The multi-armed bandit (MAB) setting is a useful abstraction of many online learning tasks which focuses on the trade-off between exploration and exploitation. In this setting, an online algorithm has a fixed set of alternatives ("arms"), and in each round it selects one arm and then observes the corresponding reward. While the case of small number of arms is by now well-understood, a lot of recent work has focused on multi-armed bandits with (infinitely) many arms, where one needs to assume extra structure in order to make the problem tractable. In particular, in the Lipschitz MAB problem there is an underlying similarity metric space, known to the algorithm, such that any two arms that are close in this metric space have similar payoffs. In this paper we consider the more realistic scenario in which the metric space is implicit -- it is defined by the available structure but not revealed to the algorithm directly.

Word embeddings that map words into a fixed-dimensional vector space are the backbone of modern NLP. Most word embedding methods encode semantic information. However, phonetic information, which is important for some tasks, is often overlooked. In this work, we develop several novel methods which leverage articulatory features to build phonetically informed word embeddings, and present a set of phonetic word embeddings to encourage their community development, evaluation and use. While several methods for learning phonetic word embeddings already exist, there is a lack of consistency in evaluating their effectiveness. Thus, we also proposes several ways to evaluate both intrinsic aspects of phonetic word embeddings, such as word retrieval and correlation with sound similarity, and extrinsic performances, such as rhyme and cognate detection and sound analogies. We hope that our suite of tasks will promote reproducibility and provide direction for future research on phonetic word embeddings.

Representation learning is an important step in the machine learning pipeline. Given the current biological sequencing data volume, learning an explicit representation is prohibitive due to the dimensionality of the resulting feature vectors. Kernel-based methods, e.g., SVM, are a proven efficient and useful alternative for several machine learning (ML) tasks such as sequence classification. Three challenges with kernel methods are (i) the computation time, (ii) the memory usage (storing an $n\times n$ matrix), and (iii) the usage of kernel matrices limited to kernel-based ML methods (difficult to generalize on non-kernel classifiers). While (i) can be solved using approximate methods, challenge (ii) remains for typical kernel methods. Similarly, although non-kernel-based ML methods can be applied to kernel matrices by extracting principal components (kernel PCA), it may result in information loss, while being computationally expensive. In this paper, we propose a general-purpose representation learning approach that embodies kernel methods' qualities while avoiding computation, memory, and generalizability challenges. This involves computing a low-dimensional embedding of each sequence, using random projections of its $k$-mer frequency vectors, significantly reducing the computation needed to compute the dot product and the memory needed to store the resulting representation. Our proposed fast and alignment-free embedding method can be used as input to any distance (e.g., $k$ nearest neighbors) and non-distance (e.g., decision tree) based ML method for classification and clustering tasks. Using different forms of biological sequences as input, we perform a variety of real-world classification tasks, such as SARS-CoV-2 lineage and gene family classification, outperforming several state-of-the-art embedding and kernel methods in predictive performance.

We define the bigraded persistent homology modules and the bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove the stability theorem for the bigraded persistent double homology modules and barcodes.

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.

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.

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.

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.

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