior, without requiring explicit behavioral annotations during training. The code is attached to the submission.

Modern neural recording techniques such as two-photon imaging or Neuropixel probes allow to acquire vast time-series datasets with responses of hundreds or thousands of neurons. Contrastive learning is a powerful self-supervised framework for learning representations of complex datasets. Existing applications for neural time series rely on generic data augmentations and do not exploit the multi-trial data structure inherent in many neural datasets. Here we present TRACE, a new contrastive learning framework that averages across different subsets of trials to generate positive pairs. TRACE allows to directly learn a two-dimensional embedding, combining ideas from contrastive learning and neighbor embeddings. We show that TRACE outperforms other methods, resolving fine response differences in simulated data. Further, using in vivo recordings, we show that the representations learned by TRACE capture both biologically relevant continuous variation, cell-type-related cluster structure, and can assist data quality control.

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly combined via a learned weight vector to represent a neuron's function. Such weight vectors, which can be thought as embeddings of neuronal function, have been proposed to define functional cell types via unsupervised clustering. However, as deep models are usually highly overparameterized, the learning problem is unlikely to have a unique solution, which raises the question if such embeddings can be used in a meaningful way for downstream analysis. In this paper, we investigate how stable neuronal embeddings are with respect to changes in model architecture and initialization. We find that $L_1$ regularization to be an important ingredient for structured embeddings and develop an adaptive regularization that adjusts the strength of regularization per neuron. This regularization improves both predictive performance and how consistently neuronal embeddings cluster across model fits compared to uniform regularization. To overcome overparametrization, we propose an iterative feature pruning strategy which reduces the dimensionality of performance-optimized models by half without loss of performance and improves the consistency of neuronal embeddings with respect to clustering neurons. Our results suggest that to achieve an objective taxonomy of cell types or a compact representation of the functional landscape, we need novel architectures or learning techniques that improve identifiability. The code is available https://github.com/pollytur/readout_reproducibility.

Understanding how biological visual systems process information is challenging because of the nonlinear relationship between visual input and neuronal responses. Artificial neural networks allow computational neuroscientists to create predictive models that connect biological and machine vision.Machine learning has benefited tremendously from benchmarks that compare different models on the same task under standardized conditions. However, there was no standardized benchmark to identify state-of-the-art dynamic models of the mouse visual system.To address this gap, we established the SENSORIUM 2023 Benchmark Competition with dynamic input, featuring a new large-scale dataset from the primary visual cortex of ten mice. This dataset includes responses from 78,853 neurons to 2 hours of dynamic stimuli per neuron, together with behavioral measurements such as running speed, pupil dilation, and eye movements.The competition ranked models in two tracks based on predictive performance for neuronal responses on a held-out test set: one focusing on predicting in-domain natural stimuli and another on out-of-distribution (OOD) stimuli to assess model generalization.As part of the NeurIPS 2023 Competition Track, we received more than 160 model submissions from 22 teams. Several new architectures for predictive models were proposed, and the winning teams improved the previous state-of-the-art model by 50\%. Access to the dataset as well as the benchmarking infrastructure will remain online at www.sensorium-competition.net.

Responses to natural stimuli in area V4-a mid-level area of the visual ventral stream-are well predicted by features from convolutional neural networks (CNNs) trained on image classification. This result has been taken as evidence for the functional role of V4 in object classification. However, we currently do not know if and to what extent V4 plays a role in solving other computational objectives. Here, we investigated normative accounts of V4 (and V1 for comparison) by predicting macaque single-neuron responses to natural images from the representations extracted by 23 CNNs trained on different computer vision tasks including semantic, geometric, 2D, and 3D types of tasks. We found that V4 was best predicted by semantic classification features and exhibited high task selectivity, while the choice of task was less consequential to V1 performance. Consistent with traditional characterizations of V4 function that show its high-dimensional tuning to various 2D and 3D stimulus directions, we found that diverse non-semantic tasks explained aspects of V4 function that are not captured by individual semantic tasks. Nevertheless, jointly considering the features of a pair of semantic classification tasks was sufficient to yield one of our top V4 models, solidifying V4's main functional role in semantic processing and suggesting that V4's selectivity to 2D or 3D stimulus properties found by electrophysiologists can result from semantic functional goals.

