The role of temporal information in predicting human gaze in dynamic scenes remains a critical open question, underscored by the paradoxical finding that strong static models can outperform complex video-based models. This suggests that the true contribution of temporal cues has been obscured by confounding architectural variables. To resolve this, we present a rigorous, controlled experiment centered on a minimal architectural pair: a spatio-temporal saliency model (UniformerSal-ST) and its identical spatial-only counterpart (UniformerSal-S), designed to unambiguously isolate the impact of temporal feature integration. Our results demonstrate that principled temporal fusion yields a substantial Information Gain (IG) of +0.20 bits on temporally coherent datasets like LEDOV. Crucially, our controlled comparison also uncovers a key failure mode: on datasets with frequent hard cuts like DIEM, the same mechanism degrades performance, incurring a 0.07 bits IG deficit. We provide a mechanistic explanation for this dichotomy, revealing how certain visual scenarios (scene discontinuities, rapid camera zooms) can disrupt current temporal fusion approaches. By precisely quantifying both the benefits and drawbacks of temporal processing, our work provides the community with clear, actionable insights into when and why temporal information should be modeled for more robust and accurate video saliency prediction. The code will be made available at https: //github.com/peterjiz/uniformersal

Adhiraj Ghosh, Sebastian Dziadzio, Ameya Prabhu, Vishaal Udandarao, Samuel Albanie, Matthias Bethge. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Model merging combines multiple "expert" models— finetuned from a base foundation model on diverse tasks and domains—into a single, more capable model. However, most existing model merging approaches assume that all experts are available simultaneously. In reality, new tasks and domains emerge progressively over time, requiring strategies to integrate the knowledge of expert models as they become available: a process we call temporal model merging. The temporal dimension introduces unique challenges not addressed in prior work, raising new questions such as: when training for a new task, should the expert model start from the merged past experts or from the original base model? Should we merge all models at each time step? Which merging techniques are best suited for temporal merging? Should different strategies be used to initialize the training and deploy the model? To answer these questions, we propose a unified framework called TIME—Temporal Integration of Model Expertise—which defines temporal model merging across three axes: (1) Initialization Phase, (2) Deployment Phase, and (3) Merging Technique. Using TIME, we study temporal model merging across model sizes, compute budgets, and learning horizons on the FoMo-in-Flux benchmark. Our comprehensive suite of experiments across TIME allows us to uncover key insights for temporal model merging, offering a better understanding of current challenges and best practices for effective temporal model merging. Our code is available here.

Recent advances in image-based saliency prediction are approaching gold standard performance levels on existing benchmarks. Despite this success, we show that predicting fixations across multiple saliency datasets remains challenging due to dataset bias. We find a significant performance drop (around 40%) when models trained on one dataset are applied to another. Surprisingly, increasing dataset diversity does not resolve this inter-dataset gap, with close to 60% attributed to dataset-specific biases. To address this remaining generalization gap, we propose a novel architecture extending a mostly dataset-agnostic encoder-decoder structure with fewer than 20 dataset-specific parameters that govern interpretable mechanisms such as multi-scale structure, center bias, and fixation spread. Adapting only these parameters to new data accounts for more than 75% of the generalization gap, with a large fraction of the improvement achieved with as few as 50 samples. Our model sets a new state-of-the-art on all three datasets of the MIT/Tuebingen Saliency Benchmark (MIT300, CAT2000, and COCO-Freeview), even when purely generalizing from unrelated datasets, but with a substantial boost when adapting to the respective training datasets. The model also provides valuable insights into spatial saliency properties, revealing complex multi-scale effects that combine both absolute and relative sizes.

The emergence of audio-visual foundation models underscores the importance of reliably assessing their multi-modal understanding. The VGGSound dataset is commonly used as a benchmark for evaluation audio-visual classification. However, our analysis identifies several limitations of VGGSound, including incomplete labelling, partially overlapping classes, and misaligned modalities. These lead to distorted evaluations of auditory and visual capabilities. To address these limitations, we introduce VGGSounder, a comprehensively re-annotated, multi-label test set that extends VGGSound and is specifically designed to evaluate audio-visual foundation models. VGGSounder features detailed modality annotations, enabling precise analyses of modality-specific performance. Furthermore, we reveal model limitations by analysing performance degradation when adding another input modality with our new modality confusion metric.

This work aims to recover the underlying states and their time evolution in a latent dynamical system from high-dimensional sensory measurements. Previous works on identifiable representation learning in dynamical systems focused on identifying the latent states, often with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. Our identifiability theory relies on two key assumptions: (i) sufficient variability in the latent noise, and (ii) the bijectivity of the augmented transition function. Drawing from this theory, we introduce a practical algorithm based on variational auto-encoders. We empirically demonstrate that it improves generalization and interpretability of target dynamical systems by (i) recovering latent state dynamics with high accuracy, (ii) correspondingly achieving high future prediction accuracy, and (iii) adapting fast to new environments. Additionally, for complex real-world dynamics, (iv) it produces state-of the-art future prediction results for long horizons, highlighting its usefulness for practical scenarios.

Out-of-Domain (OOD) generalization is the ability of a model trained on one or more domains to generalize to unseen domains. In the ImageNet era of computer vision, evaluation sets for measuring a model's OOD performance were designed to be strictly OOD with respect to style. However, the emergence of foundation models and expansive web-scale datasets has obfuscated this evaluation process, as datasets cover a broad range of domains and risk test domain contamination. In search of the forgotten domain generalization, we create large-scale datasets subsampled from LAION---LAION-Natural and LAION-Rendition---that are strictly OOD to corresponding ImageNet and DomainNet test sets in terms of style. Training CLIP models on these datasets reveals that a significant portion of their performance is explained by in-domain examples. This indicates that the OOD generalization challenges from the ImageNet era still prevail and that training on web-scale data merely creates the illusion of OOD generalization. Furthermore, through a systematic exploration of combining natural and rendition datasets in varying proportions, we identify optimal mixing ratios for model generalization across these domains. Our datasets and results re-enable meaningful assessment of OOD robustness at scale---a crucial prerequisite for improving model robustness.

Pre-trained vision language models still fall short of human visual cognition. In an effort to improve visual cognition and align models with human behavior, we introduce visual stimuli and human judgments on visual cognition tasks, allowing us to systematically evaluate performance across cognitive domains under a consistent environment. We fine-tune models on ground truth data for intuitive physics and causal reasoning and find that this improves model performance in the respective fine-tuning domain. Furthermore, it can improve model alignment with human behavior. However, we find that task-specific fine-tuning does not contribute to robust human-like generalization to data with other visual characteristics or to tasks in other cognitive domains.

As Language Model (LM) capabilities advance, evaluating and supervising them at scale is getting harder for humans. There is hope that other language models can automate both these tasks, which we refer to as AI Oversight. We study how model similarity affects both aspects of AI oversight by proposing Chance Adjusted Probabilistic Agreement (CAPA)–a metric for LM similarity based on overlap in model mistakes. Using CAPA, we first show that LLM-as-a-judge scores favor models similar to the judge, generalizing recent self-preference results. Then, we study training on LM annotations, and find complementary knowledge between the weak supervisor and strong student model plays a crucial role in gains from weak-to-strong generalization. As model capabilities increase, it becomes harder to find their mistakes, and we might defer more to AI oversight. However, we observe a concerning trend–model mistakes are becoming more similar with increasing capabilities, pointing to risks from correlated failures. Our work underscores the importance of reporting and correcting for model similarity, especially in the emerging paradigm of AI oversight.

