Graph Neural Networks (GNNs) are increasingly becoming the favorite method for graph learning. They exploit the semi-supervised nature of deep learning, and they bypass computational bottlenecks associated with traditional graph learning methods. In addition to the feature matrix $X$, GNNs need an adjacency matrix $A$ to perform feature propagation. In many cases, the adjacency matrix $A$ is missing. We introduce a graph construction scheme that constructs the adjacency matrix $A$ using unsupervised and supervised information. Unsupervised information characterizes the neighborhood around points. We used Principal Axis trees (PA-trees) as a source for unsupervised information, where we create edges between points falling onto the same leaf node. For supervised information, we used the concept of penalty and intrinsic graphs. A penalty graph connects points with different class labels, whereas an intrinsic graph connects points with the same class labels. We used the penalty and intrinsic graphs to remove or add edges to the graph constructed via PA-tree. We tested this graph construction scheme on two well-known GNNs: 1) Graph Convolutional Network (GCN) and 2) Simple Graph Convolution (SGC). The experiments show that it is better to use SGC because it is faster and delivers better or the same results as GCN. We also test the effect of oversmoothing on both GCN and SGC. We found out that the level of smoothing has to be carefully selected for SGC to avoid oversmoothing.

In peer mechanisms, the competitors for a prize also determine who wins. Each competitor may be asked to rank, grade, or nominate peers for the prize. Since the prize can be valuable, such as financial aid, course grades, or an award at a conference, competitors may be tempted to manipulate the mechanism. We survey approaches to prevent or discourage the manipulation of peer mechanisms. We conclude our survey by identifying several important research challenges.

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific combination of parameterization, noise family, and estimator. In this paper, we revisit the likelihood-based inference principle and propose to use likelihood ratios to construct any-time valid confidence sequences without requiring specialized treatment in each application scenario. Our method is especially suitable for problems with well-specified likelihoods, and the resulting sets always maintain the prescribed coverage in a model-agnostic manner. The size of the sets depends on a choice of estimator sequence in the likelihood ratio. We discuss how to provably choose the best sequence of estimators and shed light on connections to online convex optimization with algorithms such as Follow-the-Regularized-Leader. To counteract the initially large bias of the estimators, we propose a reweighting scheme that also opens up deployment in non-parametric settings such as RKHS function classes. We provide a non-asymptotic analysis of the likelihood ratio confidence sets size for generalized linear models, using insights from convex duality and online learning.

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's perspective. It describes the trade-offs, and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the $O(1/\sqrt{\text{width}})$ fluctuations of the DMFT order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently. In two layer networks, we show how feature learning can dynamically reduce the variance of the final tangent kernel and final network predictions. We also show how initialization variance can slow down online learning in wide but finite networks. In deeper networks, kernel variance can dramatically accumulate through subsequent layers at large feature learning strengths, but feature learning continues to improve the signal-to-noise ratio of the feature kernels. In discrete time, we demonstrate that large learning rate phenomena such as edge of stability effects can be well captured by infinite width dynamics and that initialization variance can decrease dynamically. For CNNs trained on CIFAR-10, we empirically find significant corrections to both the bias and variance of network dynamics due to finite width.

Facilitating online learning in spiking neural networks (SNNs) is a key step in developing event-based models that can adapt to changing environments and learn from continuous data streams in real-time. Although forward-mode differentiation enables online learning, its computational requirements restrict scalability. This is typically addressed through approximations that limit learning in deep models. In this study, we propose Online Training with Postsynaptic Estimates (OTPE) for training feed-forward SNNs, which approximates Real-Time Recurrent Learning (RTRL) by incorporating temporal dynamics not captured by current approximations, such as Online Training Through Time (OTTT) and Online Spatio-Temporal Learning (OSTL). We show improved scaling for multi-layer networks using a novel approximation of temporal effects on the subsequent layer's activity. This approximation incurs minimal overhead in the time and space complexity compared to similar algorithms, and the calculation of temporal effects remains local to each layer. We characterize the learning performance of our proposed algorithms on multiple SNN model configurations for rate-based and time-based encoding. OTPE exhibits the highest directional alignment to exact gradients, calculated with backpropagation through time (BPTT), in deep networks and, on time-based encoding, outperforms other approximate methods. We also observe sizeable gains in average performance over similar algorithms in offline training of Spiking Heidelberg Digits with equivalent hyper-parameters (OTTT/OSTL - 70.5%; OTPE - 75.2%; BPTT - 78.1%).

