We study multiclass online prediction where the learner can predict using a list of multiple labels (as opposed to just one label in the traditional setting). We characterize learnability in this model using the $b$-ary Littlestone dimension. This dimension is a variation of the classical Littlestone dimension with the difference that binary mistake trees are replaced with $(k+1)$-ary mistake trees, where $k$ is the number of labels in the list. In the agnostic setting, we explore different scenarios depending on whether the comparator class consists of single-labeled or multi-labeled functions and its tradeoff with the size of the lists the algorithm uses. We find that it is possible to achieve negative regret in some cases and provide a complete characterization of when this is possible. As part of our work, we adapt classical algorithms such as Littlestone's SOA and Rosenblatt's Perceptron to predict using lists of labels. We also establish combinatorial results for list-learnable classes, including an list online version of the Sauer-Shelah-Perles Lemma. We state our results within the framework of pattern classes -- a generalization of hypothesis classes which can represent adaptive hypotheses (i.e. functions with memory), and model data-dependent assumptions such as linear classification with margin.

Despite the tremendous successes of deep neural networks (DNNs) in various applications, many fundamental aspects of deep learning remain incompletely understood, including DNN trainability. In a trainability study, one aims to discern what makes one DNN model easier to train than another under comparable conditions. In particular, our study focuses on multi-layer perceptron (MLP) models equipped with the same number of parameters. We introduce a new notion called variability to help explain the benefits of deep learning and the difficulties in training very deep MLPs. Simply put, variability of a neural network represents the richness of landscape patterns in the data space with respect to well-scaled random weights. We empirically show that variability is positively correlated to the number of activations and negatively correlated to a phenomenon called "Collapse to Constant", which is related but not identical to the well-known vanishing gradient phenomenon. Experiments on a small stylized model problem confirm that variability can indeed accurately predict MLP trainability. In addition, we demonstrate that, as an activation function in MLP models, the absolute value function can offer better variability than the popular ReLU function can.

Recently, there has been an increasing number of studies to combine the disciplines of quantum information and machine learning, and a variety of theories to merge these fields have consistently been put forward since machine learning is under pressure due to a lack of processing power of the increased amount of data in the world, and quantum computing offers these super computational capabilities. The combination of these two fields invariably leads to a massive interest in innovative information processing mechanisms that open up a new and improved range of solutions for various domains of applications, and the first concept was the research on quantum models of neural networks; it was essentially biologically inspired, in the hope of finding explanations for brain function within the framework of quantum theory [1]. In 2013, this combination got the name quantum machine learning by Lloyd et al. [2] as a definition of an area of research that explores the combination of quantum information and ML principles. However, the development of potential quantum machine learning algorithms has made some progress; several famous classical ML algorithms already have quantum analogs, such as the quantum support vector machine (QSVM), quantum k-means clustering, quantum Boltzmann machine (QBM), and the quantum perceptron (QP) which there have been some papers that mainly overview methods and algorithms of this model. Zhou et al. [3] developed a quantum perceptron approach based on the quantum phase capable of computing the XOR function using only one neuron, then Siomau et al. [4] introduced an autonomous quantum perceptron based on calculating a set of positive valued operators and valued measurements (POVM), after that Sagheer and Zidane [5] proposed a quantum perceptron based on Siomau method capable of constructing its own set of activation operators to be applied widely in both quantum and classical applications to overcome the linearity limitation of the classical perceptron In 2018, a multidimensional input quantum perceptron (MDIQP) was proposed by Yamamoto et al. [6]; their model had an arbitrary number of inputs with different synaptic weights, being able to form large quantum artificial neural networks (QANNs).

Creating accurate predictions in the stock market has always been a significant challenge in finance. With the rise of machine learning as the next level in the forecasting area, this research paper compares four machine learning models and their accuracy in forecasting three well-known stocks traded in the NYSE in the short term from March 2020 to May 2022. We deploy, develop, and tune XGBoost, Random Forest, Multi-layer Perceptron, and Support Vector Regression models. We report the models that produce the highest accuracies from our evaluation metrics: RMSE, MAPE, MTT, and MPE. Using a training data set of 240 trading days, we find that XGBoost gives the highest accuracy despite running longer (up to 10 seconds). Results from this study may improve by further tuning the individual parameters or introducing more exogenous variables.