Scaling laws guide the development of large language models (LLMs) by offering estimates for the optimal balance of model size, tokens, and compute. More recently, loss-to-loss scaling laws that relate losses across pretraining datasets and downstream tasks have emerged as a powerful tool for understanding and improving LLM performance and generalization. In this work, we investigate which factors most strongly influence loss-to-loss scaling. Our experiments reveal that the pretraining data determines the scaling trend. In contrast, model size, optimization hyperparameters, tokenizer and even significant architectural differences, such as between transformer-based models like Llama and state-space models like Mamba, generally have limited impact. Consequently, practitioners should carefully curate pretraining datasets for optimal downstream performance, while architectures and other settings can be freely optimized for training efficiency.

Keeping large language models factually up-to-date is crucial for deployment, yet costly retraining remains a challenge. Knowledge editing offers a promising alternative, but methods are only tested on small-scale or synthetic edit benchmarks. In this work, we aim to bridge research into lifelong knowledge editing to real-world edits at practically relevant scale. We first introduce WikiBigEdit; a large-scale benchmark of real-world Wikidata edits, built to automatically extend lifelong for future-proof benchmarking. In its first instance, it includes over 500K question-answer pairs for knowledge editing alongside a comprehensive evaluation pipeline. Finally, we use WikiBigEdit to study existing knowledge editing techniques’ ability to incorporate large volumes of real-world facts and contrast their capabilities to generic modification techniques such as retrieval augmentation and continual finetuning to acquire a complete picture of the practical extent of current lifelong knowledge editing.

Understanding how humans move their eyes to gather visual information is a central question in neuroscience, cognitive science, and vision research. While recent deep learning (DL) models achieve state-of-the-art performance in predicting human scanpaths, their underlying decision processes remain opaque. At an opposite end of the modeling spectrum, cognitively inspired mechanistic models aim to explain scanpath behavior through interpretable cognitive mechanisms but lag far behind in predictive accuracy. In this work, we bridge this gap by using a high-performing deep model—DeepGaze III—to discover and test mechanisms that improve a leading mechanistic model, SceneWalk. By identifying individual fixations where DeepGaze III succeeds and SceneWalk fails, we isolate behaviorally meaningful discrepancies and use them to motivate targeted extensions of the mechanistic framework. These include time-dependent temperature scaling, saccadic momentum and an adaptive cardinal attention bias: Simple, interpretable additions that substantially boost predictive performance. With these extensions, SceneWalk’s explained variance on the MIT1003 dataset doubles from 35% to 70%, setting a new state of the art in mechanistic scanpath prediction. Our findings show how performance-optimized neural networks can serve as tools for cognitive model discovery, offering a new path toward interpretable and high-performing models of visual behavior. Our code is available at https://github.com/bethgelab/what-moves-the-eyes

Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (SWE-Bench) and mathematics (FrontierMath). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTune benchmark consists of 120 tasks collected from domain experts and a framework for validating and timing LM-synthesized solution code, which is compared to reference implementations from popular open-source packages.In addition, we develop a baseline LM agent, AlgoTuner, and evaluate its performance across a suite of frontier models.AlgoTuner achieves an average 1.58x speedup against reference solvers, including methods from packages such as SciPy, scikit-learn and CVXPY.However, we find that current models fail to discover algorithmic innovations, instead preferring surface-level optimizations. We hope that AlgoTune catalyzes the development of LM agents exhibiting creative problem solving beyond state-of-the-art human performance.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps—without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

In the last decade, the generalization and adaptation abilities of deep learning models were typically evaluated on fixed training and test distributions.Contrary to traditional deep learning, large language models (LLMs) are (i) even more overparameterized, (ii) trained on unlabeled text corpora curated from the Internet with minimal human intervention, and (iii) trained in an online fashion.These stark contrasts prevent researchers from transferring lessons learned on model generalization and adaptation in deep learning contexts to LLMs.To this end, our short paper introduces empirical observations that aim to shed light on further training of already pretrained language models.Specifically, we demonstrate that training a model on a text domain could degrade its perplexity on the test portion of the same domain.We observe with our subsequent analysis that the performance degradation is positively correlated with the similarity between the additional and the original pretraining dataset of the LLM.Our further token-level perplexity observations reveals that the perplexity degradation is due to a handful of tokens that are not informative about the domain.We hope these findings will guide us in determining when to adapt a model vs when to rely on its foundational capabilities.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

Foundation models like CLIP are trained on hundreds of millions of samples and effortlessly generalize to new tasks and inputs. Out of the box, CLIP shows stellar zero-shot and few-shot capabilities on a wide range of out-of-distribution (OOD) benchmarks, which prior works attribute mainly to today's large and comprehensive training dataset (like LAION). However, it is questionable how meaningful terms like out-of-distribution generalization are for CLIP as it seems likely that web-scale datasets like LAION simply contain many samples that are similar to common OOD benchmarks originally designed for ImageNet. To test this hypothesis, we retrain CLIP on pruned LAION splits that replicate ImageNet’s train-test similarity with respect to common OOD benchmarks. While we observe a performance drop on some benchmarks, surprisingly, CLIP’s overall performance remains high. This shows that high train-test similarity is insufficient to explain CLIP’s OOD performance, and other properties of the training data must drive CLIP to learn more generalizable representations. Additionally, by pruning data points that are dissimilar to the OOD benchmarks, we uncover a 100M split of LAION (¼ of its original size) on which CLIP can be trained to match its original OOD performance.

Recent advances in the development of vision-language models (VLMs) are yielding remarkable success in recognizing visual semantic content, including impressive instances of compositional image understanding. Here, we introduce the novel task of Visual Data-Type Identification, a basic perceptual skill with implications for data curation (e.g., noisy data-removal from large datasets, domains pecific retrieval) and autonomous vision (e.g., distinguishing changing weather conditions from camera lens staining). We develop two datasets consisting of animal images altered across a diverse set of 27 visual data-types, spanning four broad categories. An extensive zero-shot evaluation of 39 VLMs, ranging from 100M to 80B parameters, shows a nuanced performance landscape. While VLMs are reasonably good at identifying certain stylistic data-types, such as cartoons and sketches, they struggle with simpler data-types arising from basic manipulations like image rotations or additive noise. Our findings reveal that (i) model scaling alone yields marginal gains for contrastively-trained models like CLIP, and (ii) there is a pronounced drop in performance for the largest auto-regressively trained VLMs like OpenFlamingo. This finding points to a blind spot in current frontier VLMs: they excel in recognizing semantic content but fail to acquire an understanding of visual data-types through scaling. By analyzing the pre-training distributions of these models and incorporating data-type information into the captions during fine-tuning, we achieve a significant enhancement in performance. By exploring this previously uncharted task, we aim to set the stage for further advancing VLMs to equip them with visual data-type understanding.

Learning representations that generalize to novel compositions of known concepts is crucial for bridging the gap between human and machine perception. One prominent effort is learning object-centric representations, which are widely conjectured to enable compositional generalization. Yet, it remains unclear when this conjecture will be true, as a principled theoretical or empirical understanding of compositional generalization is lacking. In this work, we investigate when compositional generalization is guaranteed for object-centric representations through the lens of identifiability theory. We show that autoencoders that satisfy structural assumptions on the decoder and enforce encoder-decoder consistency will learn object-centric representations that provably generalize compositionally. We validate our theoretical result and highlight the practical relevance of our assumptions through experiments on synthetic image data.

