Regularizes RNNs to be invariant to input order.
problem Making RNNs invariant to input order.
method Stochastic regularization to enforce permutation invariance.
result Improves model performance on permutation invariant tasks.
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48 results for “Permutation Invariance”
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 …
A new knot invariant uses permutations to extend Jones polynomials.
problem Extending Jones polynomials to classical and virtual knots and links.
method Colorings by permutations of a finite set to define new knot invariants.
result Established properties and computed polynomials for small cases.
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoid…
A new method learns graph distributions invariant to node ordering.
problem Graphs are hard to model due to node ordering invariance issues.
method Score-based generative modeling with permutation equivariant graph neural network.
result The method achieves better or comparable graph generation results.
4-Legendrian permutation racks can't distinguish knots but recover classical invariants.
problem Distinguishing Legendrian knots using permutation racks.
method Study of 4-Legendrian racks and their effectiveness.
result 4-Legendrian permutation racks cannot distinguish knots but recover classical invariants.
New model preserves graph structure in large datasets.
problem Lack of permutation invariance in graph generation models for large graphs.
method Uses graph embeddings to create a scalable generative model.
result Model maintains structure in large graphs without losing invariance.
Improves modeling of sets with permutation invariant densities.
problem Challenges in calculating trace limit practicality of current methods.
method Proposes an alternative approach to define permutation equivariant transformations with closed form trace.
result Improves both training and final performance.
Improves efficiency and scalability in multi-agent reinforcement learning.
problem Non-stationarity and inefficiency in critic networks due to agent permutations.
method Proposes a permutation invariant critic (PIC) to avoid changes in critic output due to agent permutations.
result Achieves improvements of test episode reward between 15% to 50% on challenging multi-agent particle environment (MPE).
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
problem Inability of conventional GNNs to fully capture node relationships due to permutation invariance.
method Develops permutation-sensitive aggregation mechanism using permutation groups.
result Proves superior expressivity compared to 2-WL test and not less than 3-WL test.
Permutation invariant network learns Wasserstein metrics.
problem Understanding the space of probability measures and comparing distributions.
method Permutation invariant network mapping samples to a low-dimensional space.
result Network can generalize to compute distances between unseen densities and learn moments.
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
Improves full conformal prediction for stochastic non-conformity measures.
problem Inability of existing conditions to guarantee full conformal prediction validity under stochastic settings.
method Introduces a new sufficient condition: Conditional Independence & Permutation Invariance in Distribution.
result Corrects the insufficient condition and provides a new sufficient condition for full conformal prediction validity.
The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
problem Modeling and predicting financial correlation matrices from high-frequency data.
method Constructing permutation invariant Gaussian matrix models with 4 parameters, using graph theory and polynomial functions.
result The permutation invariant Gaussian matrix model predicts the expectation values of cubic and quartic polynomials with strong evidence of fit.
LMC loss barrier decreases to zero with large network width.
problem Understanding the LMC phenomenon in neural networks.
method Fine-grained analysis of LMC for two-layer ReLU networks.
result LMC loss barrier decreases to zero at a rate of O(m^-1/2) for large network width.
Permutation-equivariant neural networks improve auction mechanisms by reducing regret and sample complexity.
problem Designing optimal auction mechanisms that balance revenue and bidders' regret.
method Introduced permutation-equivariant neural networks to auction mechanisms.
result Permutation-equivariant neural networks decrease expected ex-post regret and improve model generalizability.
Deep Setscs.LG
We study the problem of designing models for machine learning tasks defined on \emph{sets}. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of populati…
Variational inference struggles with weight symmetries in neural networks, leading to biased posteriors.
problem Weight space symmetries in neural networks cause multimodal posteriors, challenging variational inference.
method Developed a symmetrization mechanism to create permutation invariant variational posteriors.
result Symmetrized variational posteriors have a better fit to the true posterior and improved predictive performance.
Neural networks learn from ensemble forecasts without considering their order.
problem Improving reliability of probabilistic weather forecasts.
method Permutation-invariant neural networks for postprocessing ensemble forecasts.
result Models achieve state-of-the-art prediction quality in surface temperature and wind gust forecasts.
PARD generates graphs efficiently and invariantly to node ordering.
problem Graph generation sensitivity to node ordering.
method Integrates autoregressive and diffusion models with a partial order for nodes and edges.
result PARD achieves state-of-the-art performance on molecular and non-molecular datasets.
We introduce a simple permutation equivariant layer for deep learning with set structure.This type of layer, obtained by parameter-sharing, has a simple implementation and linear-time complexity in the size of each set. We use deep permutation-invariant networks to perform point-could classification and MNIST-digit sum…
New model preserves symmetry in multivariate time series, improving performance.
problem Implicit ordering in MTS models violates inherent exchangeability.
method Permutation-equivariant 2D state space model with canonical architecture.
result Eliminates sequential dependency chains and simplifies stability analysis.
