arXiv subjects

Wee Chaimanowong

Publications and source records attributed to Wee Chaimanowong.

6 recordsLinked to original sources

arXiv2026

Approximating invariant functions with the sorting trick is theoretically justified

Many machine learning models leverage group invariance which is enjoyed with a wide-range of applications. For exploiting an invariance structure, one common approach is known as \emph{frame averaging}. One popular example of frame averaging is the \emph{group averaging}, where the entire group is used to symmetrize a function. Another example is the \emph{canonicalization}, where a frame at each point consists of a single group element which transforms the point to its orbit representative, for example, sorting. Compared to group averaging, canonicalization is more efficient computationally. However, it results in non-differentiability or discontinuity of the canonicalized function. As a result, the theoretical performance of canonicalization has not been given much attention. In this work, we establish an approximation theory for canonicalization. Specifically, we bound the point-wise and $L^2(\mathbb{P})$ approximation errors as well as the eigenvalue decay rates associated with a canonicalization trick applied to reproducing kernels. We discuss two key insights from our theoretical analyses and why they point to an interesting future research direction on how one can choose a design to fully leverage canonicalization in practice.

cs.LG↗

arXiv2026

Content Platform GenAI Regulation via Compensation

The use of Generative AI (GenAI) for creative content generation has gained popularity in recent years. GenAI allows creators to generate contents that are increasingly becoming indistinguishable to the human--generated counter--part at a much lower cost. While GenAI reshapes the competitive landscape of the contents market, the original creators were typically not compensated for their works that were used in the GenAI training. On the other hands, the wide--spread adoption of GenAI threatens to replace the human--generated shares of contents on content platforms, contaminating training data source for future GenAI models. In this paper, we argue that an unregulated usage of GenAI can also be harmful to the platform by causing a contents distribution distortion which can lower the consumers' engagement and the platform's profit. We show that a simple economically--driven creator compensation scheme, can incentivize more creation of high--value human--generated contents, without the need for an AI--detector. This reduces the data pollution for future GenAI training, while improves the consumer engagement and the platform's profit.

cs.CY↗

arXiv2024

Influencing Competition Through Shelf Design

Shelf design decisions strongly influence product demand. In particular, placing products in desirable locations increases demand. This primary effect on shelf position is clear, but there is a secondary effect based on the relative positioning of nearby products. Intuitively, products located next to each other are more likely to be compared having positive and negative effects. On the one hand, locations closer to relatively strong products will be undesirable, as these strong products will draw demand from others -- an effect that is stronger for those in close proximity. On the other hand, because strong products tend to attract more traffic, locations closer to them elicit high consumer attention by increased visibility. Modifying the GEV class of models to allow demand to be moderated by competitors' proximity, these two effects emerge naturally. We found that although the competition effect is usually stronger, it is not always the dominating effect. Shelf displays can achieve higher profits by exploiting the relative influence on competition from shelf design to shift demand to higher profitability products. In the paper towel category, we found profitability differences of up to 7\% and displays with 3\% higher gross profits over the best shelf design present in our data.

econ.GN↗

arXiv2020

Seiberg-Witten Theory and Topological Recursion

Kontsevich-Soibelman (2017) reformulated Eynard-Orantin topological recursion (2007) in terms of Airy structure which provides some geometrical insights into the relationship between the moduli space of curves and topological recursion. In this work, we investigate the analytical approach to this relationship using the Seiberg-Witten family of curves as the main example. In particular, we are going to show that the formula computing the Hitchin systems' Special Kahler's prepotential from the genus zero part of topological recursion as obtained by Baraglia-Huang (2017) can be generalized for a more general family of curves embedded inside a foliated symplectic surface, including the Seiberg-Witten family. Consequently, we obtain a similar formula relating the Seiberg-Witten prepotential to the genus zero part of topological recursion on a Seiberg-Witten curve.

math.DG↗

arXiv2020

Airy structures and deformations of curves in surfaces

An embedded curve in a symplectic surface $Σ\subset X$ defines a smooth deformation space $\mathcal{B}$ of nearby embedded curves. A key idea of Kontsevich and Soibelman arXiv:1701.09137 [math.AG], is to equip the symplectic surface $X$ with a foliation in order to study the deformation space $\mathcal{B}$. The foliation, together with a vector space $V_Σ$ of meromorphic differentials on $Σ$, endows an embedded curve $Σ$ with the structure of the initial data of topological recursion, which defines a collection of symmetric tensors on $V_Σ$. Kontsevich and Soibelman define an Airy structure on $V_Σ$ to be a formal quadratic Lagrangian $\mathcal{L}\subset T^*(V_Σ^*)$ which leads to an alternative construction of the tensors of topological recursion. In this paper we produce a formal series $θ$ on $\mathcal{B}$ of meromorphic differentials on $Σ$ which takes it values in $\mathcal{L}$, and use this to produce the Donagi-Markman cubic from a natural cubic tensor on $V_Σ$, giving a generalisation of a result of Baraglia and Huang, arXiv:1707.04975 [math.DG].

math.AG↗

arXiv2020

Coloured refined topological vertices and parafermion conformal field theories

We extend the definition of the refined topological vertex C to an n-coloured refined topological vertex C_n that depends on n free bosons, and compute the 5D strip partition function made of N pairs of C_n vertices and conjugate C*_n vertices. Using geometric engineering and the AGT correspondence, the 4D limit of this strip partition function is identified with a (normalized) matrix element of a (primary state) vertex operator that intertwines two (arbitrary descendant) states in a (generically non-rational) 2D conformal field theory with Z_n parafermion primary states.

hep-th↗