Entropy minimization (EM) is frequently used to increase the accuracy of classification models when they're faced with new data at test time. EM is a self-supervised learning method that optimizes classifiers to assign even higher probabilities to their top predicted classes. In this paper, we analyze why EM works when adapting a model for a few steps and why it eventually fails after adapting for many steps. We show that, at first, EM causes the model to embed test images close to training images, thereby increasing model accuracy. After many steps of optimization, EM makes the model embed test images far away from the embeddings of training images, which results in a degradation of accuracy. Building upon our insights, we present a method for solving a practical problem: estimating a model's accuracy on a given arbitrary dataset without having access to its labels. Our method estimates accuracy by looking at how the embeddings of input images change as the model is optimized to minimize entropy. Experiments on 23 challenging datasets show that our method sets the SoTA with a mean absolute error of 5.75%, an improvement of 29.62% over the previous SoTA on this task. Our code is available at: https://github.com/oripress/EntropyEnigma

Standardized benchmarks drive progress in machine learning. However, with repeated testing, the risk of overfitting grows as algorithms over-exploit benchmark idiosyncrasies. In our work, we seek to mitigate this challenge by compiling \textit{ever-expanding} large-scale benchmarks called \textit{Lifelong Benchmarks}. As exemplars of our approach, we create \textit{Lifelong-CIFAR10} and \textit{Lifelong-ImageNet}, containing (for now) 1.69M and 1.98M test samples, respectively. While reducing overfitting, lifelong benchmarks introduce a key challenge: the high cost of evaluating a growing number of models across an ever-expanding sample set. To address this challenge, we also introduce an efficient evaluation framework: \textit{Sort \& Search (S\&S)}, which reuses previously evaluated models by leveraging dynamic programming algorithms to selectively rank and sub-select test samples, enabling cost-effective lifelong benchmarking. Extensive empirical evaluations across $\sim$31,000 models demonstrate that \textit{S\&S} achieves highly-efficient approximate accuracy measurement, reducing compute cost from 180 GPU days to 5 GPU hours ($\sim$1000x reduction) on a single A100 GPU, with low approximation error. As such, lifelong benchmarks offer a robust, practical solution to the ``benchmark exhaustion'' problem.

Thousands of new scientific papers are published each month. Such information overload complicates researcher efforts to stay current with the state-of-the-art as well as to verify and correctly attribute claims. We pose the following research question: Given a text excerpt referencing a paper, could an LM act as a research assistant to correctly identify the referenced paper? We advance efforts to answer this question by building a benchmark that evaluates the abilities of LMs in citation attribution. Our benchmark, CiteME, consists of text excerpts from recent machine learning papers, each referencing a single other paper. CiteME use reveals a large gap between frontier LMs and human performance, with LMs achieving only 4.2-18.5% accuracy and humans 69.7%. We close this gap by introducing CiteAgent, an autonomous system built on the GPT-4o LM that can also search and read papers, which achieves an accuracy of 35.3% on CiteME. Overall, CiteME serves as a challenging testbed for open-ended claim attribution, driving the research community towards a future where any claim made by an LM can be automatically verified and discarded if found to be incorrect.

Humans excel at detecting and segmenting moving objects according to the {\it Gestalt} principle of “common fate”. Remarkably, previous works have shown that human perception generalizes this principle in a zero-shot fashion to unseen textures or random dots. In this work, we seek to better understand the computational basis for this capability by evaluating a broad range of optical flow models and a neuroscience inspired motion energy model for zero-shot figure-ground segmentation of random dot stimuli. Specifically, we use the extensively validated motion energy model proposed by Simoncelli and Heeger in 1998 which is fitted to neural recordings in cortex area MT. We find that a cross section of 40 deep optical flow models trained on different datasets struggle to estimate motion patterns in random dot videos, resulting in poor figure-ground segmentation performance. Conversely, the neuroscience-inspired model significantly outperforms all optical flow models on this task. For a direct comparison to human perception, we conduct a psychophysical study using a shape identification task as a proxy to measure human segmentation performance. All state-of-the-art optical flow models fall short of human performance, but only the motion energy model matches human capability. This neuroscience-inspired model successfully addresses the lack of human-like zero-shot generalization to random dot stimuli in current computer vision models, and thus establishes a compelling link between the Gestalt psychology of human object perception and cortical motion processing in the brain. Code, models and datasets are available at https://github.com/mtangemann/motion_energy_segmentation

Web-crawled pretraining datasets underlie the impressive "zero-shot" evaluation performance of multimodal models, such as CLIP for classification and Stable-Diffusion for image generation. However, it is unclear how meaningful the notion of "zero-shot" generalization is for such multimodal models, as it is not known to what extent their pretraining datasets encompass the downstream concepts targeted for during "zero-shot" evaluation. In this work, we ask: How is the performance of multimodal models on downstream concepts influenced by the frequency of these concepts in their pretraining datasets? We comprehensively investigate this question across 34 models and 5 standard pretraining datasets (CC-3M, CC-12M, YFCC-15M, LAION-400M, LAION-Aesthetics), generating over 300GB of data artifacts. We consistently find that, far from exhibiting "zero-shot" generalization, multimodal models require exponentially more data to achieve linear improvements in downstream "zero-shot" performance, following a sample inefficient log-linear scaling trend. This trend persists even when controlling for sample-level similarity between pretraining and downstream datasets, and testing on purely synthetic data distributions. Furthermore, upon benchmarking models on long-tailed data sampled based on our analysis, we demonstrate that multimodal models across the board perform poorly. We contribute this long-tail test set as the Let it Wag! benchmark to further research in this direction. Taken together, our study reveals an exponential need for training data which implies that the key to "zero-shot" generalization capabilities under large-scale training data and compute paradigms remains to be found.

Multimodal foundation models serve numerous applications at the intersection of vision and language. Still, despite being pretrained on extensive data, they become outdated over time.To keep models updated, research into continual pretraining mainly explores scenarios with either (1) infrequent, indiscriminate updates on large-scale new data, or (2) frequent, sample-level updates.However, practical model deployment often operates in the gap between these two limit cases, as real-world applications demand adaptation to specific subdomains, tasks or concepts --- spread over the entire, varying life cycle of a model. In this work, we complement current perspectives on continual pretraining through a research test bed and offer comprehensive guidance for effective continual model updates in such scenarios.We first introduce FoMo-in-Flux, a continual multimodal pretraining benchmark with realistic compute constraints and practical deployment requirements, constructed over 63 datasets with diverse visual and semantic coverage.Using FoMo-in-Flux, we explore the complex landscape of practical continual pretraining through multiple perspectives: (1) data mixtures and stream orderings that emulate real-world deployment settings, (2) methods ranging from simple fine-tuning and traditional continual learning strategies to parameter-efficient updates and model merging, (3) meta-learning-rate schedules and mechanistic design choices, and (4) model and compute scaling. Together, our insights provide a practitioner's guide to continual multimodal pretraining for real-world deployment. Benchmark and code is provided here: https://github.com/ExplainableML/fomoinflux.

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 ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by auto-regressive encoder updates. In this work, we introduce Modulated Neural ODEs (MoNODEs), a novel framework that sets apart dynamics states from underlying static factors of variation and improves the existing NODE methods. In particular, we introduce *time-invariant modulator variables* that are learned from the data. We incorporate our proposed framework into four existing NODE variants. We test MoNODE on oscillating systems, videos and human walking trajectories, where each trajectory has trajectory-specific modulation. Our framework consistently improves the existing model ability to generalize to new dynamic parameterizations and to perform far-horizon forecasting. In addition, we verify that the proposed modulator variables are informative of the true unknown factors of variation as measured by $R^2$ scores.

