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byAK and the research community

Aug 20

Can Transformers Do Enumerative Geometry?

How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of psi-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10^{-45} to 10^{45}. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer's ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. To the best of our knowledge, there has been no prior work on modeling recursive functions with such a high-variance and factorial growth. Beyond simply computing intersection numbers, we explore the enumerative "world-model" of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the the large-genus asymptotic of psi-class intersection numbers. These findings suggest that the network internalizes the parameters of the asymptotic closed-form and the polynomiality phenomenon of psi-class intersection numbers in a non-linear manner.

ACU: Analytic Continual Unlearning for Efficient and Exact Forgetting with Privacy Preservation

The development of artificial intelligence demands that models incrementally update knowledge by Continual Learning (CL) to adapt to open-world environments. To meet privacy and security requirements, Continual Unlearning (CU) emerges as an important problem, aiming to sequentially forget particular knowledge acquired during the CL phase. However, existing unlearning methods primarily focus on single-shot joint forgetting and face significant limitations when applied to CU. First, most existing methods require access to the retained dataset for re-training or fine-tuning, violating the inherent constraint in CL that historical data cannot be revisited. Second, these methods often suffer from a poor trade-off between system efficiency and model fidelity, making them vulnerable to being overwhelmed or degraded by adversaries through deliberately frequent requests. In this paper, we identify that the limitations of existing unlearning methods stem fundamentally from their reliance on gradient-based updates. To bridge the research gap at its root, we propose a novel gradient-free method for CU, named Analytic Continual Unlearning (ACU), for efficient and exact forgetting with historical data privacy preservation. In response to each unlearning request, our ACU recursively derives an analytical (i.e., closed-form) solution in an interpretable manner using the least squares method. Theoretical and experimental evaluations validate the superiority of our ACU on unlearning effectiveness, model fidelity, and system efficiency.

Many Ways to Be Lonely: Fine-Grained Characterization of Loneliness and Its Potential Changes in COVID-19

Loneliness has been associated with negative outcomes for physical and mental health. Understanding how people express and cope with various forms of loneliness is critical for early screening and targeted interventions to reduce loneliness, particularly among vulnerable groups such as young adults. To examine how different forms of loneliness and coping strategies manifest in loneliness self-disclosure, we built a dataset, FIG-Loneliness (FIne-Grained Loneliness) by using Reddit posts in two young adult-focused forums and two loneliness related forums consisting of a diverse age group. We provided annotations by trained human annotators for binary and fine-grained loneliness classifications of the posts. Trained on FIG-Loneliness, two BERT-based models were used to understand loneliness forms and authors' coping strategies in these forums. Our binary loneliness classification achieved an accuracy above 97%, and fine-grained loneliness category classification reached an average accuracy of 77% across all labeled categories. With FIG-Loneliness and model predictions, we found that loneliness expressions in the young adults related forums were distinct from other forums. Those in young adult-focused forums were more likely to express concerns pertaining to peer relationship, and were potentially more sensitive to geographical isolation impacted by the COVID-19 pandemic lockdown. Also, we showed that different forms of loneliness have differential use in coping strategies.