arXiv research

The paper proves barriers to approximating functions with small weights and depth in neural networks.

A new method generates natural-looking adversarial examples by bounding internal activation values.

SGD's escape rate depends on log loss barrier, not linear loss barrier.

Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.

LMC loss barrier decreases to zero with large network width.

Bayesian method synthesizes barrier certificates for unknown systems with latent states.

IPMs struggle with hyperbolic spaces due to polynomially growing barrier parameters.

Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.

New evidence shows computational barriers in graphon estimation using low-degree polynomials.

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

This work tackles Bayesian neural networks by addressing loss landscape symmetries.

The paper prices long-term options with a reflecting barrier model.

The conditional-mean barrier helps diagnose deterministic surrogates missing uncertainty.

A new method uses deep learning to price barrier options.

Improved regret bound for adversarial MDPs with linear function approximation.

This work refines claims about neural network connectivity, showing that simultaneous linear connectivity is possible under certain conditions.

Quantum models face barren plateaus, but specific losses can be trainable.

New bounds for online portfolio selection without smoothness assumptions.

New algorithm reduces prediction errors across various loss functions.

REPAIR mitigates variance collapse to enable linear interpolation between SGD solutions.

Paper generalizes VB-FTRL for online learning of quantum states with logarithmic loss.

We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers a closed form approximation of the option prices along the paths…

Study on size and depth of neural networks for approximating benign functions, showing barriers and explicit results.

This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical p…

Improves policy optimization with polylog(T) regret bounds for stochastic losses.

In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date could be calculate by computing a recursive integral formula upon the heat equati…

Algorithm for online decision making with unknown dynamics and aggregate feedback.

We consider the teacher-student setting of learning shallow neural networks with quadratic activations and planted weight matrix $W^*\in\mathbb{R}^{m\times d}$, where $m$ is the width of the hidden layer and $d\le m$ is the data dimension. We study the optimization landscape associated with the empirical and the popula…

Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default event without any recovery, is one of the key elementsfor pricing CVA. This pap…

We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning rate and batch-size in DNN optimization and generalization. Specifically we study…

Unified analysis of online optimization with self-concordant barriers, improving regret bounds.

Paper explores limits of high-order clustering with planted structures.

Combines RL and BF for risk-managed portfolio optimization.

Statistical-computational gap found in aligning multiple Gaussian graphs.

Improved Langevin Monte Carlo reduces energy barriers for faster optimization.

New method beats volumetric barrier for manifold recovery.

We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maxi…

The paper calculates prices for multi-step barrier options under the Black-Scholes model.

We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…

We study proper losses for discrete generative models without knowing the target distribution.

Two impossibility theorems show formal alignment certification is impossible for AI systems.

New findings on community recovery in SBM with many communities.

Analytic networks with bounded coefficients can't outperform polynomial approximations.

We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose …

We study the gain of an insider having private information which concerns the default risk of a counterparty. More precisely, the default time τis modelled as the first time a stochastic process hits a random barrier L. The insider knows this barrier (as it can be the case for example for the manager of the counterpart…

A time-dependent double-barrier option is a derivative security that delivers the terminal value $φ(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier opti…

New findings on computational limits for estimating hidden structures.

We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing metho…