Neural population responses in sensory systems are driven by external physical stimuli. This stimulus-response relationship is typically characterized by receptive fields, which have been estimated by neural system identification approaches. Such models usually require a large amount of training data, yet, the recording time for animal experiments is limited, giving rise to epistemic uncertainty for the learned neural transfer functions. While deep neural network models have demonstrated excellent power on neural prediction, they usually do not provide the uncertainty of the resulting neural representations and derived statistics, such as most exciting inputs (MEIs), from in silico experiments. Here, we present a Bayesian system identification approach to predict neural responses to visual stimuli, and explore whether explicitly modeling network weight variability can be beneficial for identifying neural response properties. To this end, we use variational inference to estimate the posterior distribution of each model weight given the training data. Tests with different neural datasets demonstrate that this method can achieve higher or comparable performance on neural prediction, with a much higher data efficiency compared to Monte Carlo dropout methods and traditional models using point estimates of the model parameters. At the same time, our variational method provides us with an effectively infinite ensemble, avoiding the idiosyncrasy of any single model, to generate MEIs. This allows us to estimate the uncertainty of stimulus-response function, which we have found to be negatively correlated with the predictive performance at model level and may serve to evaluate models. Furthermore, our approach enables us to identify response properties with credible intervals and to determine whether the inferred features are meaningful by performing statistical tests on MEIs. Finally, in silico experiments show that our model generates stimuli driving neuronal activity significantly better than traditional models in the limited-data regime.

In recent years, most exciting inputs (MEIs) synthesized from encoding models of neuronal activity have become an established method for studying tuning properties of biological and artificial visual systems. However, as we move up the visual hierarchy, the complexity of neuronal computations increases. Consequently, it becomes more challenging to model neuronal activity, requiring more complex models. In this study, we introduce a novel readout architecture inspired by the mechanism of visual attention. This new architecture, which we call attention readout, together with a data-driven convolutional core outperforms previous task-driven models in predicting the activity of neurons in macaque area V4. However, as our predictive network becomes deeper and more complex, synthesizing MEIs via straightforward gradient ascent (GA) can struggle to produce qualitatively good results and overfit to idiosyncrasies of a more complex model, potentially decreasing the MEI's model-to-brain transferability. To solve this problem, we propose a diffusion-based method for generating MEIs via Energy Guidance (EGG). We show that for models of macaque V4, EGG generates single neuron MEIs that generalize better across varying model architectures than the state-of-the-art GA, while at the same time reducing computational costs by a factor of 4.7x, facilitating experimentally challenging closed-loop experiments. Furthermore, EGG diffusion can be used to generate other neurally exciting images, like most exciting naturalistic images that are on par with a selection of highly activating natural images, or image reconstructions that generalize better across architectures. Finally, EGG is simple to implement, requires no retraining of the diffusion model, and can easily be generalized to provide other characterizations of the visual system, such as invariances. Thus, EGG provides a general and flexible framework to study the coding properties of the visual system in the context of natural images.

Prevailing theories of perception hypothesize that the brain implements perception via Bayesian inference in a generative model of the world. One prominent theory, the Neural Sampling Code (NSC), posits that neuronal responses to a stimulus represent samples from the posterior distribution over latent world state variables that cause the stimulus. Although theoretically elegant, NSC does not specify the exact form of the generative model or prescribe how to link the theory to recorded neuronal activity. Previous works assume simple generative models and test their qualitative agreement with neurophysiological data. Currently, there is no precise alignment of the normative theory with neuronal recordings, especially in response to natural stimuli, and a quantitative, experimental evaluation of models under NSC has been lacking. Here, we propose a novel formalization of NSC, that (a) allows us to directly fit NSC generative models to recorded neuronal activity in response to natural images, (b) formulate richer and more flexible generative models, and (c) employ standard metrics to quantitatively evaluate different generative models under NSC. Furthermore, we derive a stimulus-conditioned predictive model of neuronal responses from the trained generative model using our formalization that we compare to neural system identification models. We demonstrate our approach by fitting and comparing classical- and flexible deep learning-based generative models on population recordings from the macaque primary visual cortex (V1) to natural images, and show that the flexible models outperform classical models in both their generative- and predictive-model performance. Overall, our work is an important step towards a quantitative evaluation of NSC. It provides a framework that lets us \textit{learn} the generative model directly from neuronal population recordings, paving the way for an experimentally-informed understanding of probabilistic computational principles underlying perception and behavior.

