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We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. These parameter distributions are developed in the context of non-parametric regression models based on shallow neural networks, and compare favorably to well-established uniform random feature models based on conventional weight initialization. We address the cases of Heaviside and ReLU activation functions, and their smooth approximations (sigmoid and softplus), and use recent results on the harmonic analysis and sparse representation of neural networks resulting from fully trained optimal networks. Extending analytic results that give exact representation, we obtain densities that concentrate in regions of the parameter space corresponding to neurons that are well suited to model the local derivatives of the unknown function. Based on these results, we suggest simplifications of these exact densities based on approximate derivative data in the input points that allow for very efficient sampling and lead to performance of random feature models close to optimal networks in several scenarios.

We propose a new step-wise approach to proving observational equivalence, and in particular reasoning about fragility of observational equivalence. Our approach is based on what we call local reasoning. The local reasoning exploits the graphical concept of neighbourhood, and it extracts a new, formal, concept of robustness as a key sufficient condition of observational equivalence. Moreover, our proof methodology is capable of proving a generalised notion of observational equivalence. The generalised notion can be quantified over syntactically restricted contexts instead of all contexts, and also quantitatively constrained in terms of the number of reduction steps. The operational machinery we use is given by a hypergraph-rewriting abstract machine inspired by Girard's Geometry of Interaction. The behaviour of language features, including function abstraction and application, is provided by hypergraph-rewriting rules. We demonstrate our proof methodology using the call-by-value lambda-calculus equipped with (higher-order) state.

Image Edge detection (ED) is a base task in computer vision. While the performance of the ED algorithm has been improved greatly by introducing CNN-based models, current models still suffer from unsatisfactory precision rates especially when only a low error toleration distance is allowed. Therefore, model architecture for more precise predictions still needs an investigation. On the other hand, the unavoidable noise training data provided by humans would lead to unsatisfactory model predictions even when inputs are edge maps themselves, which also needs a solution. In this paper, more precise ED models are presented with cascaded skipping density blocks (CSDB). Our models obtain state-of-the-art(SOTA) predictions in several datasets, especially in average precision rate (AP), over a high-standard benchmark, which is confirmed by extensive experiments. Also, a novel modification on data augmentation for training is employed, which allows noiseless data to be employed in model training for the first time, and thus further improves the model performance. The relative Python codes can be found on //github.com/Hao-B-Shu/SDPED.

The recent cohort of publicly available generative models can produce human expert level content across a variety of topics and domains. Given a model in this cohort as a base model, methods such as parameter efficient fine-tuning, in-context learning, and constrained decoding have further increased generative capabilities and improved both computational and data efficiency. Entire collections of derivative models have emerged as a byproduct of these methods and each of these models has a set of associated covariates such as a score on a benchmark, an indicator for if the model has (or had) access to sensitive information, etc. that may or may not be available to the user. For some model-level covariates, it is possible to use "similar" models to predict an unknown covariate. In this paper we extend recent results related to embedding-based representations of generative models -- the data kernel perspective space -- to classical statistical inference settings. We demonstrate that using the perspective space as the basis of a notion of "similar" is effective for multiple model-level inference tasks.

Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices.

We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent\, -- \,also called reliability function\, -- \,is equal to the well-known sphere packing bound, which can be written as a single-letter formula optimized over Petz-R\'enyi divergences. Remarkably, there is no critical rate and as such our characterization remains tight for arbitrarily low rates below the capacity. On the achievability side, we further extend our results to fully quantum channels. Our proofs rely on semi-definite program duality and a dual representation of the Petz-R\'enyi divergences via Young inequalities. As a result of independent interest, we find that the Petz-R\'enyi divergences of order $\alpha\in[0,2]$ are upper bounded by the sandwiched R\'enyi divergences of order $1/(2-\alpha)\in[1/2,\infty]$.

Social-media platforms are one of the most prevalent communication media today. In such systems, a large amount of content is generated and available to the platform. However, not all content can be transmitted to every possible user at all times. At the other end are the users, who have their own preferences about which content they enjoy, which is often unknown ex ante to the platform. We model the interaction between the platform and the users as a signaling game with asymmetric information, where each user optimizes its preference disclosure policy, and the platform optimizes its information disclosure policy. We provide structural as well as existence of policies that constitute Bayesian Nash Equilibria, and necessary optimality conditions used to explicitly compute the optimal policies.

We propose a method utilizing physics-informed neural networks (PINNs) to solve Poisson equations that serve as control variates in the computation of transport coefficients via fluctuation formulas, such as the Green--Kubo and generalized Einstein-like formulas. By leveraging approximate solutions to the Poisson equation constructed through neural networks, our approach significantly reduces the variance of the estimator at hand. We provide an extensive numerical analysis of the estimators and detail a methodology for training neural networks to solve these Poisson equations. The approximate solutions are then incorporated into Monte Carlo simulations as effective control variates, demonstrating the suitability of the method for moderately high-dimensional problems where fully deterministic solutions are computationally infeasible.

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.