Convex Hybrid Modeling: An Operator-Based Approach

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear ones, promoting the use of operator theory, which ``universally'' represents a nonlinear system by a nonparametric operator. On the other hand, interpretability requires by a ``non-universal'', parametric nonlinear model family satisfying first principles; these constraints tend to complicate the learning procedure. This paper considers hybrid modeling by formulating convex learning problems that account for interpretability systematically and give surrogate models efficiently. Three settings are discussed -- (i) regularization around a particular ``reference model'', (ii) restriction on an ``interpretable subspace'', and more generally, (iii) restriction on a ``interpretable manifold'' that is nonlinearly parameterized. In the more general setting, by introducing an operator-theoretic technique to re-parameterize models in the ``lifted'' parameters (``canonical features'', potentially infinite-dimensional), the system is regarded as a kernel-based mixture of interpretable models. Application to both static and dynamic models are exemplified in numerical studies.

MovieTeller: Tool-augmented Movie Synopsis with ID Consistent Progressive Abstraction

With the explosive growth of digital entertainment, automated video summarization has become indispensable for applications such as content indexing, personalized recommendation, and efficient media archiving. Automatic synopsis generation for long-form videos, such as movies and TV series, presents a significant challenge for existing Vision-Language Models (VLMs). While proficient at single-image captioning, these general-purpose models often exhibit critical failures in long-duration contexts, primarily a lack of ID-consistent character identification and a fractured narrative coherence. To overcome these limitations, we propose MovieTeller, a novel framework for generating movie synopses via tool-augmented progressive abstraction. Our core contribution is a training-free, tool-augmented, fact-grounded generation process. Instead of requiring costly model fine-tuning, our framework directly leverages off-the-shelf models in a plug-and-play manner. We first invoke a specialized face recognition model as an external "tool" to establish Factual Groundings--precise character identities and their corresponding bounding boxes. These groundings are then injected into the prompt to steer the VLM's reasoning, ensuring the generated scene descriptions are anchored to verifiable facts. Furthermore, our progressive abstraction pipeline decomposes the summarization of a full-length movie into a multi-stage process, effectively mitigating the context length limitations of current VLMs. Experiments demonstrate that our approach yields significant improvements in factual accuracy, character consistency, and overall narrative coherence compared to end-to-end baselines.