Transferring knowledge embedded in trained neural networks is a core problem in areas like model compression and continual learning. Among knowledge transfer approaches, functional transfer methods such as knowledge distillation and representational distance learning are particularly promising, since they allow for transferring knowledge across different architectures and tasks. Considering various characteristics of networks that are desirable to transfer, equivariance is a notable property that enables a network to capture valuable relationships in the data. We assess existing functional transfer methods on their ability to transfer equivariance and empirically show that they fail to even transfer shift equivariance, one of the simplest equivariances. Further theoretical analysis demonstrates that representational similarity methods, in fact, cannot guarantee the transfer of the intended equivariance. Motivated by these findings, we develop a novel transfer method that learns an equivariance model from a given teacher network and encourages the student network to acquire the same equivariance, via regularization. Experiments show that our method successfully transfers equivariance even in cases where highly restrictive methods, such as directly matching student and teacher representations, fail.

We present a joint deep neural system identification model for two major sources of neural variability: stimulus-driven and stimulus-conditioned fluctuations. To this end, we combine (1) state-of-the-art deep networks for stimulus-driven activity and (2) a flexible, normalizing flow-based generative model to capture the stimulus-conditioned variability including noise correlations. This allows us to train the model end-to-end without the need for sophisticated probabilistic approximations associated with many latent state models for stimulus-conditioned fluctuations. We train the model on the responses of thousands of neurons from multiple areas of the mouse visual cortex to natural images. We show that our model outperforms previous state-of-the-art models in predicting the distribution of neural population responses to novel stimuli, including shared stimulus-conditioned variability. Furthermore, it successfully learns known latent factors of the population responses that are related to behavioral variables such as pupil dilation, and other factors that vary systematically with brain area or retinotopic location. Overall, our model accurately accounts for two critical sources of neural variability while avoiding several complexities associated with many existing latent state models. It thus provides a useful tool for uncovering the interplay between different factors that contribute to variability in neural activity.

Deep neural networks set the state-of-the-art across many tasks in computer vision, but their generalization ability to simple image distortions is surprisingly fragile. In contrast, the mammalian visual system is robust to a wide range of perturbations. Recent work suggests that this generalization ability can be explained by useful inductive biases encoded in the representations of visual stimuli throughout the visual cortex. Here, we successfully leveraged these inductive biases with a multi-task learning approach: we jointly trained a deep network to perform image classification and to predict neural activity in macaque primary visual cortex (V1) in response to the same natural stimuli. We measured the out-of-distribution generalization abilities of our resulting network by testing its robustness to common image distortions. We found that co-training on monkey V1 data indeed leads to increased robustness despite the absence of those distortions during training. Additionally, we showed that our network's robustness is often very close to that of an Oracle network where parts of the architecture are directly trained on noisy images. Our results also demonstrated that the network's representations become more brain-like as their robustness improves. Using a novel constrained reconstruction analysis, we investigated what makes our brain-regularized network more robust. We found that our monkey co-trained network is more sensitive to content than noise when compared to a Baseline network that we trained for image classification alone. Using DeepGaze-predicted saliency maps for ImageNet images, we found that the monkey co-trained network tends to be more sensitive to salient regions in a scene, reminiscent of existing theories on the role of V1 in the detection of object borders and bottom-up saliency. Overall, our work expands the promising research avenue of transferring inductive biases from biological to artificial neural networks on the representational level, and provides a novel analysis of the effects of our transfer.