Test-Time Adaptation (TTA) allows to update pre-trained models to changing data distributions at deployment time. While early work tested these algorithms for individual fixed distribution shifts, recent work proposed and applied methods for continual adaptation over long timescales. To examine the reported progress in the field, we propose the Continually Changing Corruptions (CCC) benchmark to measure asymptotic performance of TTA techniques. We find that eventually all but one state-of-the-art methods collapse and perform worse than a non-adapting model, including models specifically proposed to be robust to performance collapse. In addition, we introduce a simple baseline, "RDumb", that periodically resets the model to its pretrained state. RDumb performs better or on par with the previously proposed state-of-the-art in all considered benchmarks. Our results show that previous TTA approaches are neither effective at regularizing adaptation to avoid collapse nor able to outperform a simplistic resetting strategy.

Leveraging the compositional nature of our world to expedite learning and facilitate generalization is a hallmark of human perception. In machine learning, on the other hand, achieving compositional generalization has proven to be an elusive goal, even for models with explicit compositional priors. To get a better handle on compositional generalization, we here approach it from the bottom up: Inspired by identifiable representation learning, we investigate compositionality as a property of the data-generating process rather than the data itself. This reformulation enables us to derive mild conditions on only the support of the training distribution and the model architecture, which are sufficient for compositional generalization. We further demonstrate how our theoretical framework applies to real-world scenarios and validate our findings empirically. Our results set the stage for a principled theoretical study of compositional generalization.

Machine learning models have difficulty generalizing to data outside of the distribution they were trained on. In particular, vision models are usually vulnerable to adversarial attacks or common corruptions, to which the human visual system is robust. Recent studies have found that regularizing machine learning models to favor brain-like representations can improve model robustness, but it is unclear why. We hypothesize that the increased model robustness is partly due to the low spatial frequency preference inherited from the neural representation. We tested this simple hypothesis with several frequency-oriented analyses, including the design and use of hybrid images to probe model frequency sensitivity directly. We also examined many other publicly available robust models that were trained on adversarial images or with data augmentation, and found that all these robust models showed a greater preference to low spatial frequency information. We show that preprocessing by blurring can serve as a defense mechanism against both adversarial attacks and common corruptions, further confirming our hypothesis and demonstrating the utility of low spatial frequency information in robust object recognition.

Neural system identification aims at learning the response function of neurons to arbitrary stimuli using experimentally recorded data, but typically does not leverage normative principles such as efficient coding of natural environments. Visual systems, however, have evolved to efficiently process input from the natural environment. Here, we present a normative network regularization for system identification models by incorporating, as a regularizer, the efficient coding hypothesis, which states that neural response properties of sensory representations are strongly shaped by the need to preserve most of the stimulus information with limited resources. Using this approach, we explored if a system identification model can be improved by sharing its convolutional filters with those of an autoencoder which aims to efficiently encode natural stimuli. To this end, we built a hybrid model to predict the responses of retinal neurons to noise stimuli. This approach did not only yield a higher performance than the "stand-alone" system identification model, it also produced more biologically plausible filters, meaning that they more closely resembled neural representation in early visual systems. We found these results applied to retinal responses to different artificial stimuli and across model architectures. Moreover, our normatively regularized model performed particularly well in predicting responses of direction-of-motion sensitive retinal neurons. The benefit of natural scene statistics became marginal, however, for predicting the responses to natural movies. In summary, our results indicate that efficiently encoding environmental inputs can improve system identification models, at least for noise stimuli, and point to the benefit of probing the visual system with naturalistic stimuli.

Since 2014 transfer learning has become the key driver for the improvement of spatial saliency prediction—however, with stagnant progress in the last 3-5 years. We conduct a large-scale transfer learning study which tests different ImageNet backbones, always using the same read out architecture and learning protocol adopted from DeepGaze II. By replacing the VGG19 backbone of DeepGaze II with ResNet50 features we improve the performance on saliency prediction from 78% to 85%. However, as we continue to test better ImageNet models as backbones—such as EfficientNetB5—we observe no additional improvement on saliency prediction. By analyzing the backbones further, we find that generalization to other datasets differs substantially, with models being consistently overconfident in their fixation predictions. We show that by combining multiple backbones in a principled manner a good confidence calibration on unseen datasets can be achieved. This new model "DeepGaze IIE" yields a significant leap in benchmark performance in and out-of-domain with a 15 percent point improvement over DeepGaze II to 93% on MIT1003, marking a new state of the art on the MIT/Tuebingen Saliency Benchmark in all available metrics (AUC: 88.3%, sAUC: 79.4%, CC: 82.4%).

Contrastive learning has recently seen tremendous success in self-supervised learning. So far, however, it is largely unclear why the learned representations generalize so effectively to a large variety of downstream tasks. We here prove that feedforward models trained with objectives belonging to the commonly used InfoNCE family learn to implicitly invert the underlying generative model of the observed data. While the proofs make certain statistical assumptions about the generative model, we observe empirically that our findings hold even if these assumptions are severely violated. Our theory highlights a fundamental connection between contrastive learning, generative modeling, and nonlinear independent component analysis, thereby furthering our understanding of the learned representations as well as providing a theoretical foundation to derive more effective contrastive losses.

A few years ago, the first CNN surpassed human performance on ImageNet. However, it soon became clear that machines lack robustness on more challenging test cases, a major obstacle towards deploying machines "in the wild" and towards obtaining better computational models of human visual perception. Here we ask: Are we making progress in closing the gap between human and machine vision? To answer this question, we tested human observers on a broad range of out-of-distribution (OOD) datasets, recording 85,120 psychophysical trials across 90 participants. We then investigated a range of promising machine learning developments that crucially deviate from standard supervised CNNs along three axes: objective function (self-supervised, adversarially trained, CLIP language-image training), architecture (e.g. vision transformers), and dataset size (ranging from 1M to 1B).Our findings are threefold. (1.) The longstanding distortion robustness gap between humans and CNNs is closing, with the best models now exceeding human feedforward performance on most of the investigated OOD datasets. (2.) There is still a substantial image-level consistency gap, meaning that humans make different errors than models. In contrast, most models systematically agree in their categorisation errors, even substantially different ones like contrastive self-supervised vs. standard supervised models. (3.) In many cases, human-to-model consistency improves when training dataset size is increased by one to three orders of magnitude. Our results give reason for cautious optimism: While there is still much room for improvement, the behavioural difference between human and machine vision is narrowing. In order to measure future progress, 17 OOD datasets with image-level human behavioural data and evaluation code are provided as a toolbox and benchmark at: https://github.com/bethgelab/model-vs-human/

A precise understanding of why units in an artificial network respond to certain stimuli would constitute a big step towards explainable artificial intelligence. One widely used approach towards this goal is to visualize unit responses via activation maximization. These feature visualizations are purported to provide humans with precise information about the image features that cause a unit to be activated - an advantage over other alternatives like strongly activating dataset samples. If humans indeed gain causal insight from visualizations, this should enable them to predict the effect of an intervention, such as how occluding a certain patch of the image (say, a dog's head) changes a unit's activation. Here, we test this hypothesis by asking humans to decide which of two square occlusions causes a larger change to a unit's activation.Both a large-scale crowdsourced experiment and measurements with experts show that on average the extremely activating feature visualizations by Olah et al. (2017) indeed help humans on this task ($68 \pm 4$% accuracy; baseline performance without any visualizations is $60 \pm 3$%). However, they do not provide any substantial advantage over other visualizations (such as e.g. dataset samples), which yield similar performance ($66\pm3$% to $67 \pm3$% accuracy). Taken together, we propose an objective psychophysical task to quantify the benefit of unit-level interpretability methods for humans, and find no evidence that a widely-used feature visualization method provides humans with better "causal understanding" of unit activations than simple alternative visualizations.