In recent years, the scientific community has become increasingly interested on peptides with non-canonical amino acids due to their superior stability and resistance to proteolytic degradation. These peptides present promising modifications to biological, pharmacological, and physiochemical attributes in both endogenous and engineered peptides. Notwithstanding their considerable advantages, the scientific community exhibits a conspicuous absence of an effective pre-trained model adept at distilling feature representations from such complex peptide sequences. We herein propose PepLand, a novel pre-training architecture for representation and property analysis of peptides spanning both canonical and non-canonical amino acids. In essence, PepLand leverages a comprehensive multi-view heterogeneous graph neural network tailored to unveil the subtle structural representations of peptides. Empirical validations underscore PepLand's effectiveness across an array of peptide property predictions, encompassing protein-protein interactions, permeability, solubility, and synthesizability. The rigorous evaluation confirms PepLand's unparalleled capability in capturing salient synthetic peptide features, thereby laying a robust foundation for transformative advances in peptide-centric research domains.

In this paper, we present OtterHD-8B, an innovative multimodal model evolved from Fuyu-8B, specifically engineered to interpret high-resolution visual inputs with granular precision. Unlike conventional models that are constrained by fixed-size vision encoders, OtterHD-8B boasts the ability to handle flexible input dimensions, ensuring its versatility across various inference requirements. Alongside this model, we introduce MagnifierBench, an evaluation framework designed to scrutinize models' ability to discern minute details and spatial relationships of small objects. Our comparative analysis reveals that while current leading models falter on this benchmark, OtterHD-8B, particularly when directly processing high-resolution inputs, outperforms its counterparts by a substantial margin. The findings illuminate the structural variances in visual information processing among different models and the influence that the vision encoders' pre-training resolution disparities have on model effectiveness within such benchmarks. Our study highlights the critical role of flexibility and high-resolution input capabilities in large multimodal models and also exemplifies the potential inherent in the Fuyu architecture's simplicity for handling complex visual data.

Large Multimodal Models (LMMs) have demonstrated impressive performance across various vision and language tasks, yet their potential applications in recommendation tasks with visual assistance remain unexplored. To bridge this gap, we present a preliminary case study investigating the recommendation capabilities of GPT-4V(ison), a recently released LMM by OpenAI. We construct a series of qualitative test samples spanning multiple domains and employ these samples to assess the quality of GPT-4V's responses within recommendation scenarios. Evaluation results on these test samples prove that GPT-4V has remarkable zero-shot recommendation abilities across diverse domains, thanks to its robust visual-text comprehension capabilities and extensive general knowledge. However, we have also identified some limitations in using GPT-4V for recommendations, including a tendency to provide similar responses when given similar inputs. This report concludes with an in-depth discussion of the challenges and research opportunities associated with utilizing GPT-4V in recommendation scenarios. Our objective is to explore the potential of extending LMMs from vision and language tasks to recommendation tasks. We hope to inspire further research into next-generation multimodal generative recommendation models, which can enhance user experiences by offering greater diversity and interactivity.

Deep neural networks (DNNs) have improved NLP tasks significantly, but training and maintaining such networks could be costly. Model compression techniques, such as, knowledge distillation (KD), have been proposed to address the issue; however, the compression process could be lossy. Motivated by this, our work investigates how a distilled student model differs from its teacher, if the distillation process causes any information losses, and if the loss follows a specific pattern. Our experiments aim to shed light on the type of tasks might be less or more sensitive to KD by reporting data points on the contribution of different factors, such as the number of layers or attention heads. Results such as ours could be utilized when determining effective and efficient configurations to achieve optimal information transfers between larger (teacher) and smaller (student) models.