New method designs joint initial noises for diffusion models to improve diversity and alignment.
problem Independent initial noises limit diversity in generated images.
method Coupling of initial noises, maintaining Gaussian distribution while allowing dependence.
result Repulsive Gaussian coupling improves diversity without increasing sampling cost.
Existence of incomplete Radner equilibrium with endogenous noise tracker.
problem Existence of incomplete Radner equilibrium in a model with endogenous noise tracker.
method Proved existence through a coupled system of ODEs, reduced to two coupled ODEs.
result Endogenous noise tracker leads to higher aggregate welfare for large stock supply.
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.
U-Net trained to recover acoustic interference striations from distorted data.
problem Recovering acoustic interference striations from distorted signals.
method Training a U-Net using a random mode-coupling matrix model to generate training data.
result U-Net successfully recovers AISs under various conditions.
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Study of coupled Hawkes processes with rough-volatility limits.
problem Understanding coupled Hawkes processes with rough-volatility limits.
method Proving weak convergence of rescaled intensity vector to stochastic Volterra equations.
result Limiting components exhibit different degrees of roughness and cross-decorrelation law.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
New method uses coupled SDEs to edit images with high fidelity and consistency.
problem Challenges in editing image content with text-to-image models.
method Using coupled stochastic differential equations to guide generative model sampling.
result Achieves high prompt fidelity and near-pixel-level consistency.
A new framework for robust and coherent counterfactual transports.
problem Estimating joint distributions over counterfactual outcomes in personalized decision-making and treatment risk assessment.
method Counterfactual cocycles that use algebraic structure to provide coherence and identifiability guarantees, bridging the gap between bijective SCMs and OT methods.
result Counterfactual cocycles provide state-of-the-art performance and noise-robustness across synthetic benchmarks and a real-world study.
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources…
The paper maps time-series onto networks to reveal hidden joint information.
problem Extract hidden joint information from uncorrelated time-series.
method Discretize time-series amplitudes, map onto networks, measure coupling deviations, and compare with Gaussian distributions.
result Markets may possess joint patterns even if initially uncorrelated.
Large Sinkhorn couplings improve flow models in data generation tasks.
problem Training flow models with optimal transport couplings.
method Using large batches of source and target points, and applying entropic regularization with a low ε. result Flow models perform better with large Sinkhorn couplings and low regularization.
This paper shows how learning the phase-amplitude coupling improves bio-signal classification.
problem Discarding phase component in bio-signal feature extraction leads to poor generalization.
method Introducing a novel self-supervised learning task called Phase-Swap to detect phase-amplitude coupling.
result Neural networks trained on Phase-Swap task generalize better across subjects and recording sessions.
Study on nonsmooth contractive SA with constant stepsize and Q-learning.
problem Understanding convergence and bias in nonsmooth contractive SA with different noise types.
method Proposed prelimit coupling technique for steady-state convergence and derived asymptotic bias.
result Asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize.
We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the gene…
The paper cleans label noise in supervised classification using Bernoulli sampling.
problem Label noise degrades supervised classifier performance.
method Proposes a label noise cleaning method based on Bernoulli random sampling.
result The method separates clean and noisy observations without prior label information.
Model simulates correlation emergence in two coupled limit order books.
problem Modeling correlation emergence in coupled limit order books.
method Simulated two coupled diffusive limit order books using random walks in the fluid limit, with trader interactions.
result Demonstrated the recovery of an Epps effect from the model.
We study active learning where the labeler can not only return incorrect labels but also abstain from labeling. We consider different noise and abstention conditions of the labeler. We propose an algorithm which utilizes abstention responses, and analyze its statistical consistency and query complexity under fairly nat…
Enhances deep networks robustness with data mollification and label smoothing.
problem Improving deep neural networks' robustness against corruptions.
method Coupling data mollification (image noising and blurring) with label smoothing.
result Improved robustness and uncertainty quantification on corrupted image benchmarks.
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
Deep-neural-network (DNN) based noise suppression systems yield significant improvements over conventional approaches such as spectral subtraction and non-negative matrix factorization, but do not generalize well to noise conditions they were not trained for. In comparison to DNNs, humans show remarkable noise suppress…
Improved saliency maps for deep neural networks with reduced noise.
problem Noisy explanations in Integrated Gradients for deep neural networks.
method SmoothTaylor, adaptive noising, and SmoothGrad techniques.
result SmoothTaylor and adaptive noising generate better quality saliency maps.
Free lunch from noise reveals linear spectral features for RL.
problem Trade-off between expressiveness and tractability in RL.
method Noise assumption and Spectral Dynamics Embedding (SPEDE).
result SPEDE breaks the trade-off and completes optimistic exploration.
AlignFlow improves FGMs by optimizing noise and data alignment.
problem Optimal Transport methods for FGMs are limited by scalability issues.
method Introduces Semi-Discrete Optimal Transport (SDOT) to enhance FGM training.
result AlignFlow scales well to large datasets and model architectures.
