A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a…
The paper tackles finding optimal treatment sequences in continuous state spaces.
problem Finding counterfactually optimal action sequences in continuous state spaces.
method Formalizes the problem using finite horizon Markov decision processes and structural causal models. Develops a search method based on the A* algorithm.
result The method can find optimal action sequences in polynomial time under certain conditions.
RANDPOL uses randomized networks for efficient reinforcement learning in continuous state and action MDPs.
problem Efficient reinforcement learning in environments with continuous state and action spaces.
method RANDPOL uses randomized function approximation to represent policy and value functions, providing finite time guarantees and improved numerical performance.
result RANDPOL achieves better numerical performance and provides finite time guarantees compared to deep neural network based algorithms.
NCDSSM models irregularly sampled time series with improved imputation and forecasting.
problem Accurate modeling of irregularly sampled time series with missing observations.
method Neural Continuous-Discrete State Space Model (NCDSSM) with amortized inference for auxiliary variables and flexible dynamic state parameterizations.
result Improved imputation and forecasting performance on multiple benchmark datasets.
We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of th…
The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …
We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those …
Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good representations" to be a learned state abstraction, and "challenging problems" to be…
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets…
We consider the problem of building a state representation model for control, in a continual learning setting. As the environment changes, the aim is to efficiently compress the sensory state's information without losing past knowledge, and then use Reinforcement Learning on the resulting features for efficient policy …
We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating Bayesian belief updates into long-term expected return. However, computing an e…
This paper develops variational continual learning (VCL), a simple but general framework for continual learning that fuses online variational inference (VI) and recent advances in Monte Carlo VI for neural networks. The framework can successfully train both deep discriminative models and deep generative models in compl…
We consider the problem of building a state representation model in a continual fashion. As the environment changes, the aim is to efficiently compress the sensory state's information without losing past knowledge. The learned features are then fed to a Reinforcement Learning algorithm to learn a policy. We propose to …
We introduce a framework for model learning and planning in stochastic domains with continuous state and action spaces and non-Gaussian transition models. It is efficient because (1) local models are estimated only when the planner requires them; (2) the planner focuses on the most relevant states to the current planni…
The paper explains how continuous language models can produce discrete, interpretable meanings.
problem Semantic collapse in continuous systems of large language models.
method Formalizing large language models as Continuous State Machines (CSMs) and analyzing the associated transfer operator.
result The leading eigenfunctions of the transfer operator induce a finite number of invariant meaning basins, explaining how continuous computation can produce discrete, interpretable semantics.
In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small …