Neurons in the brain are complex machines with distinct functional compartments that interact nonlinearly. In contrast, neurons in artificial neural networks abstract away this complexity, typically down to a scalar activation function of a weighted sum of inputs. Here we emulate more biologically realistic neurons by learning canonical activation functions with two input arguments, analogous to basal and apical dendrites. We use a network-in-network architecture where each neuron is modeled as a multilayer perceptron with two inputs and a single output. This inner perceptron is shared by all units in the outer network. Remarkably, the resultant nonlinearities often produce soft XOR functions, consistent with recent experimental observations about interactions between inputs in human cortical neurons. When hyperparameters are optimized, networks with these nonlinearities learn faster and perform better than conventional ReLU nonlinearities with matched parameter counts, and they are more robust to natural and adversarial perturbations.

Training large-scale image recognition models is computationally expensive. This raises the question of whether there might be simple ways to improve the test performance of an already trained model without having to re-train or fine-tune it with new data. Here, we show that, surprisingly, this is indeed possible. The key observation we make is that the layers of a deep network close to the output layer contain independent, easily extractable class-relevant information that is not contained in the output layer itself. We propose to extract this extra class-relevant information using a simple key-value cache memory to improve the classification performance of the model at test time. Our cache memory is directly inspired by a similar cache model previously proposed for language modeling (Grave et al., 2017). This cache component does not require any training or fine-tuning; it can be applied to any pre-trained model and, by properly setting only two hyper-parameters, leads to significant improvements in its classification performance. Improvements are observed across several architectures and datasets. In the cache component, using features extracted from layers close to the output (but not from the output layer itself) as keys leads to the largest improvements. Concatenating features from multiple layers to form keys can further improve performance over using single-layer features as keys. The cache component also has a regularizing effect, a simple consequence of which is that it substantially increases the robustness of models against adversarial attacks.

Training large-scale image recognition models is computationally expensive. This raises the question of whether there might be simple ways to improve the test performance of an already trained model without having to re-train or fine-tune it with new data. Here, we show that, surprisingly, this is indeed possible. The key observation we make is that the layers of a deep network close to the output layer contain independent, easily extractable class-relevant information that is not contained in the output layer itself. We propose to extract this extra class-relevant information using a simple key-value cache memory to improve the classification performance of the model at test time. Our cache memory is directly inspired by a similar cache model previously proposed for language modeling (Grave et al., 2017). This cache component does not require any training or fine-tuning; it can be applied to any pre-trained model and, by properly setting only two hyper-parameters, leads to significant improvements in its classification performance. Improvements are observed across several architectures and datasets. In the cache component, using features extracted from layers close to the output (but not from the output layer itself) as keys leads to the largest improvements. Concatenating features from multiple layers to form keys can further improve performance over using single-layer features as keys. The cache component also has a regularizing effect, a simple consequence of which is that it substantially increases the robustness of models against adversarial attacks.

Extensive evidence suggests that items are not encoded independently in visual short-term memory (VSTM). However, previous research has not quantitatively considered how the encoding of an item influences the encoding of other items. Here, we model the dependencies among VSTM representations using a multivariate Gaussian distribution with a stimulus-dependent mean and covariance matrix. We report the results of an experiment designed to determine the specific form of the stimulus-dependence of the mean and the covariance matrix. We find that the magnitude of the covariance between the representations of two items is a monotonically decreasing function of the difference between the items' feature values, similar to a Gaussian process with a distance-dependent, stationary kernel function. We further show that this type of covariance function can be explained as a natural consequence of encoding multiple stimuli in a population of neurons with correlated responses.