A new method for joint noise removal and trend estimation from sparse signals.
problem Jointly removing noise and estimating trends from sparse signals.
method PENDANTSS combines SOOT/SPOQ penalties with BEADS algorithm in a Trust-Region block alternating variable metric forward-backward approach.
result Outperforms comparable methods in deconvolving analytical chemistry signals.
A new framework for PPLS combines noise estimation, optimization, and calibration.
problem Probabilistic PLS models need interpretable latent factors and calibrated uncertainty.
method End-to-end pipeline combining noise estimation, constrained optimization, and prediction calibration.
result Achieves near-nominal coverage and native calibrated uncertainty across benchmarks.
New method infers viral load from pooled tests.
problem Inefficient viral load inference in pooled testing.
method Message passing algorithm with PCR noise function.
result Accurate viral load inference possible.
We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows u…
Paper analyzes CLT for TTSA with Markovian noise, broadening its applications.
problem Analyzing asymptotic behavior of TTSA under Markovian noise.
method Central Limit Theorem applied to TTSA with Markovian noise.
result Uncovered coupled dynamics of TTSA influenced by Markov chain.
We propose a three-state microscopic opinion formation model for the purpose of simulating the dynamics of financial markets. In order to mimic the heterogeneous composition of the mass of investors in a market, the agent-based model considers two different types of traders: noise traders and contrarians. Agents are re…
We study the robustness properties of ℓ1 norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the ℓ1 estimator for measurements errors consisting of outliers coupled with noise. We…
Hierarchical pretraining with slow-fast ODEs
problem Causal self-attention vs. slow-fast ODEs
method Instantiating fast-slow ODE formalism as a concrete neural network
result Equilibrium manifold x=φ(y) is exactly the master-equation (ME) stationary distribution Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and sho…
Study on Langevin dynamics on planar motion group, highlighting geometric mechanism.
problem Understanding Langevin dynamics on the Lie group SE(2).
method Intrinsic formulation on SE(2), using invariant vector fields and natural projection.
result Effective macroscopic diffusion on R^2 emerges through averaging.
GD with early stopping trains shallow neural nets for nonparametric regression robustly.
problem Learning Lipschitz regression functions with noisy labels.
method Overparameterized shallow neural networks trained by GD with early stopping.
result Optimal rates of convergence for nonparametric regression.
We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: Inspired by Occam's razor, we assume that the exogenous variable is sim…
fSGLD optimizes deep learning by favoring flat regions in the loss landscape.
problem Understanding and improving the behavior and generalization of deep learning algorithms.
method Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD) that biases learning towards flat basins.
result fSGLD targets a flatness-biased Gibbs distribution with explicit excess risk guarantees.
Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect …
C-DPS improves diffusion posterior sampling for inverse problems without projection or likelihood approximation.
problem Inaccurate and unstable solutions in inverse problems due to complex or high-noise conditions.
method C-DPS introduces a forward stochastic process in measurement space evolving in parallel with data-space diffusion, leading to a closed-form posterior.
result C-DPS consistently outperforms existing methods across multiple inverse problem benchmarks.
DSPM models control noise volatility, improving financial data analysis.
problem Financial returns exhibit volatility clustering, challenging traditional models.
method DSPM uses a tempered-stable subordinator to control noise volatility, preserving kurtosis and autocorrelation.
result DSPM models accurately capture volatility clustering and noise mechanisms.
LANCA uses ANM to learn latent causal factors without supervision.
problem Learning latent causal factors without supervision.
method LANCA employs a deterministic Wasserstein Auto-Encoder coupled with a differentiable ANM Layer.
result LANCA outperforms baselines on physics and photorealistic environments.
Noise increases the Rashomon ratio, leading simpler models to perform similarly to complex ones.
problem Why simpler models perform similarly to complex models on noisy datasets.
method Analyzed the data generation process and model training choices, introduced pattern diversity.
result Noisier datasets lead to larger Rashomon ratios, explaining simpler models' performance.
Modeling financial chaos with market makers' risk appetite.
problem Unpredictable price changes in financial markets.
method Using Hamiltonian approach with anharmonic oscillators and nonlinear coupling.
result Market makers' risk appetite determines chaotic dynamics in financial markets.
In this paper we look at ergodic BSDEs in the case where the forward dynamics are given by the solution to a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck SDE with Lévy noise, taking values in a separable Hilbert space. We establish the existence of a unique bounded solution to an infinite horizon disc…
We empirically investigate the (negative) expected accuracy as an alternative loss function to cross entropy (negative log likelihood) for classification tasks. Coupled with softmax activation, it has small derivatives over most of its domain, and is therefore hard to optimize. A modified, leaky version is evaluated on…
Predicts coherence from quantum heat engine noise using machine learning.
problem Predicting coherence in quantum heat engines from nonequilibrium fluctuations.
method Developed a machine learning protocol using K-Nearest Neighbor (KNN) model.
result Machine learning successfully predicts coherence from quantum heat engine noise.
CAIRO separates ranking from scaling to improve robustness.
problem Conflating ranking and scaling in regression leads to model vulnerability.
method Two-stage approach: first learns a scoring function, then recovers scale.
result CAIRO recovers true regression function with auto-calibration guarantees.