Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is desirable. In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent Polynomial. This is facilitated by a new type of interpretable neural network block, named the “power-term approximator block”, consisting of logarithmic and exponential activation functions. GINN-LP is end-to-end differentiable, making it possible to use backpropagation for training. We propose a neural network growth strategy that will enable finding the suitable number of terms in the Laurent polynomial that represents the data, along with sparsity regularization to promote the discovery of concise equations. To the best of our knowledge, this is the first model that can discover arbitrary multivariate Laurent polynomial terms without any prior information on the order. Our approach is first evaluated on a subset of data used in SRBench, a benchmark for symbolic regression. We first show that GINN-LP outperforms the state-of-the-art symbolic regression methods on datasets generated using 48 real-world equations in the form of multivariate Laurent polynomials. Next, we propose an ensemble method that combines our method with a high-performing symbolic regression method, enabling us to discover non-Laurent polynomial equations. We achieve state-of-the-art results in equation discovery, showing an absolute improvement of 7.1% over the best contender, by applying this ensemble method to 113 datasets within SRBench with known ground-truth equations.

Neural growth is the process of growing a small neural network to a large network and has been utilized to accelerate the training of deep neural networks. One crucial aspect of neural growth is determining the optimal growth timing. However, few studies investigate this systematically. Our study reveals that neural growth inherently exhibits a regularization effect, whose intensity is influenced by the chosen policy for growth timing. While this regularization effect may mitigate the overfitting risk of the model, it may lead to a notable accuracy drop when the model underfits. Yet, current approaches have not addressed this issue due to their lack of consideration of the regularization effect from neural growth. Motivated by these findings, we propose an under/over fitting risk-aware growth timing policy, which automatically adjusts the growth timing informed by the level of potential under/overfitting risks to address both risks. Comprehensive experiments conducted using CIFAR-10/100 and ImageNet datasets show that the proposed policy achieves accuracy improvements of up to 1.3% in models prone to underfitting while achieving similar accuracies in models suffering from overfitting compared to the existing methods.

Catastrophic forgetting; the loss of old knowledge upon acquiring new knowledge, is a pitfall faced by deep neural networks in real-world applications. Many prevailing solutions to this problem rely on storing exemplars (previously encountered data), which may not be feasible in applications with memory limitations or privacy constraints. Therefore, the recent focus has been on Non-Exemplar based Class Incremental Learning (NECIL) where a model incrementally learns about new classes without using any past exemplars. However, due to the lack of old data, NECIL methods struggle to discriminate between old and new classes causing their feature representations to overlap. We propose NAPA-VQ: Neighborhood Aware Prototype Augmentation with Vector Quantization, a framework that reduces this class overlap in NECIL. We draw inspiration from Neural Gas to learn the topological relationships in the feature space, identifying the neighboring classes that are most likely to get confused with each other. This neighborhood information is utilized to enforce strong separation between the neighboring classes as well as to generate old class representative prototypes that can better aid in obtaining a discriminative decision boundary between old and new classes. Our comprehensive experiments on CIFAR-100, TinyImageNet, and ImageNet-Subset demonstrate that NAPA-VQ outperforms the State-of-the-art NECIL methods by an average improvement of 5%, 2%, and 4% in accuracy and 10%, 3%, and 9% in forgetting respectively. Our code can be found in https://github.com/TamashaM/NAPA-VQ.git.

Contemporary single-cell technologies produce data with a vast number of variables at a rapid pace, making large volumes of high-dimensional data available. The exploratory analysis of such high dimensional data can be aided by intuitive low dimensional visualizations. In this work, we investigate how both discrete and continuous structures in single cell data can be captured using the recently proposed dimensionality reduction method SONG, and compare the results with commonly used methods UMAP and PHATE. Using simulated and real-world datasets, we observed that SONG preserves a variety of patterns including discrete clusters, continuums, and branching structures. More importantly, SONG produced more/equally insightful visualizations compared to UMAP and PHATE in all considered datasets. We also quantitatively validate the high-dimensional pairwise distance preservation ability of these visualization methods in the low dimensional space for the generated visualizations.

Nonparametric dimensionality reduction techniques, such as t-distributed Stochastic Neighbor Embedding (t-SNE) and uniform manifold approximation and projection (UMAP), are proficient in providing visualizations for data sets of fixed sizes. However, they cannot incrementally map and insert new data points into an already provided data visualization. We present self-organizing nebulous growths (SONG), a parametric nonlinear dimensionality reduction technique that supports incremental data visualization, i.e., incremental addition of new data while preserving the structure of the existing visualization. In addition, SONG is capable of handling new data increments, no matter whether they are similar or heterogeneous to the already observed data distribution. We test SONG on a variety of real and simulated data sets. The results show that SONG is superior to Parametric t-SNE, t-SNE, and UMAP in incremental data visualization. Especially, for heterogeneous increments, SONG improves over Parametric t-SNE by 14.98% on the Fashion MNIST data set and 49.73% on the MNIST data set regarding the cluster quality measured by the adjusted mutual information scores. On similar or homogeneous increments, the improvements are 8.36% and 42.26%, respectively. Furthermore, even when the abovementioned data sets are presented all at once, SONG performs better or comparable to UMAP and superior to t-SNE. We also demonstrate that the algorithmic foundations of SONG render it more tolerant to noise compared with UMAP and t-SNE, thus providing greater utility for data with high variance, high mixing of clusters, or noise.

BACKGROUND: Estimating the parameters that describe the ecology of viruses,particularly those that are novel, can be made possible using metagenomic approaches. However, the best-performing existing methods require databases to first estimate an average genome length of a viral community before being able to estimate other parameters, such as viral richness. Although this approach has been widely used, it can adversely skew results since the majority of viruses are yet to be catalogued in databases. RESULTS: In this paper, we present ENVirT, a method for estimating the richness of novel viral mixtures, and for the first time we also show that it is possible to simultaneously estimate the average genome length without a priori information. This is shown to be a significant improvement over database-dependent methods, since we can now robustly analyze samples that may include novel viral types under-represented in current databases. We demonstrate that the viral richness estimates produced by ENVirT are several orders of magnitude higher in accuracy than the estimates produced by existing methods named PHACCS and CatchAll when benchmarked against simulated data. We repeated the analysis of 20 metavirome samples using ENVirT, which produced results in close agreement with complementary in virto analyses. CONCLUSIONS: These insights were previously not captured by existing computational methods. As such, ENVirT is shown to be an essential tool for enhancing our understanding of novel viral populations.