Neural networks are highly effective tools for pose estimation. However, as in other computer vision tasks, robustness to out-of-domain data remains a challenge, especially for small training sets that are common for real-world applications. Here, we probe the generalization ability with three architecture classes (MobileNetV2s, ResNets, and EfficientNets) for pose estimation. We developed a dataset of 30 horses that allowed for both "within-domain" and "out-of-domain" (unseen horse) benchmarking-this is a crucial test for robustness that current human pose estimation benchmarks do not directly address. We show that better ImageNet-performing architectures perform better on both within- and out-of-domain data if they are first pretrained on ImageNet. We additionally show that better ImageNet models generalize better across animal species. Furthermore, we introduce Horse-C, a new benchmark for common corruptions for pose estimation, and confirm that pretraining increases performance in this domain shift context as well. Overall, our results demonstrate that transfer learning is beneficial for out-of-domain robustness.

Perceiving the world in terms of objects and tracking them through time is a crucial prerequisite for reasoning and scene understanding. Recently, several methods have been proposed for unsupervised learning of object-centric representations. However, since these models were evaluated on different downstream tasks, it remains unclear how they compare in terms of basic perceptual abilities such as detection, figure-ground segmentation and tracking of objects. To close this gap, we design a benchmark with four data sets of varying complexity and seven additional test sets featuring challenging tracking scenarios relevant for natural videos. Using this benchmark, we compare the perceptual abilities of four object-centric approaches: ViMON, a video-extension of MONet, based on recurrent spatial attention, OP3, which exploits clustering via spatial mixture models, as well as TBA and SCALOR, which use explicit factorization via spatial transformers. Our results suggest that the architectures with unconstrained latent representations learn more powerful representations in terms of object detection, segmentation and tracking than the spatial transformer based architectures. We also observe that none of the methods are able to gracefully handle the most challenging tracking scenarios despite their synthetic nature, suggesting that our benchmark may provide fruitful guidance towards learning more robust object-centric video representations.

Divisive normalization (DN) is a prominent computational building block in the brain that has been proposed as a canonical cortical operation. Numerous experimental studies have verified its importance for capturing nonlinear neural response properties to simple, artificial stimuli, and computational studies suggest that DN is also an important component for processing natural stimuli. However, we lack quantitative models of DN that are directly informed by measurements of spiking responses in the brain and applicable to arbitrary stimuli. Here, we propose a DN model that is applicable to arbitrary input images. We test its ability to predict how neurons in macaque primary visual cortex (V1) respond to natural images, with a focus on nonlinear response properties within the classical receptive field. Our model consists of one layer of subunits followed by learned orientation-specific DN. It outperforms linear-nonlinear and wavelet-based feature representations and makes a significant step towards the performance of state-of-the-art convolutional neural network (CNN) models. Unlike deep CNNs, our compact DN model offers a direct interpretation of the nature of normalization. By inspecting the learned normalization pool of our model, we gained insights into a long-standing question about the tuning properties of DN that update the current textbook description: we found that within the receptive field oriented features were normalized preferentially by features with similar orientation rather than non-specifically as currently assumed.

Today’s state-of-the-art machine vision models are vulnerable to image corruptions like blurring or compression artefacts, limiting their performance in many real-world applications. We here argue that popular benchmarks to measure model robustness against common corruptions (like ImageNet-C) underestimate model robustness in many (but not all) application scenarios. The key insight is that in many scenarios, multiple unlabeled examples of the corruptions are available and can be used for unsupervised online adaptation. Replacing the activation statistics estimated by batch normalization on the training set with the statistics of the corrupted images consistently improves the robustness across 25 different popular computer vision models. Using the corrected statistics, ResNet-50 reaches 62.2% mCE on ImageNet-C compared to 76.7% without adaptation. With the more robust DeepAugment+AugMix model, we improve the state of the art achieved by a ResNet50 model up to date from 53.6% mCE to 45.4% mCE. Even adapting to a single sample improves robustness for the ResNet-50 and AugMix models, and 32 samples are sufficient to improve the current state of the art for a ResNet-50 architecture. We argue that results with adapted statistics should be included whenever reporting scores in corruption benchmarks and other out-of-distribution generalization settings.

Visual processing in the retina has been studied in great detail at all levels such that a comprehensive picture of the retina's cell types and the many neural circuits they form is emerging. However, the currently best performing models of retinal function are black-box CNN models which are agnostic to such biological knowledge. In particular, these models typically neglect the role of the many inhibitory circuits involving amacrine cells and the biophysical mechanisms underlying synaptic release. Here, we present a computational model of temporal processing in the inner retina, including inhibitory feedback circuits and realistic synaptic release mechanisms. Fit to the responses of bipolar cells, the model generalized well to new stimuli including natural movie sequences, performing on par with or better than a benchmark black-box model. In pharmacology experiments, the model replicated in silico the effect of blocking specific amacrine cell populations with high fidelity, indicating that it had learned key circuit functions. Also, more in depth comparisons showed that connectivity patterns learned by the model were well matched to connectivity patterns extracted from connectomics data. Thus, our model provides a biologically interpretable data-driven account of temporal processing in the inner retina, filling the gap between purely black-box and detailed biophysical modeling.

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.

Throughout the past five years, the susceptibility of neural networks to minimal adversarial perturbations has moved from a peculiar phenomenon to a core issue in Deep Learning. Despite much attention, however, progress towards more robust models is significantly impaired by the difficulty of evaluating the robustness of neural network models. Today's methods are either fast but brittle (gradient-based attacks), or they are fairly reliable but slow (score- and decision-based attacks). We here develop a new set of gradient-based adversarial attacks which (a) are more reliable in the face of gradient-masking than other gradient-based attacks, (b) perform better and are more query efficient than current state-of-the-art gradient-based attacks, (c) can be flexibly adapted to a wide range of adversarial criteria and (d) require virtually no hyperparameter tuning. These findings are carefully validated across a diverse set of six different models and hold for L0, L1, L2 and Linf in both targeted as well as untargeted scenarios. Implementations will soon be available in all major toolboxes (Foolbox, CleverHans and ART). We hope that this class of attacks will make robustness evaluations easier and more reliable, thus contributing to more signal in the search for more robust machine learning models.

Despite great efforts over several decades, our best models of primary visual cortex (V1) still predict spiking activity quite poorly when probed with natural stimuli, highlighting our limited understanding of the nonlinear computations in V1. Recently, two approaches based on deep learning have emerged for modeling these nonlinear computations: transfer learning from artificial neural networks trained on object recognition and data-driven convolutional neural network models trained end-to-end on large populations of neurons. Here, we test the ability of both approaches to predict spiking activity in response to natural images in V1 of awake monkeys. We found that the transfer learning approach performed similarly well to the data-driven approach and both outperformed classical linear-nonlinear and wavelet-based feature representations that build on existing theories of V1. Notably, transfer learning using a pre-trained feature space required substantially less experimental time to achieve the same performance. In conclusion, multi-layer convolutional neural networks (CNNs) set the new state of the art for predicting neural responses to natural images in primate V1 and deep features learned for object recognition are better explanations for V1 computation than all previous filter bank theories. This finding strengthens the necessity of V1 models that are multiple nonlinearities away from the image domain and it supports the idea of explaining early visual cortex based on high-level functional goals.

