Extends RSP model with net flow and capacity constraints for better network analysis.
problem Improving shortest path models with net flows and capacity constraints.
method Developed net flow RSP model and introduced capacity constraints. Proposed algorithms for computing expected routing costs and solving constrained problems using Lagrangian duality.
result Net flow RSP dissimilarity measure is competitive with state-of-the-art dissimilarities.
A zoo of deep nets is available these days for almost any given task, and it is increasingly unclear which net to start with when addressing a new task, or which net to use as an initialization for fine-tuning a new model. To address this issue, in this paper, we develop knowledge flow which moves 'knowledge' from mult…
Paper predicts turbulent flows using physics-informed deep learning.
problem Predicting turbulent flows from fluid simulations.
method Hybrid approach combining RANS and LES with trainable spectral filters and U-net.
result Significant reduction in prediction error for 60 frames ahead.
New method uses neural nets in Hilbert space for option pricing on flow forwards.
problem Pricing options on flow forwards with neural networks in Hilbert space.
method Optimization problem in Hilbert space solved by a novel feedforward neural network architecture.
result Excellent numerical efficiency and superior performance over classical methods.
Study reveals investor heterogeneity in Korean equity market cash flows.
problem Investor heterogeneity and its impact on market dynamics.
method Detrended fluctuation analysis (DFA) on aggregated cash flows.
result Persistence in cash flows varies by investor type, with retail flows showing strong persistence.
Computational Fluid Dynamics (CFD) is a hugely important subject with applications in almost every engineering field, however, fluid simulations are extremely computationally and memory demanding. Towards this end, we present Lat-Net, a method for compressing both the computation time and memory usage of Lattice Boltzm…
The study examines how shallow neural nets converge to training samples or manifold points during diffusion.
problem Understanding when and how shallow neural nets converge to training samples or manifold points during diffusion.
method Analysis of shallow ReLU neural network denoisers trained with minimal ℓ2 norm, comparing score flow and diffusion flow. result Probability flow converges to training points, sums of training points, or manifold points, depending on the diffusion time scheduler.
In this paper, we use replica analysis to determine the investment strategy that can maximize the net present value for portfolios containing multiple development projects. Replica analysis was developed in statistical mechanical informatics and econophysics to evaluate disordered systems, and here we use it to formula…
Gradient descent on normalized networks reveals sparsity preferences.
problem Understanding the inductive bias of gradient descent on normalized neural nets.
method Analysis of gradient descent on weight-normalized smooth homogeneous neural nets, focusing on SWN and EWN.
result EWN causes weights to be updated in a way that prefers asymptotic relative sparsity.
Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
Paper defines the payback period for nonconventional cash flows using axioms.
problem Defining the payback period for nonconventional cash flows is challenging.
method Used axiomatic approach to define the payback period.
result The last break-even point of the project balance is the only definition consistent with axioms.
A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent networ…
Proposes a new deep learning model for uncertainty quantification and propagation.
problem High-dimensional uncertainty quantification and propagation problems.
method Integrates U-net with Gaussian Gated Linear Network (GGLN) to create GLU-net.
result Less complex architecture with 44% fewer parameters than existing models.
The paper reformulates U-Nets as wavelet-based models and applies this to hierarchical VAEs.
problem Theoretical understanding and regularization properties of U-Nets and their relationship to wavelets.
method Formulating a multi-resolution framework to identify U-Nets as finite-dimensional truncations of infinite-dimensional models, proving average pooling corresponds to projection, and identifying HVAEs as discretizations of multi-resolution diffusion processes.
result HVAEs learn a time representation allowing for improved parameter efficiency through weight-sharing.
A major contributing factor to the recent advances in deep neural networks is structural units that let sensory information and gradients to propagate easily. Gating is one such structure that acts as a flow control. Gates are employed in many recent state-of-the-art recurrent models such as LSTM and GRU, and feedforwa…
Bayesian Neural Nets improve model stability and fit.
problem Improving model stability and fit in time series prediction.
method Assign Bayesian Neural Nets to drift and diffusion terms of SDE, infer posterior using SGLD.
result Significantly improved stability and better model fit on benchmarks.
Study examines money flow network among firms' accounts in a Japanese region.
problem Understanding the relationship between money flow and economic activities of firms.
method Employed exhaustive bank transfer data, network statistics, Hodge decomposition, and non-negative matrix factorization.
result Identified a 'walnut' structure with core and upstream/downstream components, correlated with economic activities.
PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.
problem Developing approximation theory for PCA-Net architecture.
method Combines PCA and neural networks, derives universal approximation results and lower bounds on complexity.
result PCA-Net can overcome the curse of parametric complexity for specific operators.
RDL-Net improves speech enhancement with fewer parameters and better performance.
problem Improving speech enhancement with fewer parameters and better performance.
method Proposes RDL-Net, a CNN combining residual and dense aggregations without over-allocating parameters.
result RDL-Net achieves higher speech enhancement performance with fewer parameters and lower computational requirements.
We study the multi-level order-flow imbalance (MLOFI), which is a vector quantity that measures the net flow of buy and sell orders at different price levels in a limit order book (LOB). Using a recent, high-quality data set for 6 liquid stocks on Nasdaq, we fit a simple, linear relationship between MLOFI and the conte…
Optimal feature learning strength improves generalization in deep networks.
problem Understanding how feature learning strength affects generalization in practical settings.
method Empirical studies and theoretical analysis of gradient flow dynamics in two-layer ReLU nets.
result Optimal feature learning strength yields substantial generalization gains, contrary to the prevailing intuition.
