New framework shows finite-difference estimates can be more efficient for nearly deterministic systems.
problem Understanding and improving policy gradient estimation for nearly deterministic systems.
method Developed a theoretical framework focusing on the variance of finite-difference estimates compared to the policy gradient theorem.
result Finite-difference estimates can have lower variance for nearly deterministic systems, making them more efficient.
New method calibrates predictions in chaotic systems using variational inference.
problem Uncertainty in data assimilation for chaotic systems.
method Variational inference applied to multivariate Gaussian distribution.
result Nearly perfectly calibrated predictions in chaotic Lorenz-96 dynamics.
Study the tradeoffs of bandit feedback in multiclass classification.
problem The price of using bandit feedback in multiclass classification.
method Mistake bound model, analysis of variants, and comparison of learners and adversaries.
result The optimal mistake bound under bandit feedback is at most O ( k ) O(k) O ( k ) times higher than in full information, with a tight bound of O ( k ) O(k) O ( k ) . Paper bounds PAC RL sample complexity in deterministic MDPs.
problem Identify ε-optimal policy with high probability.
method Proposes nearly matching upper and lower bounds on sample complexity, introduces deterministic return gap, uses graph-theoretical concepts and maximum-coverage exploration.
result First nearly matching upper and lower bounds on sample complexity for PAC RL in deterministic MDPs.
The subject of this paper is six-dimensional nearly (para-)Kähler geometry with pseudo-Riemannian metrics. Firstly, we derive the analogue of the well-known exterior differential system characterising a nearly Kähler manifold and prove applications to the automorphism group of a nearly (para-)Kähler structure. Secondly…
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
The goal of counterfactual learning for statistical machine translation (SMT) is to optimize a target SMT system from logged data that consist of user feedback to translations that were predicted by another, historic SMT system. A challenge arises by the fact that risk-averse commercial SMT systems deterministically lo…
Framework simulates market microstructure with stable Hawkes processes.
problem Reproduce realistic market order flow dynamics.
method Deterministic C++ LOB simulator with Hawkes-driven stochastic order flow.
result Derives stability and ergodicity proofs for Hawkes models.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
Study shows RFRR's effectiveness with nearly orthogonal data in overparameterized settings.
problem Understanding the effectiveness of random feature regression with nearly orthogonal data.
method Investigates RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime.
result Shows high-probability non-asymptotic concentration results for RFRR's training, cross-validation, and generalization errors.
Data-driven method approximates Koopman generator for system identification and control.
problem Approximating Koopman generator for system identification and control.
method gEDMD (extended dynamic mode decomposition) for deterministic and stochastic systems.
result Data-driven approximation of Koopman generator for system identification and control.
Efficient algorithm for online control with adversarial disturbances, nearly minimizing regret.
problem Online control of linear systems with adversarial disturbances.
method Developed an efficient algorithm that provides nearly tight regret bounds.
result The algorithm nearly minimizes regret for the problem of online control with adversarial disturbances.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
In this paper almost complex surfaces of the nearly Kähler S 3 × S 3 S^3\times S^3 S 3 × S 3 are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly Kähler S 3 × S 3 S^3\times S^3 S 3 × S 3 . We also find a correspondence betwe…
New concept of epiplexity quantifies useful information from data.
problem Understanding useful information content from data without unlimited computational capacity.
method Introducing epiplexity, a measure of information computationally bounded observers can learn.
result Epiplexity captures useful information content, not just randomness.
SVM generalizes well even with many support vectors in high dimensions.
problem Generalization of SVM in high-dimensional spaces with many support vectors.
method Identified new deterministic equivalences and proved conditions for support vector proliferation.
result Broadened conditions for SVM generalization in high-dimensional settings and proved converse result.
A deep learning strategy outperforms traditional methods in stocks portfolio management.
problem Optimizing stock portfolio performance using machine learning.
method Deep Deterministic Policy Gradient framework with neural networks.
result Compound annual return rate of 14.12% compared to 7 other strategies.
