Study shows continuity of non-Kähler Calabi-Yau conifold transitions.
problem Understanding the geometry of Calabi-Yau conifold transitions.
method Use of balanced and Hermitian-Yang-Mills metrics to analyze conifold transitions.
result The conifold transition is continuous in the Gromov-Hausdorff topology.
New transitions found in Spin(7) holonomy metrics related to a dynamical system.
problem Understanding the geometry of Spin(7) holonomy metrics with Aloff--Wallach spaces.
method Relating Spin(7)-equations to a 3-dimensional dynamical system.
result Discovered new transitions with Spin(7) holonomy metrics.
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
Neural models learn continuous-time Markov chain transition rates from data.
problem Learning transition rates for complex stochastic systems.
method Neural networks to model nonlinear transition rates from observed data.
result Neural models outperform traditional methods in accuracy.
The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…
New methods use machine learning to simulate rare transitions in molecular systems.
problem Simulating rare transitions between metastable states in molecular dynamics.
method Generative models and reinforcement learning for importance sampling.
result Efficiently generated transition paths linking metastable states.
PQR estimates reward functions from actions and states without assuming state-only rewards.
problem Estimating reward functions from actions and states without state-only assumptions.
method Deep learning approach that sequentially estimates policy, Q-function, and reward.
result PQR uniquely recovers true reward with known transitions and bounds error with unknown transitions.
New algorithm reduces suboptimality in imitation learning to nearly optimal levels.
problem Statistical limits of imitation learning in MDPs with known transitions.
method Mimic-MD algorithm and reduction to value estimation problem.
result Upper bound of O(∣S∣H3/2/N) for suboptimality, with efficient computation. New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
problem Achieving best-of-both-worlds guarantees with data-dependent regret bounds in MDPs with unknown transitions.
method Optimistic follow-the-regularized-leader algorithm with new optimistic Q-function estimators and transition bonus.
result First-order, second-order, and path-length bounds with polylog(T) regret in the stochastic regime.
New findings confirm parallels to De Giorgi's conjecture for phase transitions in higher dimensions.
problem Understanding phase transitions with bounded index in higher-dimensional spaces.
method Establishing parallels to De Giorgi's conjecture for general solutions of bounded Morse index.
result Finite index solutions to the Allen--Cahn equation in R4 are one-dimensional, and this holds for all 4≤n≤7. A new method for ILO with transition model disparity using an intermediary policy.
problem Learning tasks from expert observations with different transition dynamics.
method Training an intermediary policy to match the state transitions of the expert dataset.
result Our method outperforms existing ILO approaches with transition model mismatch.
We obtain explicit formulas for the trivialization functions of the SU(3) principal bundle G2→S6 over two affine charts. We also calculate the explicit transition function of this fibration over the equator of the six-sphere. In this way we obtain a new proof of the known fact that this fibration corres…
Model improves robustness of neural network sequences without transition failures.
problem Learning and generating complex sequences of motor primitives without interference.
method Inspired by thalamocortical circuit, uses specific module for motif transitions.
result Improved robustness of sequence generation with no transition failures.
Study finds phase transition in context-sensitive language model with short-range interactions.
problem Understanding phase transitions in language models with short-range interactions.
method Constructed a random language model with short-range interactions and investigated its statistical properties.
result Phase transition occurs in context-sensitive language models with constant context length.
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a …
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
Improved POMDP regret to sqrt(T) with known observation model.
problem Average-reward POMDPs with unknown transition model but known observation model.
method Optimistic algorithm using deterministic policies and novel estimation techniques.
result First approach with regret guarantee of sqrt(T) against optimal policy.
Study of symmetry distributions in Lorentzian naturally reductive nilmanifolds.
problem Understanding symmetry in Lorentzian naturally reductive nilmanifolds.
method Analysis of 2-step nilpotent Lorentzian Lie groups with transitive isometry subgroups.
result Fixed points of isotropy representation indicate the distribution of symmetry.
A vertex-transitive map X is a map on a closed surface on which the automorphism group Aut(X) acts transitively on the set of vertices. If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse…
This paper shows how post-Lie algebra structures can be induced by simply transitive NIL-affine actions.
problem Understanding which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Introducing post-Lie algebra structures and showing their correspondence with simply transitive actions.
result Simply transitive NIL-affine actions induce complete post-Lie algebra structures in the 2-step nilpotent case.
CERM calculates climate risks in bank loans.
problem Estimating climate risks in bank credit portfolios.
method Adapts credit risk models to include physical and transition risks.
result Calculates incremental credit losses due to climate risks.