We tackle the problem of one-shot segmentation: finding and segmenting a previously unseen object in a cluttered scene based on a single instruction example. We propose a novel dataset, which we call cluttered Omniglot. Using a baseline architecture combining a Siamese embedding for detection with a U-net for segmentation we show that increasing levels of clutter make the task progressively harder. Using oracle models with access to various amounts of ground-truth information, we evaluate different aspects of the problem and show that in this kind of visual search task, detection and segmentation are two intertwined problems, the solution to each of which helps solving the other. We therefore introduce MaskNet, an improved model that attends to multiple candidate locations, generates segmentation proposals to mask out background clutter and selects among the segmented objects. Our findings suggest that such image recognition models based on an iterative refinement of object detection and foreground segmentation may provide a way to deal with highly cluttered scenes.

We compare the robustness of humans and current convolutional deep neural networks (DNNs) on object recognition under twelve different types of image degradations. First, using three well known DNNs (ResNet-152, VGG-19, GoogLeNet) we find the human visual system to be more robust to nearly all of the tested image manipulations, and we observe progressively diverging classification error-patterns between humans and DNNs when the signal gets weaker. Secondly, we show that DNNs trained directly on distorted images consistently surpass human performance on the exact distortion types they were trained on, yet they display extremely poor generalisation abilities when tested on other distortion types. For example, training on salt-and-pepper noise does not imply robustness on uniform white noise and vice versa. Thus, changes in the noise distribution between training and testing constitutes a crucial challenge to deep learning vision systems that can be systematically addressed in a lifelong machine learning approach. Our new dataset consisting of 83K carefully measured human psychophysical trials provide a useful reference for lifelong robustness against image degradations set by the human visual system.

In recent years, two-photon calcium imaging has become a standard tool to probe the function of neural circuits and to study computations in neuronal populations. However, the acquired signal is only an indirect measurement of neural activity due to the comparatively slow dynamics of fluorescent calcium indicators. Different algorithms for estimating spike rates from noisy calcium measurements have been proposed in the past, but it is an open question how far performance can be improved. Here, we report the results of the spikefinder challenge, launched to catalyze the development of new spike rate inference algorithms through crowd-sourcing. We present ten of the submitted algorithms which show improved performance compared to previously evaluated methods. Interestingly, the top-performing algorithms are based on a wide range of principles from deep neural networks to generative models, yet provide highly correlated estimates of the neural activity. The competition shows that benchmark challenges can drive algorithmic developments in neuroscience.

Neural Style Transfer has shown very exciting results enabling new forms of image manipulation. Here we extend the existing method to introduce control over spatial location, colour information and across spatial scale. We demonstrate how this enhances the method by allowing high-resolution controlled stylisation and helps to alleviate common failure cases such as applying ground textures to sky regions. Furthermore, by decomposing style into these perceptual factors we enable the combination of style information from multiple sources to generate new, perceptually appealing styles from existing ones. We also describe how these methods can be used to more efficiently produce large size, high-quality stylisation. Finally we show how the introduced control measures can be applied in recent methods for Fast Neural Style Transfer.

Understanding where people look in images is an important problem in computer vision. Despite significant research, it remains unclear to what extent human fixations can be predicted by low-level (contrast) compared to highlevel (presence of objects) image features. Here we address this problem by introducing two novel models that use different feature spaces but the same readout architecture. The first model predicts human fixations based on deep neural network features trained on object recognition. This model sets a new state-of-the art in fixation prediction by achieving top performance in area under the curve metrics on the MIT300 hold-out benchmark (AUC = 88%, sAUC = 77%, NSS = 2.34). The second model uses purely low-level (isotropic contrast) features. This model achieves better performance than all models not using features pretrained on object recognition, making it a strong baseline to assess the utility of high-level features. We then evaluate and visualize which fixations are better explained by lowlevel compared to high-level image features. Surprisingly we find that a substantial proportion of fixations are better explained by the simple low-level model than the stateof- the-art model. Comparing different features within the same powerful readout architecture allows us to better understand the relevance of low- versus high-level features in predicting fixation locations, while simultaneously achieving state-of-the-art saliency prediction.

Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of “what” and “where”. Learning deep convolutional feature spaces that are shared among many neurons provides an exciting path forward, but the architectural design needs to account for data limitations: While new experimental techniques enable recordings from thousands of neurons, experimental time is limited so that one can sample only a small fraction of each neuron's response space. Here, we show that a major bottleneck for fitting convolutional neural networks (CNNs) to neural data is the estimation of the individual receptive field locations – a problem that has been scratched only at the surface thus far. We propose a CNN architecture with a sparse readout layer factorizing the spatial (where) and feature (what) dimensions. Our network scales well to thousands of neurons and short recordings and can be trained end-to-end. We evaluate this architecture on ground-truth data to explore the challenges and limitations of CNN-based system identification. Moreover, we show that our network model outperforms current state-of-the art system identification models of mouse primary visual cortex.

The rise of large-scale recordings of neuronal activity has fueled the hope to gain new insights into the collective activity of neural ensembles. How can one link the statistics of neural population activity to underlying principles and theories? One attempt to interpret such data builds upon analogies to the behaviour of collective systems in statistical physics. Divergence of the specific heat-a measure of population statistics derived from thermodynamics-has been used to suggest that neural populations are optimized to operate at a "critical point". However, these findings have been challenged by theoretical studies which have shown that common inputs can lead to diverging specific heat. Here, we connect "signatures of criticality", and in particular the divergence of specific heat, back to statistics of neural population activity commonly studied in neural coding: firing rates and pairwise correlations. We show that the specific heat diverges whenever the average correlation strength does not depend on population size. This is necessarily true when data with correlations is randomly subsampled during the analysis process, irrespective of the detailed structure or origin of correlations. We also show how the characteristic shape of specific heat capacity curves depends on firing rates and correlations, using both analytically tractable models and numerical simulations of a canonical feed-forward population model. To analyze these simulations, we develop efficient methods for characterizing large-scale neural population activity with maximum entropy models. We find that, consistent with experimental findings, increases in firing rates and correlation directly lead to more pronounced signatures. Thus, previous reports of thermodynamical criticality in neural populations based on the analysis of specific heat can be explained by average firing rates and correlations, and are not indicative of an optimized coding strategy. We conclude that a reliable interpretation of statistical tests for theories of neural coding is possible only in reference to relevant ground-truth models.

Rendering the semantic content of an image in different styles is a difficult image processing task. Arguably, a major limiting factor for previous approaches has been the lack of image representations that explicitly represent semantic information and, thus, allow to separate image content from style. Here we use image representations derived from Convolutional Neural Networks optimised for object recognition, which make high level image information explicit. We introduce A Neural Algorithm of Artistic Style that can separate and recombine the image content and style of natural images. The algorithm allows us to produce new images of high perceptual quality that combine the content of an arbitrary photograph with the appearance of numerous wellknown artworks. Our results provide new insights into the deep image representations learned by Convolutional Neural Networks and demonstrate their potential for high level image synthesis and manipulation.