New framework measures systemic risk with variable market volatility.
problem Classical risk measures fail to capture market volatility complexity.
method Proposes a new framework on L p ( ⋅ ) L^{p(\cdot)} L p ( ⋅ ) space with random exponents. result Derives dual representations of systemic risk quantification.
Physics-constrained GANs generate samples that meet deterministic constraints.
problem Ensuring GAN-generated samples comply with physical constraints.
method Enforce deterministic constraints via modified loss function.
result Physics-constrained GANs produce samples that accurately meet underlying constraints.
Study on regret minimization in deterministic MDPs.
problem Minimizing regret in deterministic reinforcement learning.
method Logarithmic regret lower bounds, leveraging graph theory and cycles.
result Explicitly quantifies the fundamental limit of performance achievable by any learning algorithm.
Linear recurrent networks explain reinforcement learning performance in partially observable settings.
problem Understanding why linear recurrent networks work in reinforcement learning with partial observability.
method Constructed and studied two linear filters for HMMs and action-controlled HMMs.
result Linear filters serve as sufficient statistics and reduce state ambiguity, explaining empirical reinforcement learning success.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field appro…
Deterministic bounds for tensor singular values and vectors, differing from matrix cases.
problem Spectral learning of higher-order orthogonally decomposable tensors.
method Deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors.
result Perturbation affects each essential singular value/vector in isolation, independent of multiplicity and distance from other singular values.
A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with near neighbor interactions. The evolution of each agent results from the competition between two factors: the agent's own tendency to grow and the environmen…
New algorithm finds optimal policy with polynomial trajectories in deterministic systems.
problem Finding optimal policy in deterministic systems with function approximation.
method Novel recursion-based algorithm with tight bounds on error and sample complexity.
result Optimal policy found using O ( dim E ) O(\dim_E) O ( dim E ) trajectories with $δ= O\left(ρ/\sqrt{\dim_E}
ight)$ . We study nearly-Kahler 6-manifolds equipped with a cohomogeneity-two Lie group action for which the principal orbits are coisotropic. If the metric is complete, then we show that this last condition is automatically satisfied, and both the acting Lie group and the principal orbits are finite quotients of $S^3 \times S^…
Approximate Bayesian Computation (ABC) is a framework for performing likelihood-free posterior inference for simulation models. Stochastic Variational inference (SVI) is an appealing alternative to the inefficient sampling approaches commonly used in ABC. However, SVI is highly sensitive to the variance of the gradient…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihoo…
Improved uncertainty estimation in neural networks with VBLL.
problem Improving uncertainty estimation in neural networks.
method Deterministic variational formulation for training Bayesian last layer neural networks.
result Improves predictive accuracy, calibration, and out-of-distribution detection.
Efficient inference for multimodal Gaussian mixture models of interacting dynamical systems.
problem Efficient inference for multimodal distributions in stochastic dynamical systems.
method Graph neural networks with moment matching for sample-free inference and structured covariance approximations.
result Sample-free inference with improved efficiency and stability compared to Monte Carlo alternatives.
Unified framework for solving fixed-point equations in deterministic and stochastic settings.
problem Solving fixed-point equations for seminorm-contractive operators in both deterministic and stochastic contexts.
method Fixed-point theorem and stochastic approximation analysis.
result Unified finite-sample bounds for various reinforcement learning algorithms.
A new method improves feature importance and model stress-testing reliability.
problem Estimating feature contributions in machine learning models for trust and transparency.
method Replacing multiple random permutations with a single, deterministic, and optimal permutation.
result Improved bias-variance tradeoffs and accuracy in challenging scenarios.
We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexio…
A new deterministic method for symbolic regression finds mathematical expressions from data.
problem Finding mathematical expressions from datasets efficiently and reliably.
method Deterministic growth of simple expressions until they fit the data.
result Results are as good as other Machine Learning methods but in lower computational time.