Residual networks (ResNets) have significantly better trainability and thus performance than feed-forward networks at large depth. Introducing skip connections facilitates signal propagation to deeper layers. In addition, previous works found that adding a scaling parameter for the residual branch further improves generalization performance. While they empirically identified a particularly beneficial range of values for this scaling parameter, the associated performance improvement and its universality across network hyperparameters yet need to be understood. For feed-forward networks (FFNets), finite-size theories have led to important insights with regard to signal propagation and hyperparameter tuning. We here derive a systematic finite-size theory for ResNets to study signal propagation and its dependence on the scaling for the residual branch. We derive analytical expressions for the response function, a measure for the network's sensitivity to inputs, and show that for deep networks the empirically found values for the scaling parameter lie within the range of maximal sensitivity. Furthermore, we obtain an analytical expression for the optimal scaling parameter that depends only weakly on other network hyperparameters, such as the weight variance, thereby explaining its universality across hyperparameters. Overall, this work provides a framework for theory-guided optimal scaling in ResNets and, more generally, provides the theoretical framework to study ResNets at finite widths.

Various hand-designed CNN architectures have been developed, such as VGG, ResNet, DenseNet, etc., and achieve State-of-the-Art (SoTA) levels on different tasks. Neural Architecture Search (NAS) now focuses on automatically finding the best CNN architecture to handle the above tasks. However, the verification of a searched architecture is very time-consuming and makes predictor-based methods become an essential and important branch of NAS. Two commonly used techniques to build predictors are graph-convolution networks (GCN) and multilayer perceptron (MLP). In this paper, we consider the difference between GCN and MLP on adjacent operation trails and then propose the Redirected Adjacent Trails NAS (RATs-NAS) to quickly search for the desired neural network architecture. The RATs-NAS consists of two components: the Redirected Adjacent Trails GCN (RATs-GCN) and the Predictor-based Search Space Sampling (P3S) module. RATs-GCN can change trails and their strengths to search for a better neural network architecture. P3S can rapidly focus on tighter intervals of FLOPs in the search space. Based on our observations on cell-based NAS, we believe that architectures with similar FLOPs will perform similarly. Finally, the RATs-NAS consisting of RATs-GCN and P3S beats WeakNAS, Arch-Graph, and others by a significant margin on three sub-datasets of NASBench-201.

Attribute graphs are ubiquitous in multimedia applications, and graph representation learning (GRL) has been successful in analyzing attribute graph data. However, incomplete graph data and missing node attributes can have a negative impact on media knowledge discovery. Existing methods for handling attribute missing graph have limited assumptions or fail to capture complex attribute-graph dependencies. To address these challenges, we propose Attribute missing Graph Contrastive Learning (AmGCL), a framework for handling missing node attributes in attribute graph data. AmGCL leverages Dirichlet energy minimization-based feature precoding to encode in missing attributes and a self-supervised Graph Augmentation Contrastive Learning Structure (GACLS) to learn latent variables from the encoded-in data. Specifically, AmGCL utilizies feature reconstruction based on structure-attribute energy minimization while maximizes the lower bound of evidence for latent representation mutual information. Our experimental results on multiple real-world datasets demonstrate that AmGCL outperforms state-of-the-art methods in both feature imputation and node classification tasks, indicating the effectiveness of our proposed method in real-world attribute graph analysis tasks.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

In robotic laser surgery, shape prediction of an one-shot ablation cavity is an important problem for minimizing errant overcutting of healthy tissue during the course of pathological tissue resection and precise tumor removal. Since it is difficult to physically model the laser-tissue interaction due to the variety of optical tissue properties, complicated process of heat transfer, and uncertainty about the chemical reaction, we propose a 3D cavity prediction model based on an entirely data-driven method without any assumptions of laser settings and tissue properties. Based on the cavity prediction model, we formulate a novel robotic laser planning problem to determine the optimal laser incident configuration, which aims to create a cavity that aligns with the surface target (e.g. tumor, pathological tissue). To solve the one-shot ablation cavity prediction problem, we model the 3D geometric relation between the tissue surface and the laser energy profile as a non-linear regression problem that can be represented by a single-layer perceptron (SLP) network. The SLP network is encoded in a novel kinematic model to predict the shape of the post-ablation cavity with an arbitrary laser input. To estimate the SLP network parameters, we formulate a dataset of one-shot laser-phantom cavities reconstructed by the optical coherence tomography (OCT) B-scan images for the data-driven modelling. To verify the method. The learned cavity prediction model is applied to solve a simplified robotic laser planning problem modelled as a surface alignment error minimization problem. The initial results report (91.1 +- 3.0)% 3D-cavity-Intersection-over-Union (3D-cavity-IoU) for the 3D cavity prediction and an average of 97.9% success rate for the simulated surface alignment experiments.

To implement machine learning, it is essential to first determine an appropriate algorithm for the dataset. Different algorithms may produce a large number of different models with different hyperparameter configurations, and it usually takes a lot of time to run the model on a large dataset when the model is relatively complex. Therefore, how to predict the performance of a model on a dataset is an fundamental problem to be solved. This thesis designs a prediction system based on matrix factorization to predict the classification accuracy of a specific model on a particular dataset. In this thesis, we conduct a comprehensive empirical research on more than fifty datasets that we collected from the openml web site.