We study mixture modeling using the elliptical gamma (EG) distribution, a non-Gaussian distribution that allows heavy and light tail and peak behaviors. We first consider maximum likelihood parameter estimation, a task that turns out to be very challenging: we must handle positive definiteness constraints, and more crucially, we must handle possibly nonconcave log-likelihoods, which makes maximization hard. We overcome these difficulties by developing algorithms based on fixed-point theory; our methods respect the psd constraint, while also efficiently solving the (possibly) nonconcave maximization to global optimality. Subsequently, we focus on mixture modeling using EG distributions: we present a closed-form expression of the KL-divergence between two EG distributions, which we then combine with our ML estimation methods to obtain an efficient split-and-merge expectation maximization algorithm. We illustrate the use of our model and algorithms on a dataset of natural image patches.

Here we introduce a new model of natural textures based on the feature spaces of convolutional neural networks optimised for object recognition. Samples from the model are of high perceptual quality demonstrating the generative power of neural networks trained in a purely discriminative fashion. Within the model, textures are represented by the correlations between feature maps in several layers of the network. We show that across layers the texture representations increasingly capture the statistical properties of natural images while making object information more and more explicit. The model provides a new tool to generate stimuli for neuroscience and might offer insights into the deep representations learned by convolutional neural networks.

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image models. We here introduce a recurrent image model based on multi-dimensional long short-term memory units which are particularly suited for image modeling due to their spatial structure. Our model scales to images of arbitrary size and its likelihood is computationally tractable. We find that it outperforms the state of the art in quantitative comparisons on several image datasets and produces promising results when used for texture synthesis and inpainting.

Following earlier studies which showed that a sparse coding principle may explain the receptive field properties of complex cells in primary visual cortex, it has been concluded that the same properties may be equally derived from a slowness principle. In contrast to this claim, we here show that slowness and sparsity drive the representations towards substantially different receptive field properties. To do so, we present complete sets of basis functions learned with slow subspace analysis (SSA) in case of natural movies as well as translations, rotations, and scalings of natural images. SSA directly parallels independent subspace analysis (ISA) with the only difference that SSA maximizes slowness instead of sparsity. We find a large discrepancy between the filter shapes learned with SSA and ISA. We argue that SSA can be understood as a generalization of the Fourier transform where the power spectrum corresponds to the maximally slow subspace energies in SSA. Finally, we investigate the trade-off between slowness and sparseness when combined in one objective function.

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.

A key hypothesis in sensory system neuroscience is that sensory representations are adapted to the statistical regularities in sensory signals and thereby incorporate knowledge about the outside world. Supporting this hypothesis, several probabilistic models of local natural image regularities have been proposed that reproduce neural response properties. Although many such physiological links have been made, these models have not been linked directly to visual sensitivity. Previous psychophysical studies of sensitivity to natural image regularities focus on global perception of large images, but much less is known about sensitivity to local natural image regularities. We present a new paradigm for controlled psychophysical studies of local natural image regularities and compare how well such models capture perceptually relevant image content. To produce stimuli with precise statistics, we start with a set of patches cut from natural images and alter their content to generate a matched set whose joint statistics are equally likely under a probabilistic natural image model. The task is forced choice to discriminate natural patches from model patches. The results show that human observers can learn to discriminate the higher-order regularities in natural images from those of model samples after very few exposures and that no current model is perfect for patches as small as 5 by 5 pixels or larger. Discrimination performance was accurately predicted by model likelihood, an information theoretic measure of model efficacy, indicating that the visual system possesses a surprisingly detailed knowledge of natural image higher-order correlations, much more so than current image models. We also perform three cue identification experiments to interpret how model features correspond to perceptually relevant image features.

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.

Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale poorly to high-dimensional stimulus spaces. Here we seek an approach which can gracefully interpolate between the two extremes. We extend two frequently used special cases of the GLM-a linear and a quadratic model-by assuming that the spike-triggered and non-spike-triggered distributions can be adequately represented using Gaussian mixtures. Because we derive the model from a generative perspective, its components are easy to interpret as they correspond to, for example, the spike-triggered distribution and the interspike interval distribution. The model is able to capture complex dependencies on high-dimensional stimuli with far fewer parameters than other approaches such as histogram-based methods. The added flexibility comes at the cost of a non-concave log-likelihood. We show that in practice this does not have to be an issue and the mixture-based model is able to outperform generalized linear and quadratic models.

We present a new learning strategy based on an efficient blocked Gibbs sampler for sparse overcomplete linear models. Particular emphasis is placed on statistical image modeling, where overcomplete models have played an important role in discovering sparse representations. Our Gibbs sampler is faster than general purpose sampling schemes while also requiring no tuning as it is free of parameters. Using the Gibbs sampler and a persistent variant of expectation maximization, we are able to extract highly sparse distributions over latent sources from data. When applied to natural images, our algorithm learns source distributions which resemble spike-and-slab distributions. We evaluate the likelihood and quantitatively compare the performance of the overcomplete linear model to its complete counterpart as well as a product of experts model, which represents another overcomplete generalization of the complete linear model. In contrast to previous claims, we find that overcomplete representations lead to significant improvements, but that the overcomplete linear model still underperforms other models.

Several studies have reported optimal population decoding of sensory responses in two-alternative visual discrimination tasks. Such decoding involves integrating noisy neural responses into a more reliable representation of the likelihood that the stimuli under consideration evoked the observed responses. Importantly, an ideal observer must be able to evaluate likelihood with high precision and only consider the likelihood of the two relevant stimuli involved in the discrimination task. We report a new perceptual bias suggesting that observers read out the likelihood representation with remarkably low precision when discriminating grating spatial frequencies. Using spectrally filtered noise, we induced an asymmetry in the likelihood function of spatial frequency. This manipulation mainly affects the likelihood of spatial frequencies that are irrelevant to the task at hand. Nevertheless, we find a significant shift in perceived grating frequency, indicating that observers evaluate likelihoods of a broad range of irrelevant frequencies and discard prior knowledge of stimulus alternatives when performing two-alternative discrimination.

Many studies have explored the impact of response variability on the quality of sensory codes. The source of this variability is almost always assumed to be intrinsic to the brain. However, when inferring a particular stimulus property, variability associated with other stimulus attributes also effectively act as noise. Here we study the impact of such stimulus-induced response variability for the case of binocular disparity inference. We characterize the response distribution for the binocular energy model in response to random dot stereograms and find it to be very different from the Poisson-like noise usually assumed. We then compute the Fisher information with respect to binocular disparity, present in the monocular inputs to the standard model of early binocular processing, and thereby obtain an upper bound on how much information a model could theoretically extract from them. Then we analyze the information loss incurred by the different ways of combining those inputs to produce a scalar single-neuron response. We find that in the case of depth inference, monocular stimulus variability places a greater limit on the extractable information than intrinsic neuronal noise for typical spike counts. Furthermore, the largest loss of information is incurred by the standard model for position disparity neurons (tuned-excitatory), that are the most ubiquitous in monkey primary visual cortex, while more information from the inputs is preserved in phase-disparity neurons (tuned-near or tuned-far) primarily found in higher cortical regions.

