Neural shape representations have recently shown to be effective in shape analysis and reconstruction tasks. Existing neural network methods require point coordinates and corresponding normal vectors to learn the implicit level sets of the shape. Nor
mal vectors are often not provided as raw data, therefore, approximation and reorientation are required as pre-processing stages, both of which can introduce noise. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal shape representation networks that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and show state-of-the-art performance compared to other unoriented methods and on-par performance compared to oriented methods.
Understanding classifier decision under novel environments is central to the community, and a common practice is evaluating it on labeled test sets. However, in real-world testing, image annotations are difficult and expensive to obtain, especially w
hen the test environment is changing. A natural question then arises: given a trained classifier, can we evaluate its accuracy on varying unlabeled test sets? In this work, we train semantic classification and rotation prediction in a multi-task way. On a series of datasets, we report an interesting finding, i.e., the semantic classification accuracy exhibits a strong linear relationship with the accuracy of the rotation prediction task (Pearsons Correlation r > 0.88). This finding allows us to utilize linear regression to estimate classifier performance from the accuracy of rotation prediction which can be obtained on the test set through the freely generated rotation labels.
Motivated by the desire to exploit patterns shared across classes, we present a simple yet effective class-specific memory module for fine-grained feature learning. The memory module stores the prototypical feature representation for each category as
a moving average. We hypothesize that the combination of similarities with respect to each category is itself a useful discriminative cue. To detect these similarities, we use attention as a querying mechanism. The attention scores with respect to each class prototype are used as weights to combine prototypes via weighted sum, producing a uniquely tailored response feature representation for a given input. The original and response features are combined to produce an augmented feature for classification. We integrate our class-specific memory module into a standard convolutional neural network, yielding a Categorical Memory Network. Our memory module significantly improves accuracy over baseline CNNs, achieving competitive accuracy with state-of-the-art methods on four benchmarks, including CUB-200-2011, Stanford Cars, FGVC Aircraft, and NABirds.
A subgraph $H$ of an edge-coloured graph is called rainbow if all of the edges of $H$ have different colours. In 1989, Andersen conjectured that every proper edge-colouring of $K_{n}$ admits a rainbow path of length $n-2$. We show that almost all opt
imal edge-colourings of $K_{n}$ admit both (i) a rainbow Hamilton path and (ii) a rainbow cycle using all of the colours. This result demonstrates that Andersens Conjecture holds for almost all optimal edge-colourings of $K_{n}$ and answers a recent question of Ferber, Jain, and Sudakov. Our result also has applications to the existence of transversals in random symmetric Latin squares.
A tight Hamilton cycle in a $k$-uniform hypergraph ($k$-graph) $G$ is a cyclic ordering of the vertices of $G$ such that every set of $k$ consecutive vertices in the ordering forms an edge. R{o}dl, Ruci{n}ski, and Szemer{e}di proved that for $kgeq 3$
, every $k$-graph on $n$ vertices with minimum codegree at least $n/2+o(n)$ contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such $k$-graphs is $exp(nln n-Theta(n))$. As a corollary, we obtain a similar estimate on the number of Hamilton $ell$-cycles in such $k$-graphs for all $ellin{0,dots,k-1}$, which makes progress on a question of Ferber, Krivelevich and Sudakov.