In compressed sensing problems, ℓ1 minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical interest to find alternative polynomial-time algorithms which perform better than $\e…
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
A new method uses deep learning to efficiently sample rare transitions for estimating committor functions.
problem Efficiently sampling rare transitions to estimate committor functions in high-dimensional problems.
method DASTR (Deep Adaptive Sampling on Transition Paths) method using deep generative models.
result Significantly improved accuracy in approximating committor functions through efficient sampling.
New model shows natural language exhibits phase transition similar to physics.
problem Understanding critical properties in natural language models.
method Created a context-sensitive random language model.
result Demonstrated a Berezinskii--Kosterlitz--Thouless phase transition.
We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to…
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics that underlie the complex phenomenon of irreversible and path dependent price or…
New algorithm reduces reinforcement learning regret for linear MDPs with unknown transitions.
problem Adversarial linear mixture MDPs with bandit feedback and unknown transition.
method Proposes a new algorithm with a least square estimator and self-normalized concentration.
result Achieves improved regret bound with high probability.
This paper studies actions of solvable Lie groups on nilpotent Lie groups.
problem Characterizing which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Using Lie algebra properties and semisimple splitting, the paper provides methods to check for such actions.
result A full description of possibilities for actions up to dimension 4.
New protocols show 1-bit mean estimation can be order-optimal without interaction.
problem Can 1-bit mean estimation be optimal without interaction?
method Adaptive and non-adaptive threshold and interval queries, with one adaptive transition.
result Arbitrary non-adaptive quantizers can match the adaptive rate, suggesting interaction is not necessary.
This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partia…
Adding metadata abruptly changes network inference outcomes.
problem Understanding the impact of metadata on network inference.
method Investigated the effect of metadata on network inference problems.
result Metadata causes abrupt transitions in inference outcomes.
Efficient RL for linear MDPs with unknown transitions.
problem Long planning horizons and unknown state transitions in linear mixture MDPs.
method Horizon-free algorithm using weighted least squares with variance and uncertainty awareness.
result Achieves optimal regret up to logarithmic factors.
The present paper analyses the formal parallelism existing between the laws of thermodynamics and some economic principles. Based on previous works, we shall show how the existence in Economics of principles analogous to those in thermodynamics involves the occurrence of economic events that remind of well-known phenom…
We study unsupervised multilingual alignment, the problem of finding word-to-word translations between multiple languages without using any parallel data. One popular strategy is to reduce multilingual alignment to the much simplified bilingual setting, by picking one of the input languages as the pivot language that w…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, the portfolio optimization is …
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
A vertex-transitive map X is a map on a surface on which the automorphism group of X acts transitively on the set of vertices of X. If the face-cycles at all the vertices in a map are of same type then the map is called a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse of this is …
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of S1-gerbes. At the same time, transitive Courant algebroids may be viewed as the higher analogue of Atiyah Lie algebroids, and the non-commutative a…
The study explores spacetimes with changing spatial curvature, leading to topological transitions.
problem The need for a model that avoids infinite matter and energy after the Big Bang.
method Investigates spacetimes with time-dependent spatial curvature, allowing it to change sign.
result Topological transitions are possible in spacetimes with time-dependent spatial curvature.
Paper tackles dynamic behavior of variable topology mechanisms, presenting new transition conditions.
problem Dynamic behavior of mechanisms with changing kinematic topology.
method Presented new transition conditions for variable topology mechanisms using projected motion equations and Voronets equations.
result Results show the dynamic behavior of joint locking in 3R and 6DOF mechanisms.
Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been mostly analyzed from an optimization perspective, without addressing the problem of exploration, or by making strong assumptions on the interaction with the environment. In …
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
Characterizes RFF regression in large n,p,N setting, providing precise learning phases and double descent curve.
problem Characterizes RFF regression in large n,p,N setting. method Characterizes the exact asymptotics of random Fourier feature (RFF) regression in the realistic setting of large n,p,N. result Characterizes two qualitatively different phases of learning and the corresponding double descent test error curve.
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…
Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.
problem Recovering signals through an inhomogeneous low-rank matrix channel.
method Derive and analyze an approximate message-passing algorithm (AMP) and a spectral method.
result The AMP iteration matches the conjectured optimal computational phase transition.
Abstract: Investigates the role of activation functions in neural networks and their physical basis.
problem Understanding the role of activation functions in neural networks and their physical basis.
method Formalizes the use of activation functions in neural inference by relating them to phase transitions in statistical physics.
result Reveals the physical justification for the performance of typical activation functions in neural networks.