Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance of images. Kernels based on the \textit{maximum} similarity over a group of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show that positive definiteness indeed holds \textit{with high probability} for kernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime. We also show how additional properties such as their ability to incorporate local features at multiple spatial scales, e.g., as done in CNNs through max pooling, and to provide the benefits of composition through the architecture of multiple layers, can also be embedded into SVMs. We verify through experiments on widely available image sets that the resulting SVMs do provide superior accuracy in comparison to well-established deep neural network benchmarks for small sample sizes.

Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance of images. Kernels based on the \textit{maximum} similarity over a group of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show that positive definiteness indeed holds \textit{with high probability} for kernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime.

The utilization of Very Low Frequency (VLF) electromagnetic signals in navigation systems is widespread. However, the non-stationary behavior of lightning signals can affect VLF electromagnetic signal transmission. Accurately classifying lightning signals is important for reducing interference and noise in VLF, thereby improving the reliability and overall performance of navigation systems. In recent years, the evolution of deep learning, specifically Convolutional Neural Network (CNNs), has sparked a transformation in lightning classification, surpassing traditional statistical methodologies. Existing CNN models have limitations as they overlook the diverse attributes of lightning signals across different scales and neglect the significance of temporal sequencing in sequential signals. This study introduces an innovative multi-scale residual transform (MRTransformer) that not only has the ability to discern intricate fine-grained patterns while also weighing the significance of different aspects within the input lightning signal sequence. This model performs the attributes of the lightning signal across different scales and the level of accuracy reached 90% in the classification. In future work, this model has the potential applied to a comprehensive understanding of the localization and waveform characteristics of lightning signals.

Analyzing high resolution whole slide images (WSIs) with regard to information across multiple scales poses a significant challenge in digital pathology. Multi-instance learning (MIL) is a common solution for working with high resolution images by classifying bags of objects (i.e. sets of smaller image patches). However, such processing is typically performed at a single scale (e.g., 20x magnification) of WSIs, disregarding the vital inter-scale information that is key to diagnoses by human pathologists. In this study, we propose a novel cross-scale MIL algorithm to explicitly aggregate inter-scale relationships into a single MIL network for pathological image diagnosis. The contribution of this paper is three-fold: (1) A novel cross-scale MIL (CS-MIL) algorithm that integrates the multi-scale information and the inter-scale relationships is proposed; (2) A toy dataset with scale-specific morphological features is created and released to examine and visualize differential cross-scale attention; (3) Superior performance on both in-house and public datasets is demonstrated by our simple cross-scale MIL strategy. The official implementation is publicly available at https://github.com/hrlblab/CS-MIL.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

A new class of neural network aimed at early visual processing is described; we call it a Neural Analog Diffusion-Enhancement Layer or "NADEL." The network consists of two levels which are coupled through feedfoward and shunted feedback connections. The lower level is a two-dimensional diffusion map which accepts visual features as input, and spreads activity over larger scales as a function of time. The upper layer is periodically fed the activity from the diffusion layer and locates local maxima in it (an extreme form of contrast enhancement) using a network of local comparators. These local maxima are fed back to the diffusion layer using an on-center/off-surround shunting anatomy.

Simon did an introductory talk about deep learning techniques applied for natural language processing: CNNs, LSTMs, bi-LSTMs, CRF bi-LSTMs are networks often used to label sentences at the word, or even the character level. Tan did a visual introduction to Topological Data Analysis (TDA), the application of discrete topology to study point clouds. These techniques allow for a robust description of the point clouds properties at multiple scales via persistence diagrams. Robustness and persistence of patterns at multiple scales are a desirable properties, especially in the case of noisy and highly stochastic financial time series. Tan uses the persistence diagrams as features to a machine learning classifier (say XGBoost) to predict ETFs returns.

I co-authored a book that claims consciousness has been "solved". One of the greatest neuroscientists of our generation who is largely ignored within the field and unknown outside has conclusively put this thousand-year mystery to rest after sixty-five years of work. Many are skeptical of this claim, as you might guess. This article is not another attempt to convince the skeptics. Instead, it is to help understand why it is hard for us to believe we have an answer to the mystery of consciousness. It is to help understand why understanding consciousness is more important now -- at the dawn of the AI age -- than ever before in the history of humanity.

Once again, we see how radiology and chest imaging can benefit from image analysis methods that originated in other fields after they are translated by a capable group of experts who develop and test new tools that advance chest image analysis. In addition, we see the vocabulary of radiology expands to incorporate novel concepts from medical image analysis, such as isophotes, scale space, and invariants, that enrich our clinical literature. Author declared no funding for this work.

The keen-eyed among you will also have noticed that each image has a different background, is captured from different angles, and also has different objects in the foreground (in some cases). I'm sure all of this took you a fraction of a second to figure out. It doesn't matter if the image is rotated at a weird angle or zoomed in to show only half of the Tower. This is primarily because you have seen the images of the Eiffel Tower multiple times and your memory easily recalls its features. We naturally understand that the scale or angle of the image may change but the object remains the same.