深神经网络实施了一系列逐层操作，每个操作都相对容易理解，但是总的总体计算通常很难理解。我们开发了一个简单的想法，可以解释有用表示的逐层结构：每一层的作用是重新格式化信息以减少目标输出的“距离”。我们通过利用最近的指标代表性相似性的工作来形式化“距离”的直观概念，并展示它如何导致几何概念的丰富空间。通过此框架，深度神经网络实施的层计算可以被视为高维表示空间中的路径。我们开发工具以在距离，角度和大地学方面表征这些几何形状。然后，我们提出在CIFAR-10训练的残留网络的三组问题：（1）路径的直线程度如何，以及每层对目标有何贡献？ （2）这些特性如何在培训上出现？ （3）更广泛的网络与更深的网络采取的路径有多相似？我们通过勾勒出其他方式来结论，这种代表性几何形状可用于理解和解释网络培训，或者规定改善网络体系结构以适合任务。

随时间变化数据的因果发现（CD）在神经科学，医学和机器学习中很重要。 CD的技术包括通常没有偏见但昂贵的随机实验。它还包括诸如回归，匹配和Granger因果关系之类的算法，这些算法仅在人类设计师做出的强烈假设下正确。但是，正如我们在机器学习的其他领域发现的那样，人类通常不太正确，通常比数据驱动的方法表现出色。在这里，我们测试是否可以以数据驱动的方式改善因果发现。我们采用了一个具有大量因果成分（晶体管），MOS 6502处理器和元学习的系统，该系统为神经网络代表的因果发现程序。我们发现，该程序的表现远远超过了人为设计的因果发现程序，例如相互信息和Granger因果关系。我们认为，因果关系领域应在可能的情况下考虑一种有监督的方法，其中从具有已知因果关系的大型数据集中学习了CD程序，而不是由人类专家设计。我们的发现有望在神经和医学数据以及更广泛的机器学习社区中采用新的CD方法。

Accurate determination of a small molecule candidate (ligand) binding pose in its target protein pocket is important for computer-aided drug discovery. Typical rigid-body docking methods ignore the pocket flexibility of protein, while the more accurate pose generation using molecular dynamics is hindered by slow protein dynamics. We develop a tiered tensor transform (3T) algorithm to rapidly generate diverse protein-ligand complex conformations for both pose and affinity estimation in drug screening, requiring neither machine learning training nor lengthy dynamics computation, while maintaining both coarse-grain-like coordinated protein dynamics and atomistic-level details of the complex pocket. The 3T conformation structures we generate are closer to experimental co-crystal structures than those generated by docking software, and more importantly achieve significantly higher accuracy in active ligand classification than traditional ensemble docking using hundreds of experimental protein conformations. 3T structure transformation is decoupled from the system physics, making future usage in other computational scientific domains possible.

Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior collapse as a problem of latent variable non-identifiability. We prove that the posterior collapses if and only if the latent variables are non-identifiable in the generative model. This fact implies that posterior collapse is not a phenomenon specific to the use of flexible distributions or approximate inference. Rather, it can occur in classical probabilistic models even with exact inference, which we also demonstrate. Based on these results, we propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. This model class resolves the problem of latent variable non-identifiability by leveraging bijective Brenier maps and parameterizing them with input convex neural networks, without special variational inference objectives or optimization tricks. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.

Differentiable Architecture Search (DARTS) has attracted considerable attention as a gradient-based Neural Architecture Search (NAS) method. Since the introduction of DARTS, there has been little work done on adapting the action space based on state-of-art architecture design principles for CNNs. In this work, we aim to address this gap by incrementally augmenting the DARTS search space with micro-design changes inspired by ConvNeXt and studying the trade-off between accuracy, evaluation layer count, and computational cost. To this end, we introduce the Pseudo-Inverted Bottleneck conv block intending to reduce the computational footprint of the inverted bottleneck block proposed in ConvNeXt. Our proposed architecture is much less sensitive to evaluation layer count and outperforms a DARTS network with similar size significantly, at layer counts as small as 2. Furthermore, with less layers, not only does it achieve higher accuracy with lower GMACs and parameter count, GradCAM comparisons show that our network is able to better detect distinctive features of target objects compared to DARTS.