In recent years, artificial neural networks have achieved state-of-the-art performance for predicting the responses of neurons in the visual cortex to natural stimuli. However, they require a time consuming parameter optimization process for accurately modeling the tuning function of newly observed neurons, which prohibits many applications including real-time, closed-loop experiments. We overcome this limitation by formulating the problem as $K$-shot prediction to directly infer a neuron's tuning function from a small set of stimulus-response pairs using a Neural Process. This required us to developed a Factorized Neural Process, which embeds the observed set into a latent space partitioned into the receptive field location and the tuning function properties. We show on simulated responses that the predictions and reconstructed receptive fields from the Factorized Neural Process approach ground truth with increasing number of trials. Critically, the latent representation that summarizes the tuning function of a neuron is inferred in a quick, single forward pass through the network. Finally, we validate this approach on real neural data from visual cortex and find that the predictive accuracy is comparable to --- and for small $K$ even greater than --- optimization based approaches, while being substantially faster. We believe this novel deep learning systems identification framework will facilitate better real-time integration of artificial neural network modeling into neuroscience experiments.

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We propose to regularize CNNs using large-scale neuroscience data to learn more robust neural features in terms of representational similarity. We presented natural images to mice and measured the responses of thousands of neurons from cortical visual areas. Next, we denoised the notoriously variable neural activity using strong predictive models trained on this large corpus of responses from the mouse visual system, and calculated the representational similarity for millions of pairs of images from the model's predictions. We then used the neural representation similarity to regularize CNNs trained on image classification by penalizing intermediate representations that deviated from neural ones. This preserved performance of baseline models when classifying images under standard benchmarks, while maintaining substantially higher performance compared to baseline or control models when classifying noisy images. Moreover, the models regularized with cortical representations also improved model robustness in terms of adversarial attacks. This demonstrates that regularizing with neural data can be an effective tool to create an inductive bias towards more robust inference.

To better understand the representations in visual cortex, we need to generate better predictions of neural activity in awake animals presented with their ecological input: natural video. Despite recent advances in models for static images, models for predicting responses to natural video are scarce and standard linear-nonlinear models perform poorly. We developed a new deep recurrent network architecture that predicts inferred spiking activity of thousands of mouse V1 neurons simultaneously recorded with two-photon microscopy, while accounting for confounding factors such as the animal's gaze position and brain state changes related to running state and pupil dilation. Powerful system identification models provide an opportunity to gain insight into cortical functions through in silico experiments that can subsequently be tested in the brain. However, in many cases this approach requires that the model is able to generalize to stimulus statistics that it was not trained on, such as band-limited noise and other parameterized stimuli. We investigated these domain transfer properties in our model and find that our model trained on natural images is able to correctly predict the orientation tuning of neurons in responses to artificial noise stimuli. Finally, we show that we can fully generalize from movies to noise and maintain high predictive performance on both stimulus domains by fine-tuning only the final layer's weights on a network otherwise trained on natural movies. The converse, however, is not true.

We present a novel non-parametric method for finding a subspace of stimulus features that contains all information about the response of a system. Our method generalizes similar approaches to this problem such as spike triggered average, spike triggered covariance, or maximally informative dimensions. Instead of maximizing the mutual information between features and responses directly, we use integral probability metrics in kernel Hilbert spaces to minimize the information between uninformative features and the combination of informative features and responses. Since estimators of these metrics access the data via kernels, are easy to compute, and exhibit good theoretical convergence properties, our method can easily be generalized to populations of neurons or spike patterns. By using a particular expansion of the mutual information, we can show that the informative features must contain all information if we can make the uninformative features independent of the rest.

Divisive normalization has been proposed as a nonlinear redundancy reduction mechanism capturing contrast correlations. Its basic function is a radial rescaling of the population response. Because of the saturation of divisive normalization, however, it is impossible to achieve a fully independent representation. In this letter, we derive an analytical upper bound on the inevitable residual redundancy of any saturating radial rescaling mechanism.

