Approximately Hadamard matrices and Riesz bases in random frames

An $n \times n$ matrix with $\pm 1$ entries which acts on $\mathbb{R}^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with $\pm 1$ entries which act as approximate scaled isometries in $\mathbb{R}^n$ for all $n$. More precisely, the matrices we construct have condition numbers bounded by a constant independent of $n$. Using this construction, we establish a phase transition for the probability that a random frame contains a Riesz basis. Namely, we show that a random frame in $\mathbb{R}^n$ formed by $N$ vectors with independent identically distributed coordinates having a non-degenerate symmetric distribution contains many Riesz bases with high probability provided that $N \ge \exp(Cn)$. On the other hand, we prove that if the entries are subgaussian, then a random frame fails to contain a Riesz basis with probability close to $1$ whenever $N \le \exp(cn)$, where $c<C$ are constants depending on the distribution of the entries

Understanding Dark Scenes by Contrasting Multi-Modal Observations

Understanding dark scenes based on multi-modal image data is challenging, as both the visible and auxiliary modalities provide limited semantic information for the task. Previous methods focus on fusing the two modalities but neglect the correlations among semantic classes when minimizing losses to align pixels with labels, resulting in inaccurate class predictions. To address these issues, we introduce a supervised multi-modal contrastive learning approach to increase the semantic discriminability of the learned multi-modal feature spaces by jointly performing cross-modal and intra-modal contrast under the supervision of the class correlations. The cross-modal contrast encourages same-class embeddings from across the two modalities to be closer and pushes different-class ones apart. The intra-modal contrast forces same-class or different-class embeddings within each modality to be together or apart. We validate our approach on a variety of tasks that cover diverse light conditions and image modalities. Experiments show that our approach can effectively enhance dark scene understanding based on multi-modal images with limited semantics by shaping semantic-discriminative feature spaces. Comparisons with previous methods demonstrate our state-of-the-art performance. Code and pretrained models are available at https://github.com/palmdong/SMMCL

The Discussion of aoInfanta Problem: The Situation and Trends of Chinese Childrens Animation

The problem Infant in Chinese animation will be analyzed the differences between Chilren s Animation and Infant will be declaired then it will be point out that Childish view in Chinese public opinion is wrong There are shown that the Chinese animation s experiences and trend

Interaction-aware Kalman Neural Networks for Trajectory Prediction

Forecasting the motion of surrounding obstacles (vehicles, bicycles, pedestrians and etc.) benefits the on-road motion planning for intelligent and autonomous vehicles. Complex scenes always yield great challenges in modeling the patterns of surrounding traffic. For example, one main challenge comes from the intractable interaction effects in a complex traffic system. In this paper, we propose a multi-layer architecture Interaction-aware Kalman Neural Networks (IaKNN) which involves an interaction layer for resolving high-dimensional traffic environmental observations as interaction-aware accelerations, a motion layer for transforming the accelerations to interaction aware trajectories, and a filter layer for estimating future trajectories with a Kalman filter network. Attributed to the multiple traffic data sources, our end-to-end trainable approach technically fuses dynamic and interaction-aware trajectories boosting the prediction performance. Experiments on the NGSIM dataset demonstrate that IaKNN outperforms the state-of-the-art methods in terms of effectiveness for traffic trajectory prediction.Comment: 8 pages, 4 figures, Accepted for IEEE Intelligent Vehicles Symposium (IV) 202