Non-integrability of dominated splitting on T2\mathbb{T}^2

We construct a diffeomorphism $f$ on 2-torus with a dominated splitting $E \oplus F$ such that there exists an open neighborhood $\mathcal{U} \ni f$ satisfying that for any $g \in \mathcal{U}$, neither $E_g$ nor $F_g$ is integrable

Hierarchically Structured Reinforcement Learning for Topically Coherent Visual Story Generation

We propose a hierarchically structured reinforcement learning approach to address the challenges of planning for generating coherent multi-sentence stories for the visual storytelling task. Within our framework, the task of generating a story given a sequence of images is divided across a two-level hierarchical decoder. The high-level decoder constructs a plan by generating a semantic concept (i.e., topic) for each image in sequence. The low-level decoder generates a sentence for each image using a semantic compositional network, which effectively grounds the sentence generation conditioned on the topic. The two decoders are jointly trained end-to-end using reinforcement learning. We evaluate our model on the visual storytelling (VIST) dataset. Empirical results from both automatic and human evaluations demonstrate that the proposed hierarchically structured reinforced training achieves significantly better performance compared to a strong flat deep reinforcement learning baseline.Comment: Accepted to AAAI 201

AttnGAN: Fine-Grained Text to Image Generation with Attentional Generative Adversarial Networks

In this paper, we propose an Attentional Generative Adversarial Network (AttnGAN) that allows attention-driven, multi-stage refinement for fine-grained text-to-image generation. With a novel attentional generative network, the AttnGAN can synthesize fine-grained details at different subregions of the image by paying attentions to the relevant words in the natural language description. In addition, a deep attentional multimodal similarity model is proposed to compute a fine-grained image-text matching loss for training the generator. The proposed AttnGAN significantly outperforms the previous state of the art, boosting the best reported inception score by 14.14% on the CUB dataset and 170.25% on the more challenging COCO dataset. A detailed analysis is also performed by visualizing the attention layers of the AttnGAN. It for the first time shows that the layered attentional GAN is able to automatically select the condition at the word level for generating different parts of the image