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to solve the Blasius function. This method eliminates the process of changing the non-linear differential equation to an initial value problem. Also, it tackles the convergence issue arising in the conventional series solution. It is seen that this method produces results that are at par with the numerical and conventional methods. The solution is extended to the negative axis to show that PINNs capture the singularity of the function at $\eta=-5.69$

The Government of Kerala had increased the frequency of supply of free food kits owing to the pandemic, however, these items were static and not indicative of the personal preferences of the consumers. This paper conducts a comparative analysis of various clustering techniques on a scaled-down version of a real-world dataset obtained through a conjoint analysis-based survey. Clustering carried out by centroid-based methods such as k means is analyzed and the results are plotted along with SVD, and finally, a conclusion is reached as to which among the two is better. Once the clusters have been formulated, commodities are also decided upon for each cluster. Also, clustering is further enhanced by reassignment, based on a specific cluster loss threshold. Thus, the most efficacious clustering technique for designing a food kit tailored to the needs of individuals is finally obtained.

Learning efficient and interpretable policies has been a challenging task in reinforcement learning (RL), particularly in the visual RL setting with complex scenes. While neural networks have achieved competitive performance, the resulting policies are often over-parameterized black boxes that are difficult to interpret and deploy efficiently. More recent symbolic RL frameworks have shown that high-level domain-specific programming logic can be designed to handle both policy learning and symbolic planning. However, these approaches rely on coded primitives with little feature learning, and when applied to high-dimensional visual scenes, they can suffer from scalability issues and perform poorly when images have complex object interactions. To address these challenges, we propose \textit{Differentiable Symbolic Expression Search} (DiffSES), a novel symbolic learning approach that discovers discrete symbolic policies using partially differentiable optimization. By using object-level abstractions instead of raw pixel-level inputs, DiffSES is able to leverage the simplicity and scalability advantages of symbolic expressions, while also incorporating the strengths of neural networks for feature learning and optimization. Our experiments demonstrate that DiffSES is able to generate symbolic policies that are simpler and more and scalable than state-of-the-art symbolic RL methods, with a reduced amount of symbolic prior knowledge.

Tumor-stroma ratio (TSR) is a prognostic factor for many types of solid tumors. In this study, we propose a method for automated estimation of TSR from histopathological images of colorectal cancer. The method is based on convolutional neural networks which were trained to classify colorectal cancer tissue in hematoxylin-eosin stained samples into three classes: stroma, tumor and other. The models were trained using a data set that consists of 1343 whole slide images. Three different training setups were applied with a transfer learning approach using domain-specific data i.e. an external colorectal cancer histopathological data set. The three most accurate models were chosen as a classifier, TSR values were predicted and the results were compared to a visual TSR estimation made by a pathologist. The results suggest that classification accuracy does not improve when domain-specific data are used in the pre-training of the convolutional neural network models in the task at hand. Classification accuracy for stroma, tumor and other reached 96.1$\%$ on an independent test set. Among the three classes the best model gained the highest accuracy (99.3$\%$) for class tumor. When TSR was predicted with the best model, the correlation between the predicted values and values estimated by an experienced pathologist was 0.57. Further research is needed to study associations between computationally predicted TSR values and other clinicopathological factors of colorectal cancer and the overall survival of the patients.

There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could generate clusters such that different groups are disadvantaged within different clusters. We develop a clustering algorithm, building upon the centroid clustering paradigm pioneered by classical algorithms such as $k$-means, where we focus on mitigating the unfairness experienced by the most-disadvantaged group within each cluster. Our method uses an iterative optimisation paradigm whereby an initial cluster assignment is modified by reassigning objects to clusters such that the worst-off sensitive group within each cluster is benefitted. We demonstrate the effectiveness of our method through extensive empirical evaluations over a novel evaluation metric on real-world datasets. Specifically, we show that our method is effective in enhancing cluster-level group representativity fairness significantly at low impact on cluster coherence.