In the last years, neural networks (NN) have evolved from laboratory environments to the state-of-the-art for many real-world problems. It was shown that NN models (i.e., their weights and biases) evolve on unique trajectories in weight space during training. Following, a population of such neural network models (referred to as model zoo) would form structures in weight space. We think that the geometry, curvature and smoothness of these structures contain information about the state of training and can reveal latent properties of individual models. With such model zoos, one could investigate novel approaches for (i) model analysis, (ii) discover unknown learning dynamics, (iii) learn rich representations of such populations, or (iv) exploit the model zoos for generative modelling of NN weights and biases.

Air pollution is one of the most concerns for urban areas. Many countries have constructed monitoring stations to hourly collect pollution values. Recently, there is a research in Daegu city, Korea for real-time air quality monitoring via sensors installed on taxis running across the whole city. The collected data is huge (1-second interval) and in both Spatial and Temporal format. In this paper, based on this spatiotemporal Big data, we propose a real-time air pollution prediction model based on Convolutional Neural Network (CNN) algorithm for image-like Spatial distribution of air pollution. Regarding to Temporal information in the data, we introduce a combination of a Long Short-Term Memory (LSTM) unit for time series data and a Neural Network model for other air pollution impact factors such as weather conditions to build a hybrid prediction model. This model is simple in architecture but still brings good prediction ability.

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate optimization solver amounts to estimating a global solution function that maps varying problem input parameters to the corresponding optimal solutions. Work in multiparametric programming (mp) has shown that solutions to quadratic programs (QP) are piece-wise linear functions of the parameters, and researchers have suggested leveraging this property to model mp-QP using NN with ReLU activation functions, which also exhibit piecewise linear behaviour. This paper proposes a NN modeling approach and learning algorithm that discovers the exact closed-form solution to QP with linear constraints, by analytically deriving NN model parameters directly from the problem coefficients without training. Whereas generic DNN cannot guarantee accuracy outside the training distribution, the closed-form NN model produces exact solutions for every discovered critical region of the solution function. To evaluate the closed-form NN model, it was applied to DC optimal power flow problems in electricity management. In terms of Karush-Kuhn-Tucker (KKT) optimality and feasibility of solutions, it outperformed a classically trained DNN and was competitive with, or outperformed, a commercial analytic solver (Gurobi) at far less computational cost. For a long-range energy planning problem, it was able to produce optimal and feasible solutions for millions of input parameters within seconds.

Robust yield curve estimation is crucial in fixed-income markets for accurate instrument pricing, effective risk management, and informed trading strategies. Traditional approaches, including the bootstrapping method and parametric Nelson-Siegel models, often struggle with overfitting or instability issues, especially when underlying bonds are sparse, bond prices are volatile, or contain hard-to-remove noise. In this paper, we propose a neural networkbased framework for robust yield curve estimation tailored to small mortgage bond markets. Our model estimates the yield curve independently for each day and introduces a new loss function to enforce smoothness and stability, addressing challenges associated with limited and noisy data. Empirical results on Swedish mortgage bonds demonstrate that our approach delivers more robust and stable yield curve estimates compared to existing methods such as Nelson-Siegel-Svensson (NSS) and Kernel-Ridge (KR). Furthermore, the framework allows for the integration of domain-specific constraints, such as alignment with risk-free benchmarks, enabling practitioners to balance the trade-off between smoothness and accuracy according to their needs.

A recent line of research has highlighted the existence of a "double descent"