RLHC uses multiple critics at different levels to enhance RL performance.
problem Speed up RL learning and increase cumulative rewards in competition tasks.
method Introducing multiple cooperative critics at two levels of a hierarchy to provide global information.
result RLHC outperforms PPO in tennis and soccer competitions.
Study lower bounds for connectivity of distance function level sets in convex sets.
problem Understanding connectivity of distance function level sets in convex sets.
method Lower bound calculation using critical points of the distance function.
result Provide a lower bound for the range of connectivity.
The paper characterizes potential functions whose level sets are orbits in mechanical systems.
problem Characterizing smooth potential energy functions on the plane with specific level set properties.
method Analyzing inverse curvature flow and properties of level sets.
result Analytic or functions with totally path-disconnected critical sets must be radial, while every compact convex set is a critical set of a Levi potential.
The paper examines how the topology of level sets changes with critical points in Morse theory.
problem Understanding how the topology of level sets changes with critical points in Morse theory.
method Study of sublevel sets and level sets of Morse functions, analysis of critical points and their indices.
result For a general class of functions, the topology of a regular level set changes when passing a single critical point, unless the index is half the dimension of the manifold.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Characterizes level-set families of harmonic functions without critical points.
problem Understanding level-set families of harmonic functions without critical points.
method Characterization via local differential-geometric condition and construction from geometric data.
result Evolution of gradient of harmonic functions determined by mean curvature of level sets.
For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy le…
Model criticism tool evaluates text coherence and structure in generated long-form text.
problem Evaluate the high-level structure of generated text for coherence, coreference, and topicality.
method Apply model criticism in latent space to compare real and generated data distributions.
result Transformer-based models struggle with maintaining structural coherence and coreference.
New Morse-Bott function defined on Stiefel manifolds, revealing complex critical structures.
problem Defining Morse-Bott functions on non-linear Stiefel manifolds.
method Replacing linear height function with a quadratic one, proving it as a Morse-Bott function.
result Critical submanifolds are fibrations of products of Grassmannians, not Grassmannians themselves.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
Analyzes properties of transnormal Finsler functions on compact manifolds.
problem Properties of transnormal Finsler functions on compact manifolds.
method Analyzes critical level sets and partition properties of transnormal functions.
result Critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition. New method identifies self-organized states in stock market declines.
problem Understanding the structure of financial time series.
method Identifying stock declines, finding a critical level, interpreting as phase transition.
result Evidence of self-organization in stock market indices, not in random series.
A theorem connects integral of second-order derivatives to function rise.
problem Understanding the integral of second-order derivatives over regions.
method Proves integral proportional to function rise over specified regions.
result Integral of second-order derivatives equals rise in function value.
Study solid angles to find Seifert hypersurfaces.
problem Understanding solid angles and their relation to Seifert hypersurfaces.
method Analyze the solid angle function and its critical levels.
result Non-critical level sets of the solid angle function are Seifert hypersurfaces.
The paper finds infinitely many magnetic geodesics on non-compact manifolds.
problem Existence and multiplicity of periodic orbits of magnetic flows.
method Morse theory applied to non-compact manifolds with energy levels above the Mañé critical value.
result Infinitely many noncontractible closed magnetic geodesics found.
Deep learning depends on tuning layers near critical points.
problem Understanding how deep learning architectures depend on tuning parameters.
method Random energy approach to analyze statistical dependence in deep belief networks.
result Statistical dependence can propagate only if layers are tuned near critical points.
New proofs of Cheeger-like inequalities for coexact 1-forms on hyperbolic manifolds.
problem Cheeger-like inequalities for coexact 1-forms on hyperbolic manifolds.
method Properties of magnetic geodesic flow and behavior at Mañé's critical energy level.
result Improved Cheeger constants and volume dependence in proofs.
Deep Learning identifies 20 critical proteins linked to FLT3-ITD mutation in leukemia.
problem Identifying critical proteins associated with FLT3-ITD mutation in leukemia.
method Hierarchical Deep Learning network using autoencoders for feature extraction.
result Deep Learning accurately correlates 20 critical proteins with FLT3-ITD mutation (97% accuracy).
