We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending previous work on rotation equivariant networks that considers rescaling activations in less generality. We prove universal approximation theorems for radial neural networks, including in the more difficult cases of bounded widths and unbounded domains. Our proof techniques are novel, distinct from those in the pointwise case. Additionally, radial neural networks exhibit a rich group of orthogonal change-of-basis symmetries on the vector space of trainable parameters. Factoring out these symmetries leads to a practical lossless model compression algorithm. Optimization of the compressed model by gradient descent is equivalent to projected gradient descent for the full model.

Structured prediction has been widely used in various machine learning fields in the past 20 years, including applications like social network analysis, computer vision, molecular biology, natural language processing (NLP), among others. A common objective in these tasks is assigning / recovering labels, that is, given some possibly noisy observation, the goal is to output a group label for each entity in the task. In social network analysis, this could be detecting communities based on user profiles and preferences [Kelley et al., 2012]. In computer vision, researchers want the AI to decide whether a pixel is in the foreground or background [Nowozin et al., 2011]. In biology, it is sometimes desirable to cluster molecules by structural similarity [Nugent and Meila, 2010].

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

Includes Narration from Randal Shaffer. Agile scrum is a simple method for managing and completing even the most complex project, even in difficult situations . Based on my experience, it is the number one most popular way to deliver projects on-time while maintaining a high degree of quality. Who should take is course? Whether you are acrum Master, Project Manager, Product Owner or Team Member or simply someone who wants the answer to the question "how do I deal with difficult/challenging situations using scrum", this is definitely the class is for you.

Robotic grasping aims to detect graspable points and their corresponding gripper configurations in a particular scene, and is fundamental for robot manipulation. Existing research works have demonstrated the potential of using a transformer model for robotic grasping, which can efficiently learn both global and local features. However, such methods are still limited in grasp detection on a 2D plane. In this paper, we extend a transformer model for 6-Degree-of-Freedom (6-DoF) robotic grasping, which makes it more flexible and suitable for tasks that concern safety. The key designs of our method are a serialization module that turns a 3D voxelized space into a sequence of feature tokens that a transformer model can consume and skip-connections that merge multiscale features effectively. In particular, our method takes a Truncated Signed Distance Function (TSDF) as input. After serializing the TSDF, a transformer model is utilized to encode the sequence, which can obtain a set of aggregated hidden feature vectors through multi-head attention. We then decode the hidden features to obtain per-voxel feature vectors through deconvolution and skip-connections. Voxel feature vectors are then used to regress parameters for executing grasping actions. On a recently proposed pile and packed grasping dataset, we showcase that our transformer-based method can surpass existing methods by about 5% in terms of success rates and declutter rates. We further evaluate the running time and generalization ability to demonstrate the superiority of the proposed method.

This paper compares the parametric design space with a feature space generated by the extraction of design features using deep learning (DL) as an alternative way for design space exploration. In this comparison, the parametric design space is constructed by creating a synthetic dataset of 15.000 elements using a parametric algorithm and reducing its dimensions for visualization. The feature space -- reduced-dimensionality vector space of embedded data features -- is constructed by training a DL model on the same dataset. We analyze and compare the extracted design features by reducing their dimension and visualizing the results. We demonstrate that parametric design space is narrow in how it describes the design solutions because it is based on the combination of individual parameters. In comparison, we observed that the feature design space can intuitively represent design solutions according to complex parameter relationships. Based on our results, we discuss the potential of translating the features learned by DL models to provide a mechanism for intuitive design exploration space and visualization of possible design solutions.

In this paper, we prove that separable negative log-likelihood losses for structured prediction are not necessarily Bayes consistent, or, in other words, minimizing these losses may not result in a model that predicts the most probable structure in the data distribution for a given input. This fact opens the question of whether these losses are well-adapted for structured prediction and, if so, why.

Tensor network regression has emerged as a promising and active area of machine learning research, having achieved impressive results on common benchmark tasks such as the Movie 100K [1], MNIST [2][3][4][5], and Fashion MNIST [3][4][5] datasets. The effectiveness of these models can be attributed to the tensor-product transformation that is applied to the data features, which maps the original feature vector into an exponentially large vector space. By performing linear operations on this expanded feature space, tensor network models are able to generate regression outputs that are highly non-linear functions of the original features. In most tensor network models, the tensor-product transformation is constructed from a set of vector-valued functions that each act on only a single data feature. The form of these functions is important to the operation of the model, as it determines how regression on the transformed space is related to regression on the original feature space. Conventional wisdom regarding the choice of these functions can be traced back to the parallel works of Stoudenmire and Schwab [2] and Novikov et al. [1], who each proposed a different transformation scheme.

We investigate the effects on authorship identification tasks of a fundamental shift in how to conceive the vectorial representations of documents that are given as input to a supervised learner. In ``classic'' authorship analysis a feature vector represents a document, the value of a feature represents (an increasing function of) the relative frequency of the feature in the document, and the class label represents the author of the document. We instead investigate the situation in which a feature vector represents an unordered pair of documents, the value of a feature represents the absolute difference in the relative frequencies (or increasing functions thereof) of the feature in the two documents, and the class label indicates whether the two documents are from the same author or not. This latter (learner-independent) type of representation has been occasionally used before, but has never been studied systematically. We argue that it is advantageous, and that in some cases (e.g., authorship verification) it provides a much larger quantity of information to the training process than the standard representation. The experiments that we carry out on several publicly available datasets (among which one that we here make available for the first time) show that feature vectors representing pairs of documents (that we here call Diff-Vectors) bring about systematic improvements in the effectiveness of authorship identification tasks, and especially so when training data are scarce (as it is often the case in real-life authorship identification scenarios). Our experiments tackle same-author verification, authorship verification, and closed-set authorship attribution; while DVs are naturally geared for solving the 1st, we also provide two novel methods for solving the 2nd and 3rd that use a solver for the 1st as a building block.

But when it came to visual datasets, the field immediately stepped towards the algorithmic side. One of the fundamental reasons was the amount of information needed to translate from an image. But with the introduction of convolutional networks and transfer learning [1], [2], [3], it is possible to convert an image or a visual object into feature vectors without losing too much information about the entity under concern. It defined a way to use feature maps to compare and distinguish one visual object from another [4]. There has been a lot of work in using these feature vector conversions in systems like content-based image retrievals [5], using feature vectors as representations of different scenarios [6], [7]. It is critical to understand that there is a difference between the way a machine looks at the data and the way we do. There are scenarios in which the interpretation through features is a little different from the interpretation of humans. DSI is there to bridge the gap and understand the machine's perspective before molding it to shape better architectures, in turn, better model performances. I think two concepts could be linked together to understand a machine's viewpoint while working with visual