Work in deep clustering focuses on finding a single partition of data.

This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering techniques to measure the distances between the predictions of a trained neural network and class centroids. By analyzing these distances, the MLM provides a comprehensive view of the model's misclassification tendencies, enabling decision-makers to identify the most common and critical sources of errors. The MLM allows for the prioritization of model improvements and the establishment of decision thresholds based on acceptable risk levels. The approach is evaluated on the MNIST dataset using a Convolutional Neural Network (CNN) and a perturbed version of the dataset to simulate distribution shifts. The results demonstrate the effectiveness of the MLM in assessing the reliability of predictions and highlight its potential in enhancing the interpretability and risk mitigation capabilities of neural networks. The implications of this work extend beyond image classification, with ongoing applications in autonomous systems, such as self-driving cars, to improve the safety and reliability of decision-making in complex, real-world environments.

The product of experts learning procedure [1] can discover a set of stochastic binary features that constitute a non-linear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, it is helpful to learn a hierarchy of separate models for each digit class. Each model in the hierarchy has one layer of hidden units and the nth level model is trained on data that consists of the activities of the hidden units in the already trained (n - l)th level model. After train(cid:173) ing, each level produces a separate, unnormalized log probabilty score.

We propose a novel local learning rule for spiking neural networks in which spike propagation times undergo activity-dependent plasticity. Our plasticity rule aligns pre-synaptic spike times to produce a stronger and more rapid response. Inputs are encoded by latency coding and outputs decoded by matching similar patterns of output spiking activity. We demonstrate the use of this method in a three-layer feedfoward network with inputs from a database of handwritten digits. Networks consistently improve their classification accuracy after training, and training with this method also allowed networks to generalize to an input class unseen during training. Our proposed method takes advantage of the ability of spiking neurons to support many different time-locked sequences of spikes, each of which can be activated by different input activations. The proof-of-concept shown here demonstrates the great potential for local delay learning to expand the memory capacity and generalizability of spiking neural networks.

Fair and unbiased machine learning is an important and active field of research, as decision processes are increasingly driven by models that learn from data. Unfortunately, any biases present in the data may be learned by the model, thereby inappropriately transferring that bias into the decision making process. We identify the connection between the task of bias reduction and that of isolating factors common between domains whilst encouraging domain specific invariance. To isolate the common factors we combine the theory of deep latent variable models with information bottleneck theory for scenarios whereby data may be naturally paired across domains and no additional supervision is required. The result is the Nested Variational AutoEncoder (NestedVAE). Two outer VAEs with shared weights attempt to reconstruct the input and infer a latent space, whilst a nested VAE attempts to reconstruct the latent representation of one image, from the latent representation of its paired image. In so doing, the nested VAE isolates the common latent factors/causes and becomes invariant to unwanted factors that are not shared between paired images. We also propose a new metric to provide a balanced method of evaluating consistency and classifier performance across domains which we refer to as the Adjusted Parity metric. An evaluation of NestedVAE on both domain and attribute invariance, change detection, and learning common factors for the prediction of biological sex demonstrates that NestedVAE significantly outperforms alternative methods.

An ideal cognitively-inspired memory system would compress and organize incoming items. The Kanerva Machine (Wu et al., 2018b;a) is a Bayesian model that naturally implements online memory compression. However, the organization of the Kanerva Machine is limited by its use of a single Gaussian random matrix for storage. Here we introduce the Product Kanerva Machine, which dynamically combines many smaller Kanerva Machines. Its hierarchical structure provides a principled way to abstract invariant features and gives scaling and capacity advantages over single Kanerva Machines. We show that it can exhibit unsupervised clustering, find sparse and combinatorial allocation patterns, and discover spatial tunings that approximately factorize simple images by object.

A discrete system's heterogeneity is measured by the R\'enyi heterogeneity family of indices (also known as Hill numbers or Hannah-Kay indices), whose units are known as the numbers equivalent, and whose scaling properties are consistent and intuitive. Unfortunately, numbers equivalent heterogeneity measures for non-categorical data require a priori (A) categorical partitioning and (B) pairwise distance measurement on the space of observable data. This precludes their application to problems in disciplines where categories are ill-defined or where semantically relevant features must be learned as abstractions from some data. We thus introduce representational R\'enyi heterogeneity (RRH), which transforms an observable domain onto a latent space upon which the R\'enyi heterogeneity is both tractable and semantically relevant. This method does not require a priori binning nor definition of a distance function on the observable space. Compared with existing state-of-the-art indices on a beta-mixture distribution, we show that RRH more accurately detects the number of distinct mixture components. We also show that RRH can measure heterogeneity in natural images whose semantically relevant features must be abstracted using deep generative models. We further show that RRH can uniquely capture heterogeneity caused by distinct components in mixture distributions. Our novel approach will enable measurement of heterogeneity in disciplines where a priori categorical partitions of observable data are not possible, or where semantically relevant features must be inferred using latent variable models.

In this work we propose a model that enables controlled manipulation of visual attributes of real "target" images (e.g. lighting, expression or pose) using only implicit supervision with synthetic "source" exemplars. Specifically, our model learns a shared low-dimensional representation of input images from both domains in which a property of interest is isolated from other content features of the input. By using triplets of synthetic images that demonstrate modification of the visual property that we would like to control (for example mouth opening) we are able to perform disentanglement of image representations with respect to this property without using explicit attribute labels in either domain. Since our technique relies on triplets instead of explicit labels, it can be applied to shape, texture, lighting, or other properties that are difficult to measure or represent as explicit conditioners. We quantitatively analyze the degree to which trained models learn to isolate the property of interest from other content features with a proof-of-concept digit dataset and demonstrate results in a far more difficult setting, learning to manipulate real faces using a synthetic 3D faces dataset. We also explore limitations of our model with respect to differences in distributions of properties observed in two domains.

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods also introduce a bias, either by starting from the assumption of a particular geometric form of the clusters, or by using iterative schemes to enhance cluster contours, with uncontrollable consequences. The goal of data analysis should, however, be to encode and detect structural data features at all scales and densities simultaneously, without assuming a parametric form of data point distances, or modifying them. We propose a novel approach that directly encodes data point neighborhood similarities as a sparse graph. Our non-iterative framework permits a transparent interpretation of data, without altering the original data dimension and metric. Several natural and synthetic data applications demonstrate the efficacy of our novel approach.