Paper resolves ambiguity in non-convex bilevel optimization problems.
problem Ambiguity in bilevel optimization with non-convex lower-level objectives.
method Introduces selection maps to define critical points and resolves ambiguity.
result Validates new analytical tools in Morse theory for implicit differentiation.
In this paper, we present theorems specifying the critical values for series associated with debts arranged in the order of their duration.
The paper classifies functions with isolated critical points on a compact surface and develops a criterion for their global equivalence.
problem Classifying functions with isolated critical points on the boundary of a compact surface.
method Topological classification in a neighborhood of critical points, construction of chord diagrams, and development of a criterion for global equivalence.
result A criterion for global topological equivalence of functions with three critical points on a compact surface.
Empirical study on trends reversion in financial markets.
problem Understanding when trends in financial markets revert.
method Polynomial regression and bootstrapping on 30 years of daily futures prices.
result Trends revert when they reach a critical level of statistical significance.
New RL method MAC improves performance in sparse reward settings.
problem Slow mixing in large state spaces or sparse rewards.
method Multi-level Monte Carlo Actor-Critic (MAC) algorithm.
result Achieves convergence rate comparable to state-of-the-art AC algorithms.
We continue the study of the variation of the p--modulus of a foliation initiated by the first author. We derive the formula for the second variation which allows to study p--stable foliations. We obtain some results concerning codimension one p--stable foliations. Moreover, we derive the equation for the critica…
The paper analyzes how SGD visits different regions of a non-convex problem's state space.
problem Understanding the long-run distribution of stochastic gradient descent in non-convex problems.
method Large deviations theory and randomly perturbed dynamical systems.
result The long-run distribution of SGD resembles the Boltzmann-Gibbs distribution with temperature equal to the step-size.
Study of symmetries of sphere divisions induced by functions with isolated critical points.
problem Understanding symmetries of sphere divisions induced by functions with isolated critical points.
method Analyzing the group of diffeomorphisms that leave invariant a connected component of a level set and its complement.
result The group of such diffeomorphisms is isomorphic to a finite subgroup of SO(3). CSEAL uses cognitive structure to personalize learning paths.
problem Personalized learning paths based on learners' evolving knowledge levels and item structures.
method CSEAL integrates knowledge levels and item structures using a Markov Decision Process and actor-critic algorithm.
result CSEAL effectively personalizes learning paths, improving learning outcomes.
We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We al…
Policy certifies inventory levels meeting service requirements.
problem Maintaining stock levels meeting service requirements despite unknown demand.
method Data-driven order policy using online learning and integral action.
result Valid inference method for finite samples.
We prove that for a uniformly convex Lagrangian system L on a compact manifold M, almost all energy levels contain a periodic orbit. We also prove that below Ma ne's critical value of the lift of the Lagrangian to the universal cover, almost all energy levels have conjugate points. We prove that if the energy level [E=…
Classification of ground state solutions to critical Dirac equation on spheres.
problem Classifying ground state solutions of the critical Dirac equation.
method Exploiting conformal covariance and relating to the Yamabe equation.
result Ground state solutions are given by Killing spinors up to conformal diffeomorphisms.
Deep nets mislead on subtle perturbed inputs.
problem Vulnerability of DNNs to adversarial examples.
method Visual analytics approach to explain datapaths of adversarial examples.
result Visualization helps experts investigate datapaths from high-level layers to neuron activations.
In this paper we introduce two models of opinion dynamics in oligopoly markets and apply them to a situation, where a new entrant challenges two incumbents of the same size. The models differ in the way the two forces influencing consumer choice -- (local) social interactions and (global) advertising -- interact. We st…
The paper explores the structure of Reeb spaces for smooth functions on manifolds.
problem Understanding the structure of Reeb spaces for smooth functions on manifolds.
method Proving the structure of Reeb spaces and showing that any graph can be realized as a Reeb space.
result The Reeb space of a smooth function on a closed manifold with finitely many critical values has a graph structure.
