Motivation: Predicting cellular responses to genetic perturbations is essential for understanding biological systems and developing targeted therapeutic strategies. While variational autoencoders (VAEs) have shown promise in modeling perturbation responses, their limited explainability poses a significant challenge, as the learned features often lack clear biological meaning. Nevertheless, model explainability is one of the most important aspects in the realm of biological AI. One of the most effective ways to achieve explainability is incorporating the concept of gene regulatory networks (GRNs) in designing deep learning models such as VAEs. GRNs elicit the underlying causal relationships between genes and are capable of explaining the transcriptional responses caused by genetic perturbation treatments. Results: We propose GPO-VAE, an explainable VAE enhanced by GRN-aligned Parameter Optimization that explicitly models gene regulatory networks in the latent space. Our key approach is to optimize the learnable parameters related to latent perturbation effects towards GRN-aligned explainability. Experimental results on perturbation prediction show our model achieves state-of-the-art performance in predicting transcriptional responses across multiple benchmark datasets. Furthermore, additional results on evaluating the GRN inference task reveal our model's ability to generate meaningful GRNs compared to other methods. According to qualitative analysis, GPO-VAE posseses the ability to construct biologically explainable GRNs that align with experimentally validated regulatory pathways. GPO-VAE is available at https://github.com/dmis-lab/GPO-VAE

In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which boasts excellent generalizing capabilities but cannot estimate the uncertainty associated with its predictions. RP-WNO, unlike the vanilla WNO, comes with inherent uncertainty quantification module and hence, is expected to be extremely useful for scientists and engineers alike. RP-WNO utilizes randomized prior networks, which can account for prior information and is easier to implement for large, complex deep-learning architectures than its Bayesian counterpart. Four examples have been solved to test the proposed framework, and the results produced advocate favorably for the efficacy of the proposed framework.

We study the interpolation, or memorization, power of deep ReLU neural networks. Specifically, we consider the question of how efficiently, in terms of the number of parameters, deep ReLU networks can interpolate values at $N$ datapoints in the unit ball which are separated by a distance $\delta$. We show that $\Omega(N)$ parameters are required in the regime where $\delta$ is exponentially small in $N$, which gives the sharp result in this regime since $O(N)$ parameters are always sufficient. This also shows that the bit-extraction technique used to prove lower bounds on the VC dimension cannot be applied to irregularly spaced datapoints.

Generative adversarial networks (GANs), a class of distribution-learning methods based on a two-player game between a generator and a discriminator, can generally be formulated as a minmax problem based on the variational representation of a divergence between the unknown and the generated distributions. We introduce structure-preserving GANs as a data-efficient framework for learning distributions with additional structure such as group symmetry, by developing new variational representations for divergences. Our theory shows that we can reduce the discriminator space to its projection on the invariant discriminator space, using the conditional expectation with respect to the $\sigma$-algebra associated to the underlying structure. In addition, we prove that the discriminator space reduction must be accompanied by a careful design of structured generators, as flawed designs may easily lead to a catastrophic "mode collapse" of the learned distribution. We contextualize our framework by building symmetry-preserving GANs for distributions with intrinsic group symmetry, and demonstrate that both players, namely the equivariant generator and invariant discriminator, play important but distinct roles in the learning process. Empirical experiments and ablation studies across a broad range of data sets, including real-world medical imaging, validate our theory, and show our proposed methods achieve significantly improved sample fidelity and diversity -- almost an order of magnitude measured in Fr\'echet Inception Distance -- especially in the small data regime.

In many practical applications, such as fraud detection, credit risk modeling or medical decision making, classification models for assigning instances to a predefined set of classes are required to be both precise as well as interpretable. Linear modeling methods such as logistic regression are often adopted, since they offer an acceptable balance between precision and interpretability. Linear methods, however, are not well equipped to handle categorical predictors with high-cardinality or to exploit non-linear relations in the data. As a solution, data preprocessing methods such as weight-of-evidence are typically used for transforming the predictors. The binning procedure that underlies the weight-of-evidence approach, however, has been little researched and typically relies on ad-hoc or expert driven procedures. The objective in this paper, therefore, is to propose a formalized, data-driven and powerful method. To this end, we explore the discretization of continuous variables through the binning of spline functions, which allows for capturing non-linear effects in the predictor variables and yields highly interpretable predictors taking only a small number of discrete values. Moreover, we extend upon the weight-of-evidence approach and propose to estimate the proportions using shrinkage estimators. Together, this offers an improved ability to exploit both non-linear and categorical predictors for achieving increased classification precision, while maintaining interpretability of the resulting model and decreasing the risk of overfitting. We present the results of a series of experiments in a fraud detection setting, which illustrate the effectiveness of the presented approach. We facilitate reproduction of the presented results and adoption of the proposed approaches by providing both the dataset and the code for implementing the experiments and the presented approach.

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The quality of those statistics critically affect the accuracy of the inference. Existing methods to select the best subset out of a pool of candidate statistics do not scale well with large pools. Since it is imperative for good performance this becomes a serious bottleneck when doing inference on complex and high-dimensional problems. This paper proposes a convolutional neural network architecture for automatically learning informative summary statistics of temporal responses. We show that the proposed network can effectively circumvent the statistics selection problem as a preprocessing step to ABC for a challenging inference problem learning parameters in a high-dimensional stochastic genetic oscillator. We also study the impact of experimental design on network performance by comparing different data richness and different data acquisition strategies.

Improving sparsity of deep neural networks (DNNs) is essential for network compression and has drawn much attention. In this work, we disclose a harmful sparsifying process called filter collapse, which is common in DNNs with batch normalization (BN) and rectified linear activation functions (e.g. ReLU, Leaky ReLU). It occurs even without explicit sparsity-inducing regularizations such as $L_1$. This phenomenon is caused by the normalization effect of BN, which induces a non-trainable region in the parameter space and reduces the network capacity as a result. This phenomenon becomes more prominent when the network is trained with large learning rates (LR) or adaptive LR schedulers, and when the network is finetuned. We analytically prove that the parameters of BN tend to become sparser during SGD updates with high gradient noise and that the sparsifying probability is proportional to the square of learning rate and inversely proportional to the square of the scale parameter of BN. To prevent the undesirable collapsed filters, we propose a simple yet effective approach named post-shifted BN (psBN), which has the same representation ability as BN while being able to automatically make BN parameters trainable again as they saturate during training. With psBN, we can recover collapsed filters and increase the model performance in various tasks such as classification on CIFAR-10 and object detection on MS-COCO2017.