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

Models trained with self-supervised learning objectives have recently matched or surpassed models trained with traditional supervised object recognition in their ability to predict neural responses of object-selective neurons in the primate visual system. A self-supervised learning objective is arguably a more biologically plausible organizing principle, as the optimization does not require a large number of labeled examples. However, typical self-supervised objectives may result in network representations that are overly invariant to changes in the input. Here, we show that a representation with structured variability to the input transformations is better aligned with known features of visual perception and neural computation. We introduce a novel framework for converting standard invariant SSL losses into "contrastive-equivariant" versions that encourage preserving aspects of the input transformation without supervised access to the transformation parameters. We further demonstrate that our proposed method systematically increases models' ability to predict responses in macaque inferior temporal cortex. Our results demonstrate the promise of incorporating known features of neural computation into task-optimization for building better models of visual cortex.

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural networks yield similar neural predictions, but it remains unclear how to differentiate among models that perform equally well at predicting neural responses. To gain insight into this, we use a recent theoretical framework that relates the generalization error from regression to the spectral properties of the model and the target. We apply this theory to the case of regression between model activations and neural responses and decompose the neural prediction error in terms of the model eigenspectra, alignment of model eigenvectors and neural responses, and the training set size. Using this decomposition, we introduce geometrical measures to interpret the neural prediction error. We test a large number of deep neural networks that predict visual cortical activity and show that there are multiple types of geometries that result in low neural prediction error as measured via regression. The work demonstrates that carefully decomposing representational metrics can provide interpretability of how models are capturing neural activity and points the way towards improved models of neural activity.

Contemporary speech enhancement predominantly relies on audio transforms that are trained to reconstruct a clean speech waveform. The development of high-performing neural network sound recognition systems has raised the possibility of using deep feature representations as 'perceptual' losses with which to train denoising systems. We explored their utility by first training deep neural networks to classify either spoken words or environmental sounds from audio. We then trained an audio transform to map noisy speech to an audio waveform that minimized the difference in the deep feature representations between the output audio and the corresponding clean audio. The resulting transforms removed noise substantially better than baseline methods trained to reconstruct clean waveforms, and also outperformed previous methods using deep feature losses. However, a similar benefit was obtained simply by using losses derived from the filter bank inputs to the deep networks. The results show that deep features can guide speech enhancement, but suggest that they do not yet outperform simple alternatives that do not involve learned features.

Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems. Recent work has proposed adding biologically-inspired components to visual neural networks as a way to improve their adversarial robustness. One surprisingly effective component for reducing adversarial vulnerability is response stochasticity, like that exhibited by biological neurons. Here, using recently developed geometrical techniques from computational neuroscience, we investigate how adversarial perturbations influence the internal representations of standard, adversarially trained, and biologically-inspired stochastic networks. We find distinct geometric signatures for each type of network, revealing different mechanisms for achieving robust representations. Next, we generalize these results to the auditory domain, showing that neural stochasticity also makes auditory models more robust to adversarial perturbations. Geometric analysis of the stochastic networks reveals overlap between representations of clean and adversarially perturbed stimuli, and quantitatively demonstrate that competing geometric effects of stochasticity mediate a tradeoff between adversarial and clean performance. Our results shed light on the strategies of robust perception utilized by adversarially trained and stochastic networks, and help explain how stochasticity may be beneficial to machine and biological computation.

Deep neural networks have been embraced as models of sensory systems, instantiating representational transformations that appear to resemble those in the visual and auditory systems. To more thoroughly investigate their similarity to biological systems, we synthesized model metamers – stimuli that produce the same responses at some stage of a network’s representation. We generated model metamers for natural stimuli by performing gradient descent on a noise signal, matching the responses of individual layers of image and audio networks to a natural image or speech signal. The resulting signals reflect the invariances instantiated in the network up to the matched layer. We then measured whether model metamers were recognizable to human observers – a necessary condition for the model representations to replicate those of humans. Although model metamers from early network layers were recognizable to humans, those from deeper layers were not. Auditory model metamers became more human-recognizable with architectural modifications that reduced aliasing from pooling operations, but those from the deepest layers remained unrecognizable. We also used the metamer test to compare model representations. Cross-model metamer recognition dropped off for deeper layers, roughly at the same point that human recognition deteriorated, indicating divergence across model representations. The results reveal discrepancies between model and human representations, but also show how metamers can help guide model refinement and elucidate model representations.

Encouraged by the success of deep convolutional neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. At the same time, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network. Finally, we find that the deep representations carry out significant temporal untangling by efficiently extracting task-relevant features at each time step of the computation. Taken together, these findings shed light on how deep auditory models process their time dependent input signals to carry out invariant speech recognition, and show how different concepts emerge through the layers of the network.