Crypto crashes show no consistent early warning signal, suggesting they are abrupt shocks rather than critical transitions.
problem Identifying early warning signals for crypto crashes.
method Analysis of seven major BTC liquidation cascades using minute-level price and leverage/order-flow data.
result No variable is event-invariant, and the critical-slowing-down signature is present in only five out of seven events.
Study critical metrics on manifolds, proving specific isometries.
problem Investigating critical metrics on complete manifolds.
method Analyzing volume functional and proving isometries.
result Critical metrics on specific manifolds are isometric to standard models.
Enhanced tracking control for AUVs with improved policy gradient method.
problem Trajectory tracking problem for underactuated AUVs with unknown dynamics and constrained inputs.
method Hybrid actors-critics architecture with multiple actors and critics, Pseudo Q-learning, and deterministic policy gradient.
result High-level tracking control accuracy and stable learning of AUVs.
We prove that the number of critical points of a Li-Tam Green's function on a complete open Riemannian surface of finite type admits a topological upper bound, given by the first Betti number of the surface. In higher dimensions, we show that there are no topological upper bounds on the number of critical points by con…
This paper tackles multilayer graph clustering via convex layer aggregation.
problem Challenges in clustering multilayer graphs and combining information from each layer.
method Theoretical framework for multilayer spectral graph clustering via convex layer aggregation.
result Establishes a critical value on the noise level for reliable cluster separation.
LICA learns credit assignment for cooperative agents without explicit formulation.
problem Credit assignment among cooperative agents.
method Centralized critic as hypernetwork, adaptive entropy regularization.
result Significantly outperforms previous methods on benchmarks.
Study estimates personalized effects of maternal PM2.5 exposure on birth weight.
problem Identify critical windows and heterogeneity in maternal PM2.5 exposure effects on birth weight.
method Heterogeneous Distributed Lag Models and Bayesian Additive Regression Trees.
result Evidence of heterogeneity in PM2.5-birth weight relationship, with some dyads showing 3x larger decrease.
Research tackles safety of deep learning in safety-critical tasks.
problem Safety concerns of deep learning in perception tasks for autonomous agents.
method Technical enumeration and discussions on safety concerns and mitigation methods.
result Need for more mitigation methods to ensure safety of deep learning.
Parastatistic distribution of a total debt owed to a large number of creditors considered in relation to the duration of these debts. The process of debt calculation depends on the fractal dimension of economic system in which this process takes place. Two actual variants of these dimensions are investigated. Critical …
Bayesian CNN improves MRI stroke diagnosis accuracy and uncertainty quantification.
problem Uncertainty quantification in automated image analysis for medical decision-making.
method Bayesian Convolutional Neural Network (CNN) with aggregation methods for patient-level diagnoses.
result Bayesian CNN achieved 95.33% accuracy on 511 patients, 2% higher than non-Bayesian.
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O(K−1/2) rate. The study finds infinitely many periodic orbits just above a critical value on a 2-sphere.
problem Finding periodic orbits just above a critical value on a 2-sphere.
method Introduced a new critical value c∞(L) and showed its strict inequality to the Mañé critical value c(L), proving the existence of infinitely many periodic orbits on energy levels e∈(c(L),c∞(L)). result Infinitely many periodic orbits exist on energy levels just above the Mañé critical value.
We present the complete analytical classification of the atoms arising at the critical points of rank 1 of the Kowalevski-Yehia gyrostat. To classify the Smale-Fomenko diagrams, all separating values of the gyrostatic momentum are found. We present a kind of constructor of the Fomenko graphs; its application gives the …
Level set flow's singularities are type I under 2-convexity, leading to specific curvature blow-up rates.
problem Understanding the nature and behavior of singularities in level set flow.
method Analytical approach using Lojasiewicz inequality and curvature blow-up rates.
result The arrival time is C2 near a critical point if and only if it satisfies a Lojasiewicz inequality.