Divisive normalization in primary visual cortex has been linked to adaptation to natural image statistics in accordance to Barlow's redundancy reduction hypothesis. Using recent advances in natural image modeling, we show that the previously studied static model of divisive normalization is rather inefficient in reducing local contrast correlations, but that a simple temporal contrast adaptation mechanism of the half-saturation constant can substantially increase its efficiency. Our findings reveal the experimentally observed temporal dynamics of divisive normalization to be critical for redundancy reduction.

We introduce a new family of distributions, called $L_p${\em -nested symmetric distributions}, whose densities access the data exclusively through a hierarchical cascade of $L_p$-norms. This class generalizes the family of spherically and $L_p$-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family also includes the Independent Subspace Analysis (ISA) model, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. $L_p$-nested distributions are easy to estimate and allow us to explore the variety of models between ISA and the $L_p$-spherically symmetric models. Our main findings are that, without a preprocessing step of contrast gain control, the independent subspaces of ISA are in fact more dependent than the individual filter coefficients within a subspace and, with contrast gain control, where ISA finds more than one subspace, the filter responses were almost independent anyway.

Orientation selectivity is the most striking feature of simple cell coding in V1 that has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding, it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. To assess the tenability of this hypothesis, it is an important empirical question how much more redundancy can be removed with ICA in comparison to PCA or other second-order decorrelation methods. Although some previous studies have concluded that the amount of higher-order correlation in natural images is generally insignificant, other studies reported an extra gain for ICA of more than 100%. A consistent conclusion about the role of higher-order correlations in natural images can be reached only by the development of reliable quantitative evaluation methods. Here, we present a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss, we compute complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is small. At the same time, we show that a simple spherically symmetric distribution with only two parameters can fit the data significantly better than the probabilistic model underlying ICA. This finding suggests that, although the amount of higher-order correlation in natural images can in fact be significant, the feature of orientation selectivity does not yield a large contribution to redundancy reduction within the linear filter bank models of V1 simple cells.

Bandpass filtering, orientation selectivity, and contrast gain control are prominent features of sensory coding at the level of V1 simple cells. While the effect of bandpass filtering and orientation selectivity can be assessed within a linear model, contrast gain control is an inherently nonlinear computation. Here we employ the class of $L_p$ elliptically contoured distributions to investigate the extent to which the two features---orientation selectivity and contrast gain control---are suited to model the statistics of natural images. Within this framework we find that contrast gain control can play a significant role for the removal of redundancies in natural images. Orientation selectivity, in contrast, has only a very limited potential for redundancy reduction.

We study a pattern classification algorithm which has recently been proposed by Vapnik and coworkers. It builds on a new inductive principle which assumes that in addition to positive and negative data, a third class of data is available, termed the Universum. We assay the behavior of the algorithm by establishing links with Fisher discriminant analysis and oriented PCA, as well as with an SVM in a pro- jected subspace (or, equivalently, with a data-dependent reduced kernel). We also provide experimental results.

Convex learning algorithms, such as Support Vector Machines (SVMs), are often seen as highly desirable because they offer strong practical properties and are amenable to theoretical analysis. However, in this work we show how non-convexity can provide scalability advantages over convexity. We show how concave-convex programming can be applied to produce (i) faster SVMs where training errors are no longer support vectors, and (ii) much faster Transductive SVMs.

In this paper we study a new framework introduced by Vapnik (1998) and Vapnik (2006) that is an alternative capacity concept to the large margin approach. In the particular case of binary classification, we are given a set of labeled examples, and a collection of "non-examples" that do not belong to either class of interest. This collection, called the Universum, allows one to encode prior knowledge by representing meaningful concepts in the same domain as the problem at hand. We describe an algorithm to leverage the Universum by maximizing the number of observed contradictions, and show experimentally that this approach delivers accuracy improvements over using labeled data alone.

We show how the concave-convex procedure can be applied to transductive SVMs, which traditionally require solving a combinatorial search problem. This provides for the first time a highly scalable algorithm in the nonlinear case. Detailed experiments verify the utility of our approach. Software is available at http://www.kyb.tuebingen.mpg.de/bs/people/fabee/transduction.html.