Ruoqi Sun

Ruoqi Sun

This paper establishes a theoretical framework connecting neural network learning with abstract algebraic structures. We first present a minimal counterexample demonstrating that standard neural networks completely fail on compositional generalization tasks (0% accuracy). By introducing a logical constraint -- the Ternary Gamma Semiring -- the same architecture learns a perfectly structured feature space, achieving 100% accuracy on novel combinations. We prove that this learned feature space constitutes a finite commutative ternary $Γ$-semiring, whose ternary operation implements the majority vote rule. Comparing with the recently established classification of Gokavarapu et al., we show that this structure corresponds precisely to the Boolean-type ternary $Γ$-semiring with $|T|=4$, $|Γ|=1$}, which is unique up to isomorphism in their enumeration. Our findings reveal three profound conclusions: (i) the success of neural networks can be understood as an approximation of mathematically ``natural'' structures; (ii) learned representations generalize because they internalize algebraic axioms (symmetry, idempotence, majority property); (iii) logical constraints guide networks to converge to these canonical forms. This work provides a rigorous mathematical framework for understanding neural network generalization and inaugurates the new interdisciplinary direction of Computational $Γ$-Algebra.

Wanli Chen, Xinge Zhu, Ruoqi Sun et al.

Context information plays an indispensable role in the success of semantic segmentation. Recently, non-local self-attention based methods are proved to be effective for context information collection. Since the desired context consists of spatial-wise and channel-wise attentions, 3D representation is an appropriate formulation. However, these non-local methods describe 3D context information based on a 2D similarity matrix, where space compression may lead to channel-wise attention missing. An alternative is to model the contextual information directly without compression. However, this effort confronts a fundamental difficulty, namely the high-rank property of context information. In this paper, we propose a new approach to model the 3D context representations, which not only avoids the space compression but also tackles the high-rank difficulty. Here, inspired by tensor canonical-polyadic decomposition theory (i.e, a high-rank tensor can be expressed as a combination of rank-1 tensors.), we design a low-rank-to-high-rank context reconstruction framework (i.e, RecoNet). Specifically, we first introduce the tensor generation module (TGM), which generates a number of rank-1 tensors to capture fragments of context feature. Then we use these rank-1 tensors to recover the high-rank context features through our proposed tensor reconstruction module (TRM). Extensive experiments show that our method achieves state-of-the-art on various public datasets. Additionally, our proposed method has more than 100 times less computational cost compared with conventional non-local-based methods.

Ruoqi Sun, Chen Huang, Jianping Shi et al.

The task of face attribute manipulation has found increasing applications, but still remains challenging with the requirement of editing the attributes of a face image while preserving its unique details. In this paper, we choose to combine the Variational AutoEncoder (VAE) and Generative Adversarial Network (GAN) for photorealistic image generation. We propose an effective method to modify a modest amount of pixels in the feature maps of an encoder, changing the attribute strength continuously without hindering global information. Our training objectives of VAE and GAN are reinforced by the supervision of face recognition loss and cycle consistency loss for faithful preservation of face details. Moreover, we generate facial masks to enforce background consistency, which allows our training to focus on manipulating the foreground face rather than background. Experimental results demonstrate our method, called Mask-Adversarial AutoEncoder (M-AAE), can generate high-quality images with changing attributes and outperforms prior methods in detail preservation.