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Machine learning models underpin many modern financial systems for use cases such as fraud detection and churn prediction. Most are based on supervised learning with hand-engineered features, which relies heavily on the availability of…

Neural networks are widely used, yet their analysis and verification remain challenging. In this work, we present a Lean 4 formalization of neural networks, covering both deterministic and stochastic models. We first formalize Hopfield…

We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…

We conduct a comprehensive investigation into the dynamics of gradient descent using large-order constant step-sizes in the context of quadratic regression models. Within this framework, we reveal that the dynamics can be encapsulated by a…

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…

Cortical circuits exhibit high levels of response diversity, even across apparently uniform neuronal populations. While emerging data-driven approaches exploit this heterogeneity to infer effective models of cortical circuit computation…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…

Recently, there has been a surge in the use of generated data to enhance the performance of downstream models, largely due to the advancements in pre-trained language models. However, most prevailing methods trained generative and…

The increasing prevalence of synthetic data in training loops has raised concerns about model collapse, where generative models degrade when trained on their own outputs. While prior work focuses on this self-consuming process, we study an…

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Decisions to pursue higher education are not fully explained by economic incentives, with social influence and peer effects playing a crucial, yet dynamically understudied, role. This paper develops a theoretical non-linear dynamics model…

Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…

There is a rapidly growing interest in controlling consistency across multiple generated images using diffusion models. Among various methods, recent works have found that simply manipulating attention modules by concatenating features from…

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…

Collaborative learning, which enables collaborative and decentralized training of deep neural networks at multiple institutions in a privacy-preserving manner, is rapidly emerging as a valuable technique in healthcare applications. However,…

Model collapse, the severe degradation of generative models when iteratively trained on their own outputs, has gained significant attention in recent years. This paper examines Chain of Diffusion, where a pretrained text-to-image diffusion…

Generative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain…

Much research has been conducted on how consumption is related to human relations, for example, consumer communities organized around specific brands, or the way people use products to define their own identity and transmit a desired image.…