New algorithm uses GNNs to optimize rewards in graph-structured data.
problem Optimizing rewards in molecule design with graph-structured data.
method Embedding permutation invariance into GNNs and using GNTK for regret bounds.
result First GNN confidence bound and phased-elimination algorithm with sublinear regret.
MEM learns set functions from permutation-invariant data.
problem Learning from sets of instances with labels only on sets, not instances.
method Memory-based Exchangeable Model (MEM) with self-attention mechanism.
result Achieved 84.84% accuracy on lung cancer classification.
In this paper, we consider the problem of learning functions over sets, i.e., functions that are invariant to permutations of input set items. Recent approaches of pooling individual element embeddings can necessitate extremely large embedding sizes for challenging functions. We address this challenge by allowing stand…
A formula for triangle area in Deep Sets form.
problem Finding a polynomial formula for triangle area in Deep Sets form.
method Expressing area as a permutation-invariant function and finding a suitable Deep Sets form.
result Explicit polynomial formula for triangle area in Deep Sets form.
Drinfel'd used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e., we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3-braids. We v…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries of the image domain. In comparison, there are a number of problems in which the…
We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph representation for graphs of varying dimensions through a differentiable node attention po…
HistNetQ improves quantification tasks by optimizing loss functions and eliminating label requirements.
problem Quantification of class prevalence in bags of examples.
method Permutation-invariant Histograms and deep neural networks.
result HistNetQ outperforms other quantification methods and optimizes custom loss functions.
We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to rela…
This work improves multi-modal generative models by using permutation-invariant neural networks.
problem Improving multi-modal generative models with tighter variational objectives.
method Developed more flexible aggregation schemes based on permutation-invariant neural networks.
result Our variational objective and flexible aggregation models can better approximate the true joint distribution.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
We propose a permutation-invariant loss function designed for the neural networks reconstructing a set of elements without considering the order within its vector representation. Unlike popular approaches for encoding and decoding a set, our work does not rely on a carefully engineered network topology nor by any addit…
New model closes gap in understanding equivariant set functions.
problem Understanding universality of equivariant set functions.
method Proves PointNet not equivariant universal and introduces PointNetST.
result PointNetST is the simplest permutation equivariant universal model.
We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group We demonstrate the power of permutation data in programming and discuss an algorithm we have developed that takes the permutation data as input and determi…
Generates valid Euclidean distance matrices for molecular structures.
problem Generating point clouds in arbitrary rotations and translations is challenging.
method Developed a neural network architecture that produces valid Euclidean distance matrices invariant to rotations and translations.
result The architecture can generate molecular structures in a one-shot fashion by producing Euclidean distance matrices with a three-dimensional embedding.
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper, we consider a specific class of invariant and equivariant networks, for which we …
New neural network architectures use signed permutation representations for finite groups, improving performance.
problem Designing and optimizing neural networks for finite groups with signed permutation representations.
method Introduces -invariant deep neural networks with densely connected layers and signed permutation representations.
result Signed permutation representations lead to significantly better performance in classification tasks.
Dida learns meta-features invariant to feature permutations.
problem Learning invariant meta-features from dataset samples.
method Distribution-based deep architecture inheriting universal approximation and robustness.
result Dida outperforms state-of-the-art methods on dataset-level tasks.
New graph foundation models respect symmetries for broader applicability.
problem Tailored graph machine learning architectures limit broader applicability.
method Investigates symmetries for label and feature permutations, proving network universal approximator.
result Universal approximator on multisets respecting node and feature permutations.
Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alterna…
Study links and quivers, proving polynomial equality conjecture.
problem Link and quiver invariants and their relations.
method Cluster algebra invariants, point count polynomials, skein relations.
result Equality conjecture between plabic graph link polynomial and quiver point count polynomial proved for specific cases.
Single-microphone, speaker-independent speech separation is normally performed through two steps: (i) separating the specific speech sources, and (ii) determining the best output-label assignment to find the separation error. The second step is the main obstacle in training neural networks for speech separation. Recent…
ABI adapts to graph data for fast, scalable inference.
problem Challenges in inference on graph-structured data.
method Amortized Bayesian Inference (ABI) framework for graph data.
result ABI successfully addresses challenges in graph data inference.
The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples whic…
New model learns multisets to predict containment and sizes of differences.
problem Learning permutation invariant representations for flexible containment.
method Formalize multisets, propose training on predicting symmetric difference sizes.
result Model outperforms DeepSets on predicting containment and sizes of symmetric differences.
Permutation of Weierstrass points on Veech surfaces in classified by discriminant.
problem Classifying permutations of Weierstrass points on Veech surfaces in based on discriminant.
method Analyzing the permutation group induced by the affine group on Weierstrass points, considering both affine and Dehn multitwists.
result The permutation group is , , or depending on the discriminant value.