Journées de l'optimisation 2024

HEC Montréal, Québec, Canada, 6 — 8 mai 2024

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TB3 - CP-AI-OR --- Symbolic AI for Machine Learning

7 mai 2024 13h30 – 15h10

Salle: METRO INC. (jaune)

Présidée par Gilles Pesant

3 présentations

  • 13h30 - 13h55

    Music Generation with Long-Term Structure Using Constraint Programming and Transformer-Based Decoders

    • Liliane-Caroline Demers, prés., Polytechnique Montréal
    • Gilles Pesant, Polytechnique Montréal

    Successful music generation with AI techniques requires musical consistency, referring to the repetition of identical or similar musical segments. Sequences generated with Machine Learning (ML) models can imitate the dataset quite fruitfully but have difficulty exhibiting long-term structure. Previous work combined constraint programming (CP) with an ML model at inference time to provide structure to the generated sequences. We explore this work further by automatically injecting constraints closely related to the style of the corpus on which the ML model was trained. We first execute pattern detection on our dataset regarding pitches, rhythms and intervals, and then identify trends within the noted patterns that are used to create musically meaningful constraints in the CP models. Our goal is to produce music samples that express the intended long-term structure while still remaining faithful to the style of the corpus.

  • 13h55 - 14h20

    SAT-based Optimal Decision Trees For Interpretable Clustering with Constraints

    • Pouya Shati, University of Toronto
    • Yuliang Song, prés., University of Toronto
    • Eldan Cohen, University of Toronto
    • Sheila McIlraith, University of Toronto

    Constrained clustering is the semi-supervised task of identifying meaningful groups within data while satisfying a set of provided constraints. The constraints can represent domain-specific knowledge and have been shown to significantly enhance clustering accuracy. While constrained clustering can be solved using using exact optimization formulations, existing approaches lack interpretability. Decision trees have recently been considered as inherently interpretable solutions for clustering, however these approaches do not support constraints and do not provide theoretical guarantees. We introduce a novel SAT-based encoding for decision tree clustering with constraints, combining interpretable and constrained clustering for the first time. Our approach guarantees approximation of a Pareto optimal solution for a well-known bi-criteria objective. We further present insight into the trade-off between interpretability and feasibility, propose soft constraints to utilize infeasible constraint sets, and show how to provide approximations of the whole Pareto front. Extensive experiments on real-world and synthetic datasets demonstrate that our constrained decision tree clustering approach can produce high-quality and highly interpretable solutions. Further, we show that soft constraints successfully overcome the problem of infeasibility and that we are able to obtain superior solutions by exploring the approximate Pareto front.

  • 14h20 - 14h45

    An Improved Neuro-Symbolic Architecture to Fine-Tune Generative AI Systems

    • Chao Yin, prés., Polytechnique Montréal
    • Gilles Pesant, Polytechnique Montréal
    • Quentin Cappart, Polytechnique Montréal

    RL-Tuner, a reinforcement learning framework designed for the fine-tuning of a neural model to adhere to given constraints, was enhanced to learn from the output of two constraint programming models. The first model computes a score representing the number of constraint violations from the currently generated token while the second model provides the marginal probability of that token being generated if no additional violation is allowed.
    In this paper, we significantly enhance the latter framework in three ways. First, we propose a simplified architecture that requires only a single constraint programming model. Second, we evaluate constraint violations in a more accurate and consistent manner. Third, we propose a reward signal based on belief propagation on this new model that further improves performance.
    Our experiments, conducted on the same learning task of music generation, demonstrate that our approach surpasses the previous framework both in terms of convergence speed during training and in post-training accuracy. Additionally, our approach exhibits superior generalization to longer sequences than those used during training.

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