Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions

We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence of the memory of the Hawkes intensity, this problem does not fall within classical stochastic control theory outside particular Markovian kernels. We first develop a finite-dimensional Markovianization procedure and algorithm to approximate multivariate Hawkes processes with mixtures of exponential kernels. We prove the convergence of the Markovianized approximation of the Hawkes process, its intensity, and the value of the problem to the original non-Markovian processes and the value of the primal problem. We then formulate continuous-time deterministic policy gradient learning on the Markovianized approximation of the problem, called Hawkes-CT DDPG. We propose a model-free algorithm to solve the non-Markovian Hawkes-driven optimization by observing only the event times of the process, the realization of the solution to the SDE, and a chosen set of decay filters, while the Hawkes kernel coefficients remain unknown. We compare our continuous time reinforcement learning Hawkes-CT DDPG method with discrete time reinforcement learning techniques under three different types of kernels: simple exponential, Erlang, and power-law kernels.

Mais de arXiv AI Papers

Entre para seguir esta fonte

arXiv AI Papers·há 3 dias☆

Can Language Models Play the Wikipedia Game?↗

Language models increasingly support or automate information retrieval from document collections too large to index. This task is difficult when it requires specialist linguistic or scientific knowledge. We used the Wikipedia Game to test language models on an analogous information retrieval task. In the game, players must reach a target article using only article links. We compared sentence embedding models and LLMs across five Wikipedia languages and five academic-literature datasets. We construct very large local graphs of Wikipedia pages and of paper citations using OpenAlex and provide code to build and navigate them. This allows the study of language models' navigation capabilities without relying on third-party APIs. We compared the models with human and TF-IDF benchmarks. The Wikipedia Game format enables robust comparisons across techniques, languages, and domains. No model significantly outperformed humans, although the best models (GPT-o3 mini, GPT-4o, QwQ:32B, and DeepSeek-R1:70B) achieved comparable success. Performance and rankings varied across languages and topics, with implications for practitioners utilising these techniques.

en

arXiv AI Papers·há 3 dias☆

Hide and Seek: HIDE Concepts to SEEK explanations for black box models↗

Interpreting machine learning model predictions is a central challenge, particularly for black-box vision models. Concept-based attribution methods interpret models using human-understandable concepts. Existing concept-based methods can only interpret classification and regression models. They require access to model weights or large concept-annotated datasets, and most methods cannot provide image-level attribution. We propose Hide and Seek (HnS), a new method for concept-level attribution that does not require access to model weights or labeled concept datasets. HnS can interpret a wide range of vision models. Given a concept and image set, HnS retrieves concept-aligned images using a vision-language model, localizes the concept within each image, masks the localized region, and measures attribution from the change in the black-box model's output between the original and masked images. This enables faithful attribution by directly measuring the model's behavior and supporting local attributions. We validated HnS on CelebA and COCO-Stuff. Compared to existing methods, HnS showed better agreement with ground-truth attributions. We demonstrated the applicability of HnS on diverse tasks, including image captioning and satellite image segmentation, where no existing concept attribution method can be used. We provided our anonymous code in the supplementary material.

en

arXiv AI Papers·há 3 dias☆

Constructive Bounds for the Topological Expressivity of Neural Networks↗

The expressivity of a neural network Φ describes the class of functions that a network can express. The term topological expressivity refers to a family of measures particularly suited to understand binary classification and is often formulated in terms of the Betti numbers of a decision boundary β(Φ^{-1}(0)). Despite its popularity, this measure is not as useful for regression and other problems that do not involve a decision boundary. Instead, we propose to study topological expressivity in terms of the Betti numbers of the output of a neural network β(Φ(X)). We formally prove that a ReLU network with architecture (d,_{k=1}^{d } β_k(3k+2),_{k=1}^{d}β_k(k+1)) can express spaces homotopy equivalent to wedge sums of spheres with arbitrary Betti numbers. This gives upper bounds for any arbitrary connected (β_0=1) sequence of Betti numbers, but by constructing spaces homotopy equivalent to products of N spheres of dimension d_1,...,d_N we achieve much better bounds $(_{n=1} d_n, 3_{n=1}^N d_n + 2N, _{n=1}^N d_n + N) for Betti numbers given by _n (1+x^{d_n})$. Finally we conjecture a much stronger tight bound which gives the architectural bound (d,d+1,d+1) for a space homeomorphic to the sphere.

en

arXiv AI Papers·há 3 dias☆

AI Models Can Provably Hide Arbitrary Capabilities↗

Capability evaluations aim to surface dangerous model behaviors before deployment, but their reliability depends on the assumption that hidden capabilities can be elicited. We show this assumption does not hold under adversarial conditions by constructing backdoor attacks that embed encrypted neural networks within host model weights, decrypting and executing them only upon receiving a secret trigger. Using digital lockers, these hidden circuits remain provably hard to elicit and interpret under cryptographic assumptions, even given full access to model weights, extending prior work from hiding fixed strings to arbitrary computations. We implement our proof of concept constructions in PyTorch and evaluate elicitation through fine-tuning, weight noising, gradient-based trigger search, and latent adversarial training on a small chemical reaction prediction task - a proxy for CBRN-relevant capabilities. Our results demonstrate resistance to these methods and, together with our cryptographic guarantees, reveal a limit of elicitation-based capability audits. We release our models to support the improvement of defenses.

en