Neural Information Processing Systems http://nips.cc/

We consider the problem of estimating the parameters of a $d$-dimensional rectified Gaussian distribution from i.i.d.

We consider a set of data samples such that a fraction of the samples are arbitrary outliers, and the rest are the output samples of a single-layer neural network with rectified linear unit (ReLU) activation. Our goal is to estimate the parameters (weight matrix and bias vector) of the neural network, assuming the bias vector to be non-negative. We estimate the network parameters using the gradient descent algorithm combined with either the median-or trimmed mean-based filters to mitigate the effect of the arbitrary outliers.

This study focuses on the feature extraction problem in multi-modal data regression. To address three core challenges in real-world scenarios: limited and non-IID data, effective extraction and fusion of multi-modal information, and susceptibility to catastrophic forgetting in model learning, a task-driven supervised multi-modal federated feature extraction method is proposed. The method integrates multi-modal information extraction and contrastive learning mechanisms, and can adapt to different neural network structures as the latent mapping functions for data of each modality. It supports each client to independently learn low-dimensional representations of multi-modal data, and can flexibly control the degree of retention of effective information about the response variable in the predictive variables within the low-dimensional features through parameter tuning. The multi-constraint learning framework constructed by the method guarantees regression accuracy using Mean Squared Error loss. Through the synergistic effect of mutual information preservation constraint, symmetric Kullback-Leibler divergence constraint, and inter-model contrastive constraint, it achieves the retention of task-related information, the extraction, fusion, and alignment of multi-modal features, and the mitigation of representation drift and catastrophic forgetting in non-IID scenarios, respectively. This ensures that the feature extraction process always centers on improving the performance of downstream regression tasks. Experimental results from simulations and real-world data analysis demonstrate that the proposed method achieves more significant performance improvement on downstream regression tasks compared with classical feature extraction techniques.

Low-cost micro-electromechanical accelerometers are widely used in navigation, robotics, and consumer devices for motion sensing and position estimation. However, their performance is often degraded by bias errors. To eliminate deterministic bias terms a calibration procedure is applied under stationary conditions. It requires accelerom- eter leveling or complex orientation-dependent calibration procedures. To overcome those requirements, in this paper we present a model-free learning-based calibration method that estimates accelerometer bias under stationary conditions, without requiring knowledge of the sensor orientation and without the need to rotate the sensors. The proposed approach provides a fast, practical, and scalable solution suitable for rapid field deployment. Experimental validation on a 13.39-hour dataset collected from six accelerometers shows that the proposed method consistently achieves error levels more than 52% lower than traditional techniques. On a broader scale, this work contributes to the advancement of accurate calibration methods in orientation-free scenarios. As a consequence, it improves the reliability of low-cost inertial sensors in diverse scientific and industrial applications and eliminates the need for leveled calibration.

We introduce a novel convolutional neural network architecture, termed the \emph{periodic CNN}, which incorporates periodic boundary conditions into the convolutional layers. Our main theoretical contribution is a rigorous approximation theorem: periodic CNNs can approximate ridge functions depending on $d-1$ linear variables in a $d$-dimensional input space, while such approximation is impossible in lower-dimensional ridge settings ($d-2$ or fewer variables). This result establishes a sharp characterization of the expressive power of periodic CNNs. Beyond the theory, our findings suggest that periodic CNNs are particularly well-suited for problems where data naturally admits a ridge-like structure of high intrinsic dimension, such as image analysis on wrapped domains, physics-informed learning, and materials science. The work thus both expands the mathematical foundation of CNN approximation theory and highlights a class of architectures with surprising and practically relevant approximation capabilities.

A rectified Gaussian distribution is defined by passing a standard Gaussian distribution through a one-layer ReLU neural network. We give a simple algorithm to estimate the parameters (i.e., the