The relative merits of different population coding schemes have mostly been analyzed in the framework of stimulus reconstruction using Fisher Information. Here, we consider the case of stimulus discrimination in a two alternative forced choice paradigm and compute neurometric functions in terms of the minimal discrimination error and the Jensen-Shannon information to study neural population codes. We first explore the relationship between minimum discrimination error, Jensen-Shannon Information and Fisher Information and show that the discrimination framework is more informative about the coding accuracy than Fisher Information as it defines an error for any pair of possible stimuli. In particular, it includes Fisher Information as a special case. Second, we use the framework to study population codes of angular variables. Specifically, we assess the impact of different noise correlations structures on coding accuracy in long versus short decoding time windows. That is, for long time window we use the common Gaussian noise approximation. To address the case of short time windows we analyze the Ising model with identical noise correlation structure. In this way, we provide a new rigorous framework for assessing the functional consequences of noise correlation structures for the representational accuracy of neural population codes that is in particular applicable to short-time population coding.

Second-order maximum-entropy models have recently gained much interest for describing the statistics of binary spike trains. Here, we extend this approach to take continuous stimuli into account as well. By constraining the joint second-order statistics, we obtain a joint Gaussian-Boltzmann distribution of continuous stimuli and binary neural firing patterns, for which we also compute marginal and conditional distributions. This model has the same computational complexity as pure binary models and fitting it to data is a convex problem. We show that the model can be seen as an extension to the classical spike-triggered average/covariance analysis and can be used as a non-linear method for extracting features which a neural population is sensitive to. Further, by calculating the posterior distribution of stimuli given an observed neural response, the model can be used to decode stimuli and yields a natural spike-train metric. Therefore, extending the framework of maximum-entropy models to continuous variables allows us to gain novel insights into the relationship between the firing patterns of neural ensembles and the stimuli they are processing.

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or -counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and provides the basis for decoding studies. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex.

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.

Spike trains recorded from populations of neurons can exhibit substantial pairwise correlations between neurons and rich temporal structure. Thus, for the realistic simulation and analysis of neural systems, it is essential to have efficient methods for generating artificial spike trains with specified correlation structure. Here we show how correlated binary spike trains can be simulated by means of a latent multivariate gaussian model. Sampling from the model is computationally very efficient and, in particular, feasible even for large populations of neurons. The entropy of the model is close to the theoretical maximum for a wide range of parameters. In addition, this framework naturally extends to correlations over time and offers an elegant way to model correlated neural spike counts with arbitrary marginal distributions.

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.

Maximum entropy analysis of binary variables provides an elegant way for study- ing the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory cod- ing, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analy- sis feasible for very high-dimensional data—the model parameters can be derived in closed form and sampling is easy. Therefore, our NearMaxEnt approach can serve as a tool for testing predictions from a pairwise maximum entropy model not only for low-dimensional marginals, but also for high dimensional measurements of more than thousand units. We demonstrate its usefulness by studying natural images with dichotomized pixel intensities. Our results indicate that the statistics of such higher-dimensional measurements exhibit additional structure that are not predicted by pairwise correlations, despite the fact that pairwise correlations ex- plain the lower-dimensional marginal statistics surprisingly well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

Generalized linear models are the most commonly used tools to describe the stim- ulus selectivity of sensory neurons. Here we present a Bayesian treatment of such models. Using the expectation propagation algorithm, we are able to approximate the full posterior distribution over all weights. In addition, we use a Laplacian prior to favor sparse solutions. Therefore, stimulus features that do not critically influence neural activity will be assigned zero weights and thus be effectively excluded by the model. This feature selection mechanism facilitates both the in- terpretation of the neuron model as well as its predictive abilities. The posterior distribution can be used to obtain confidence intervals which makes it possible to assess the statistical significance of the solution. In neural data analysis, the available amount of experimental measurements is often limited whereas the pa- rameter space is large. In such a situation, both regularization by a sparsity prior and uncertainty estimates for the model parameters are essential. We apply our method to multi-electrode recordings of retinal ganglion cells and use our uncer- tainty estimate to test the statistical significance of functional couplings between neurons. Furthermore we used the sparsity of the Laplace prior to select those filters from a spike-triggered covariance analysis that are most informative about the neural response.

Stimulus selectivity of sensory neurons is often characterized by estimating their receptive field properties such as orientation selectivity. Receptive fields are usually derived from the mean (or covariance) of the spike-triggered stimulus ensemble. This approach treats each spike as an independent message but does not take into account that information might be conveyed through patterns of neural activity that are distributed across space or time. Can we find a concise description for the processing of a whole population of neurons analogous to the receptive field for single neurons? Here, we present a generalization of the linear receptive field which is not bound to be triggered on individual spikes but can be meaningfully linked to distributed response patterns. More precisely, we seek to identify those stimulus features and the corresponding patterns of neural activity that are most reliably coupled. We use an extension of reverse-correlation methods based on canonical correlation analysis. The resulting population receptive fields span the subspace of stimuli that is most informative about the population response. We evaluate our approach using both neuronal models and multi-electrode recordings from rabbit retinal ganglion cells. We show how the model can be extended to capture nonlinear stimulus-response relationships using kernel canonical correlation analysis, which makes it possible to test different coding mechanisms. Our technique can also be used to calculate receptive fields from multi-dimensional neural measurements such as those obtained from dynamic imaging methods.

Here we derive optimal gain functions for minimum mean square re(cid:173) construction from neural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the under(cid:173) lying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase tran(cid:173) sition analytically. The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results. We conclude that under most circumstances relevant to informa(cid:173) tion processing in the brain, rate coding can be better ascribed to a binary (low-entropy) code than to the other extreme of rich analog coding. 1 Optimal neuronal gain functions for short decoding time windows The use of action potentials (spikes) as a means of communication is the striking feature of neurons in the central nervous system. Since the discovery by Adrian [1] that action poten(cid:173) tials are generated by sensory neurons with a frequency that is substantially determined by the stimulus, the idea of rate coding has become a prevalent paradigm in neuroscience [2]. In particular, today the coding properties of many neurons from various areas in the cortex have been characterized by tuning curves, which describe the average firing rate response as a function of certain stimulus parameters. This way of description is closely related to the idea of analog coding, which constitutes the basis for many neural network models. Reliablv inference from the observed number of spikes about the underlying firing rate of a neuronal response, however, requires a sufficiently long time interval, while integration times of neurons in vivo [3] as well as reaction times of humans or animals when per(cid:173) forming classification tasks [4, 5] are known to be rather short. Therefore, it is important to understand, how neural rate coding is affected by a limited time window available for decoding. While rate codes are usually characterized by tuning functions relating the intensity of the ,f *http://www.neuro.urn-bremen.dermbethge neuronal response to a particular stimulus parameter, the question, how relevant the idea of analog coding actually is does not depend on the particular entity represented by a neuron. Instead it suffices to determine the shape of the gain function, which displays the mean fir(cid:173) ing rate as a function of the actual analog signal to be sent to subsequent neurons. Here we seek for optimal gain functions that minimize the minimum average squared reconstruction error for a uniform source signal transmitted through a Poisson channel as a function of the maximum mean number of spikes. In formal terms, the issue is to optimally encode a real random variable x in the number of pulses emitted by a neuron within a certain time window. Thereby, x stands for the intended analog output of the neuron that shall be signaled to subsequent neurons. The latter, however, can only observe a number of spikes k integrated within a time interval of length T. The statistical dependency between x and k is specified by the assumption of Poisson noise p(kIJL(x)) = (JL~))k exp{-JL(X)} ,

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal firing rate f(max) (power constraint), and the maximal average rate (f)(max) (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (f(min)T, f(max)T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.