The study introduces backward baselines to distinguish past prediction from future prediction in machine learning models.
problem Differentiating between past and future prediction in machine learning models.
method Theoretical, empirical, and normative arguments support a family of simple and efficient statistical tests called backward baselines.
result The study provides a meaningful backward baseline for auditing black-box prediction systems.
We propose a simple technique for encouraging generative RNNs to plan ahead. We train a "backward" recurrent network to generate a given sequence in reverse order, and we encourage states of the forward model to predict cotemporal states of the backward model. The backward network is used only during training, and play…
The study examines backward compatibility issues in ML systems, especially with noisy data.
problem Backward compatibility challenges in ML systems, especially with noisy data.
method Empirical analysis of ML systems across different architectures and datasets, focusing on data shifts and noise.
result Backward compatibility issues arise even without data shift due to optimization stochasticity and training on large-scale noisy datasets can significantly decrease compatibility.
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
Extends SABR model for pricing RFR caplets.
problem Pricing backward RFR caplets in a post-Libor market.
method Closed-form effective SABR parameters for backward RFR caplets.
result Closed-form solution for backward RFR caplets.
Optimal wealth strategy derived for jump-diffusion models with liabilities.
problem Maximizing utility in jump-diffusion models with random liabilities.
method Forward Backward SDEs system for optimal strategy.
result Explicit results for pure jump model and exponential utilities.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
The paper develops methods to price options under rough volatility models using BSPDEs.
problem Pricing options in models with non-Markovian dynamics.
method Backward stochastic partial differential equations (BSPDEs) and deep learning for numerical approximations.
result Existence and uniqueness of weak solutions for general nonlinear BSPDEs.
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a…
A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
BC-Aligner maintains backward compatibility of embeddings after frequent updates.
problem Updating embeddings without requiring consumer teams to retrain their models.
method Learning backward compatible embeddings through BC-Aligner.
result BC-Aligner maintains backward compatibility with existing unintended tasks after multiple model version updates.
We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward a…
Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.
problem Hidden-state stability in RNNs
method Backward coherence analysis
result Almost-sure convergence, rates under mixing, interpretable limiting representation, finite pathwise stopping times, and theoretical framework for time-uniform confidence sequences.
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensi…
This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse,…
Bayesian units improve speech recognition with minimal parameters.
problem Improving speech recognition models with fewer parameters.
method Derived Bayesian recurrent units integrated into deep learning frameworks.
result Adding Bayesian units improves speech recognition performance.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Paper presents IMRCs for evolving tasks with forward and backward learning.
problem Incremental learning of evolving tasks with few samples per task.
method Incremental minimax risk classifiers (IMRCs) that exploit forward and backward learning.
result IMRCs provide significant performance improvement, especially with reduced sample sizes.
Backwards uniqueness proved for flows with asymptotically conical singularities.
problem Proving uniqueness of mean curvature flows with specific singularities.
method Developed new global tools to handle singularities, asymptotic structure, and smooth parts of flows.
result Backwards uniqueness for mean curvature flows with asymptotically conical singularities proved.
SGD converges with perturbed forward-backward passes, explained by geometric amplification.
problem Analyzing convergence of SGD with perturbed forward-backward passes in composite optimization.
method Characterized propagation and amplification of perturbations, derived convergence guarantees for non-convex and PL objectives.
result Perturbations cascade through the computational graph, affecting convergence order under specific conditions.
In this note, we will show a backwards uniqueness theorem of the mean curvature flow with bounded second fundamental form in arbitrary codimension.
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backwa…
In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final val…
In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the origin…
Backward SDEs help price XVA for OTC derivatives.
problem XVA valuation for OTC derivatives with default risk.
method Review and apply BSDEs with random horizon.
result Explicit formula for XVA correction terms.
Unified approach solves Kyle model with dynamic information.
problem Solving a generalized Kyle model with dynamic information.
method Monge-Kantorovich duality and backward stochastic partial differential equations.
result Characterization of optimal strategies and pricing rules.
New HMC method handles features in POS tagging, outperforming MEMM.
problem HMC struggles with arbitrary features in POS tagging.
method Introduced Entropic Forward-Backward (EFB) probabilities to compute HMC restorations.
result EFB-based HMC outperforms MEMM in POS tagging.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
Backward propagation rules for warped products under Ricci flow.
problem Understanding how warped product structures behave under Ricci flow.
method Establishing sufficient conditions for backward propagation of warped product structures.
result Asymptotically conical shrinkers are multiply-warped products over Einstein manifolds.
Gradient descent implicitly regularizes neural networks by penalizing large loss gradients.
problem How to optimize deep neural networks without explicit regularization.
method Backward error analysis to calculate implicit gradient regularization and demonstrate its effectiveness empirically.
result Implicit gradient regularization biases gradient descent toward flat minima, improving model robustness and test errors.
Paper tackles backwards-compatible data adaptation for confounded covariate and label shifts.
problem Adapt covariates to predict labels confounded with covariate shifts.
method Proposes confounded shift framework based on minimizing divergence between source and target conditional distributions, conditioning on confounders.
result Demonstrates approach on synthetic and real datasets, achieving backwards-compatible data adaptation.
We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. We also discuss suitable initial and boundary…
In this paper, we prove a unique continuation or ``backwards-uniqueness'' theorem for solutions to the Ricci flow. A particular consequence is that the isometry group of a solution cannot expand within the lifetime of the solution.
Study BSΔE on lattices for asset price analysis.
problem Optimal investment and market equilibrium analysis in asset price models.
method Backward stochastic difference equations on lattices.
result Applications to optimal investment and market equilibrium analysis.
The paper defines a frequency for mean curvature flow and proves its monotonicity.
problem Backwards uniqueness for solutions of mean curvature flow.
method Defining and proving monotonicity of a parabolic frequency for mean curvature flows.
result Frequency monotonicity implies backwards uniqueness for mean curvature flow solutions.
Improved state estimation in nonlinear models using amortized backward variational inference.
problem State estimation in general state-space models.
method Amortized backward variational inference with neural network parameters.
result Linear growth of variational approximation error in number of observations.
DG improves policy gradient efficiency by selectively backpropagating only valuable samples.
problem Expensive backward passes in policy gradient methods reduce efficiency.
method Introduces 'delight' as a forward-pass signal of learning value and a Kondo gate to selectively backpropagate.
result Selective backpropagation reduces backward pass costs without sacrificing learning quality.
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
Study optimal investment in large populations of competitive, heterogeneous agents.
problem Maximizing utility in a large, interacting agent system with relative performance concerns.
method Analyzes stochastic utility maximization game in finite and infinite agent settings, using graphon models and backward stochastic differential equations.
result Convergence of Nash equilibria and optimal utilities from finite to infinite agent models under specific conditions.
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
Paper proves stability of complex equations under various conditions.
problem Stability of backward stochastic differential equations with jumps.
method General framework for convergent sequences of data and solutions.
result Convergent sequence of solutions for associated data.
We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the e…
This paper proposes BRIEF, a backward reduction algorithm that explores compact CNN-model designs from the information flow perspective. This algorithm can remove substantial non-zero weighting parameters (redundant neural channels) of a network by considering its dynamic behavior, which traditional model-compaction te…
New method improves adversarial training efficiency and robustness.
problem High computational costs and lack of stability in adversarial training.
method Backward smoothing for randomized smoothing of random initialization.
result Our method achieves similar model robustness as state-of-the-art methods but with significantly less training time.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…