We study pseudoholomorphic curves in the nearly Kalher C P 3 \mathbf{CP}^3 CP 3 . It is shown that a class of curves called null-torsion are in one to one correspondence with the integrals of a holomorphic contact system on the usual Kahler C P 3 \mathbb{CP}^3 CP 3 studied by Bryant. Browing Bryant's result we get plenty of such curves. …
New method distinguishes stochastic from deterministic signals using excursion counts.
problem Distinguishing between stochastic and deterministic signals in discrete time series.
method Excursion and crossing theorems for continuous semimartingales, comparing empirical excursion counts to theoretical expectation.
result A robust data-driven diffusion test that classifies signals based on log-log slope deviation.
Proposes a deterministic LIME for CAD systems.
problem Instability in LIME explanations.
method Uses agglomerative HC and KNN to select relevant clusters and trains a linear model.
result DLIME is more stable than LIME.
New algorithm reduces regret for linear bandits with unknown noise variance.
problem Finding optimal actions in linear bandits with varying noise variance.
method Adaptive algorithm with Freedman-type concentration inequality and multi-layer structure.
result Achieves i l d e O ( d ∑ k = 1 K σ k 2 + d ) ilde{O}(d \sqrt{\sum_{k = 1}^K σ_k^2} + d) i l d e O ( d ∑ k = 1 K σ k 2 + d ) regret for linear bandits. This paper presents a fast Bayesian filtering technique for state estimation.
problem Bottleneck in Bayesian inference for state estimation from noisy sensor data.
method Processor-native uncertainty tracking for uncertainty propagation and inference.
result Deterministic approximate filtering with up to 805x speedup and competitive accuracy.
New method ensures consistent inference across different tensor parallel sizes for large language models.
problem Non-deterministic inference in large language models due to inconsistent reduction orders across GPUs.
method Tree-Based Invariant Kernels (TBIK) that align intra- and inter-GPU reduction orders through a unified hierarchical binary tree structure.
result Bit-wise identical results across different tensor parallel sizes for RL training.
We develop a mean-field theory for multi-component ICA in high dimensions.
problem Understanding multi-component ICA in high-dimensional settings.
method Asymptotically exact mean-field theory for multi-component online ICA.
result Explicit learnability boundaries and competition conditions linking step size, data moments, and initialization.
DAOC provides stable clustering for large networks.
problem Stable clustering of large networks with accuracy and robustness.
method DAOC uses Overlap Decomposition for deterministic fine-grained clusters and Mutual Maximal Gain for robustness.
result DAOC yields stable clusters that are 25% more accurate than state-of-the-art deterministic algorithms.
We analyze deep neural networks in the large size and iteration limit, revealing a deterministic system of equations.
problem Understanding the behavior of deep neural networks in the asymptotic regime of large network sizes and iterations.
method Sequential limit of each hidden layer and characterization of parameter evolution, using weak convergence and stochastic analysis.
result The limit neural network recovers a global minimum with zero loss for the objective function.
We test whether the futures prices of some commodity and energy markets are determined by stochastic rules or exhibit nonlinear deterministic endogenous fluctuations. As for the methodologies, we use the maximal Lyapunov exponents (MLE) and a determinism test, both based on the reconstruction of the phase space. In par…
PNNs model aleatoric uncertainty in scientific machine learning with high accuracy.
problem Aleatoric uncertainty in scientific systems with unequal variance.
method Developed a probabilistic distance metric to optimize PNN architecture and used it in material science applications.
result PNNs yield remarkably accurate output mean estimates and high correlation in predicted intervals.
New methods reduce constraint violations to certainty in stochastic optimization.
problem Finding a point with certain constraint satisfaction and near-stationarity.
method Single-loop variance-reduced stochastic first-order methods with truncated momentum schemes.
result Achieves strong convergence guarantees for ε ε ε -stochastic stationary points with certain constraint satisfaction. This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…