The utility of Potential Future Exposure (PFE) for counterparty trading limits is being challenged by new market developments, notably widespread regulatory Initial Margin (using 99% 10-day exposure), and netting of trade and collateral flows. However PFE has pre-existing challenges w.r.t. portfolios/distributions, col…
Clarifies interest rate cap rules for loans with unconventional cash flows.
problem Ambiguity in applying interest rate caps to loans with non-conventional internal rate of return (IRR).
method Clarified conventional IRR definition, axiomatized, and extended to all loans.
result Unique extension of interest rate cap rule for all loans, based on net present value test.
DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
HCNAF models complex conditional distributions for probabilistic occupancy forecasting.
problem Modeling complex conditional probability density functions for occupancy forecasting.
method Hyper-Conditioned Neural Autoregressive Flow (HCNAF) combining AF and hyper-network.
result HCNAF achieves state-of-the-art performance in self-driving datasets.
Study optimal strategies for unwinding uncertain order flows in financial trading desks.
problem Optimizing strategies for handling uncertain order flows in financial trading desks.
method Modeling and solving the problem for a general class of in-flow processes, enabling an analytic solution.
result Optimal strategies depend on the autocorrelation of orders; only truth-telling flow is unwound myopically.
The paper forecasts joint electricity demand across 14 British regions using additive models.
problem Forecasting regional electricity demand with cross-regional dependencies.
method Modified Cholesky parametrisation for multivariate Gaussian model, gradient boosting for model selection.
result The proposed model outperforms non-Gaussian copula-based models in forecasting.
Sobolev training helps neural nets fit function values and derivatives.
problem Training neural nets to match function values and derivatives accurately.
method Using Sobolev loss with gradient flow for overparameterized networks.
result Gradient flow from random initialization can fit any function and its derivatives.
In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. Each private actor aims to maximize its expected terminal logarithmic utility. The…
Machine learning predicts greenhouse gas emissions for undisclosed companies.
problem Lack of GHG emissions data for most companies.
method Trained machine learning model on disclosed data to estimate emissions.
result Model accurately predicts emissions for undisclosed companies.
PIP-Net predicts pedestrian crossing intentions with up to 4-second lead.
problem Accurate pedestrian intention prediction for autonomous vehicles in real-world scenarios.
method Recurrent and temporal attention-based model using kinematic and spatial features.
result PIP-Net predicts pedestrian crossing intentions up to 4 seconds in advance.
Theory explains why neural nets better learn Calabi-Yau metrics.
problem Learning Calabi-Yau metrics with neural networks.
method Developed a theory of metric flows in neural network space.
result Finite-width neural networks learn Calabi-Yau metrics better than fixed kernel methods.
Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. …
In this paper, we consider three problems related to survival, growth, and goal reaching maximization of an investment portfolio with proportional net cash flow. We solve the problems in a market constrained due to borrowing prohibition. To solve the problems, we first construct an auxiliary market and then apply the d…
The paper explores discrete isothermic nets using checkerboard patterns in quadrilateral nets.
problem Defining and understanding discrete isothermic nets in quadrilateral nets.
method Using checkerboard patterns and discrete differential geometry to define and analyze isothermic nets.
result The class of isothermic nets is invariant under dualization and Moebius transformations.
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, Q∗-nets and conical…
Cash managers make daily decisions based on predicted monetary inflows from debtors and outflows to creditors. Usual assumptions on the statistical properties of daily net cash flow include normality, absence of correlation and stationarity. We provide a comprehensive study based on a real-world cash flow data set from…
We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book (LOB) before and after the arrival of a market order. For each of the stocks that we study, we identify a sequence of distinct phases across which the net flow of orders differs considerably. We note …
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …
Deep nets trained with MSE loss exhibit Neural Collapse, collapsing features and classifiers to class means.
problem Understanding Neural Collapse in MSE-trained deep nets.
method Developed a new MSE loss decomposition and introduced the central path concept.
result Exact dynamics of Neural Collapse along the central path can be predicted.
Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-rever…
Discretizes special surfaces using Koenigs nets.
problem Integrable structure of special surfaces.
method Discretisation via Koenigs nets.
result Preserves integrable structure in discretization.
Paper develops models to forecast private equity fund cash flows.
problem Limited literature on illiquid alternative asset cash flow forecasting.
method Develops benchmark model and two novel approaches (direct vs. indirect) using LSTM/GRU models and macroeconomic indicators.
result Direct model performs better and aligns with actual cash flows, but indirect model's performance is less clear.
We discuss discretization of Koenigs nets (conjugate nets with equal Laplace invariants) and of isothermic surfaces. Our discretization is based on the notion of dual quadrilaterals: two planar quadrilaterals are called dual, if their corresponding sides are parallel, and their non-corresponding diagonals are parallel.…
Classifies nets with area-preserving transformations into two types.
problem Classifying nets with area-preserving transformations.
method Classification using Combescure transformations and isotropic metric duality.
result Found two classes of nets: cone nets and Koenigs nets.
Defines CAMC discrete nets and their properties.
problem Understanding CAMC discrete nets and their properties.
method Defining CAMC discrete nets and proving properties.
result Properties of CAMC discrete nets are equivalent to properties of compatible interpolating quadrics.
We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation g…