skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If car- ried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic opti- mization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.  more » « less
Award ID(s):
1816499
PAR ID:
10105513
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
International Conference on Learning Representations (ICLR 2019)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition)
    null (Ed.)
    Learning pose invariant representation is a fundamental problem in shape analysis. Most existing deep learning algorithms for 3D shape analysis are not robust to rotations and are often trained on synthetic datasets consisting of pre-aligned shapes, yielding poor generalization to unseen poses. This observation motivates a growing interest in rotation invariant and equivariant methods. The field of rotation equivariant deep learning is developing in recent years thanks to a well established theory of Lie group representations and convolutions. A fundamental problem in equivariant deep learning is to design activation functions which are both informative and preserve equivariance. The recently introduced Tensor Field Network (TFN) framework provides a rotation equivariant network design for point cloud analysis. TFN features undergo a rotation in feature space given a rotation of the input pointcloud. TFN and similar designs consider nonlinearities which operate only over rotation invariant features such as the norm of equivariant features to preserve equivariance, making them unable to capture the directional information. In a recent work entitled "Gauge Equivariant Mesh CNNs: Anisotropic Convolutions on Geometric Graphs" Hann et al. interpret 2D rotation equivariant features as Fourier coefficients of functions on the circle. In this work we transpose the idea of Hann et al. to 3D by interpreting TFN features as spherical harmonics coefficients of functions on the sphere. We introduce a new equivariant nonlinearity and pooling for TFN. We show improvments over the original TFN design and other equivariant nonlinearities in classification and segmentation tasks. Furthermore our method is competitive with state of the art rotation invariant methods in some instances. 
    more » « less
  2. ; ; (, AAAI/Graphs and more Complex structures for Learning and Reasoning Workshop)
    We address the problem of graph regression using graph convolutional neural networks and permutation invariant representation. Many graph neural network algorithms can be abstracted as a series of message passing functions between the nodes, ultimately producing a set of latent features for each node. Processing these latent features to produce a single estimate over the entire graph is dependent on how the nodes are ordered in the graph’s representation. We propose a permutation invariant mapping that produces graph representations that are invariant to any ordering of the nodes. This mapping can serve as a pivotal piece in leveraging graph convolutional networks for graph classification and graph regression problems. We tested out this method and validated our solution on the QM9 dataset. 
    more » « less
  3. ; ; (, Mathematics of Operations Research)
    We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and sign-invariant norm with a cardinality constraint. This gives a nonlinear formulation for the feasible set of sparse principal component analysis (PCA) and an alternative proof of the K-support norm. Second, we characterize the convex hull of sets of matrices defined by constraining their singular values. As a consequence, we generalize an earlier result that characterizes the convex hull of rank-constrained matrices whose spectral norm is below a given threshold. Third, we derive convex and concave envelopes of various permutation-invariant nonlinear functions and their level sets over hypercubes, with congruent bounds on all variables. Finally, we develop new relaxations for the exterior product of sparse vectors. Using these relaxations for sparse PCA, we show that our relaxation closes 98% of the gap left by a classical semidefinite programming relaxation for instances where the covariance matrices are of dimension up to 50 × 50. 
    more » « less
  4. ; (, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022))
    Boucher, Christina; Rahmann, Sven (Ed.)
    Many bioinformatics applications involve bucketing a set of sequences where each sequence is allowed to be assigned into multiple buckets. To achieve both high sensitivity and precision, bucketing methods are desired to assign similar sequences into the same bucket while assigning dissimilar sequences into distinct buckets. Existing k-mer-based bucketing methods have been efficient in processing sequencing data with low error rate, but encounter much reduced sensitivity on data with high error rate. Locality-sensitive hashing (LSH) schemes are able to mitigate this issue through tolerating the edits in similar sequences, but state-of-the-art methods still have large gaps. Here we generalize the LSH function by allowing it to hash one sequence into multiple buckets. Formally, a bucketing function, which maps a sequence (of fixed length) into a subset of buckets, is defined to be (d₁, d₂)-sensitive if any two sequences within an edit distance of d₁ are mapped into at least one shared bucket, and any two sequences with distance at least d₂ are mapped into disjoint subsets of buckets. We construct locality-sensitive bucketing (LSB) functions with a variety of values of (d₁,d₂) and analyze their efficiency with respect to the total number of buckets needed as well as the number of buckets that a specific sequence is mapped to. We also prove lower bounds of these two parameters in different settings and show that some of our constructed LSB functions are optimal. These results provide theoretical foundations for their practical use in analyzing sequences with high error rate while also providing insights for the hardness of designing ungapped LSH functions. 
    more » « less
  5. ; ; (, Proceedings of the 14th Workshop on the Economics of Networks, Systems and Computation)
    We consider an InterDependent Security (IDS) game with networked agents and positive externality where each agent chooses an effort/investment level for securing itself. The agents are interdependent in that the state of security of one agent depends not only on its own investment but also on the other agents' effort/investment. Due to the positive externality, the agents under-invest in security which leads to an inefficient Nash equilibrium (NE). While much has been analyzed in the literature on the under-investment issue, in this study we take a different angle. Specifically, we consider the possibility of allowing agents to pool their resources, i.e., allowing agents to have the ability to both invest in themselves as well as in other agents. We show that the interaction of strategic and selfish agents under resource pooling (RP) improves the agents' effort/investment level as well as their utility as compared to a scenario without resource pooling. We show that the social welfare (total utility) at the NE of the game with resource pooling is higher than the maximum social welfare attainable in a game without resource pooling but by using an optimal incentive mechanism. Furthermore, we show that while voluntary participation in this latter scenario is not generally true, it is guaranteed under resource pooling. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email