A new method evaluates invariant performance of IRM-based representations.
problem Impact of data changes on machine learning model performance.
method Proposes a novel method to evaluate invariant performance of IRM-based representations.
result Establishes a robust criterion to assess invariant performance of various representation techniques.
This paper tackles domain generalization by learning invariant class conditional distributions.
problem Learning invariant representations across different domains with varying distributions.
method Proposes a conditional invariant representation to ensure invariance of class conditional distributions.
result Guarantees invariance of the joint distribution P(h(X),Y) if class prior P(Y) remains invariant. Proposes an alternative invariance penalty to address domain generalization issues.
problem Addressing domain generalization problems by finding invariant representations.
method Revisits the Gramian matrix of the data representation to propose an alternative invariance penalty.
result The proposed approach guarantees recovery of an invariant representation under mild conditions.
TCRI improves domain generalization by enforcing conditional independence constraints.
problem Limitations of existing domain generalization methods due to incomplete constraints.
method TCRI implements regularizers motivated by conditional independence constraints.
result TCRI achieves cross-domain stability and outperforms baselines in worst-domain accuracy.
Paper shows deep nets can't guarantee domain adaptation without invariant features.
problem Learning domain-invariant features for successful domain adaptation.
method Proposes a counterexample and a new generalization upper bound.
result Shows conditional shift and characterizes a fundamental tradeoff.
We combine conditional variational autoencoders (VAE) with adversarial censoring in order to learn invariant representations that are disentangled from nuisance/sensitive variations. In this method, an adversarial network attempts to recover the nuisance variable from the representation, which the VAE is trained to pre…
Study real GIT and Wick-rotations of pseudo-Riemannian manifolds.
problem Understanding Wick-rotations and their conditions for pseudo-Riemannian manifolds.
method Extending earlier results, providing sufficient and necessary conditions for Wick-rotatability, and deriving an invariance theorem.
result Derived sufficient and necessary conditions for pseudo-Riemannian manifolds to be Wick-rotatable.
The paper connects knot representations and spherical quandle colorings.
problem Defining the Casson-Lin invariant for knots.
method One-to-one correspondence between SU(2)-representations and spherical quandle colorings. result Geometric interpretation of the trace-free condition for the Casson-Lin invariant.
New method improves transfer and robustness of supervised contrastive learning.
problem Class collapse in supervised contrastive learning leads to poor representation quality.
method Adding a weighted class-conditional InfoNCE loss and a class-conditional autoencoder.
result Improves transfer and robustness on 5 standard datasets and 3 worst-group robustness datasets.
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
Modern automatic speech recognition (ASR) systems need to be robust under acoustic variability arising from environmental, speaker, channel, and recording conditions. Ensuring such robustness to variability is a challenge in modern day neural network-based ASR systems, especially when all types of variability are not s…
New risk decompositions clarify domain adaptation issues.
problem Domain adaptation challenges with different training and test distributions.
method Representation Bayesian Risk Decompositions, hybrid argument.
result Clarifies factors (2) and (3) as reasons for generalization failure.
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation that realizes these invariants. The current article is restricted to surfaces wi…
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective ho…
Adversarial techniques learn invariant representations across multiple domains.
problem Domain generalization from diverse studies to unseen domains.
method Adversarial censoring techniques for invariant representation learning.
result Limiting behavior of adversarial loss function as the number of domains grows.
Efficiently infers cluster assignments in probabilistic models.
problem Efficiently inferring cluster assignments in probabilistic models.
method Amortized approximate Bayesian inference mapping cluster representations into conditional probabilities.
result Parallelizable, yields iid samples with similar computational cost to Gibbs sampling.
New approach improves domain adaptation with label shift assumptions.
problem Improving domain adaptation when label distributions differ between source and target domains.
method Proposes generalized label shift (GLS) and modifies three DA algorithms (JAN, DANN, CDAN) to handle label distribution mismatches. result Modified DA algorithms outperform base versions, especially with large label distribution mismatches.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
problem Learning invariant graph representations from eigenvectors.
method SignNet and BasisNet neural architectures that are invariant to sign flips and basis symmetries.
result Proven to be universal, approximating any continuous function of eigenvectors with desired invariances.
The paper generalizes knot signatures to tori using representations and invariants.
problem Generalizing knot signatures to tori and defining new invariants.
method Defining a signed count of irreducible representations for tori complements and relating it to known invariants.
result Defines a new invariant for tori that recovers known invariants and connects to Floer homology.
Activity2vec learns representations from wearable activity data.
problem Proactive screening and monitoring of chronic conditions.
method Adversarial unsupervised representation learning with three components.
result Activity2vec outperforms many baselines in disorder prediction tasks.
We study an invariant of a 3-manifold which consists of Reidemeister torsion for linear representations which pass through a finite group. We show a Dehn surgery formula on this invariant and compute that of a Seifert manifold over S2. As a consequence we obtain a necessary condition for a result of Dehn surgery alo…
Unified framework for scale-invariant representation learning using MAPCA.
problem Learning invariant representations in data.
method Metric-Aware Principal Component Analysis (MAPCA) based on generalized eigenproblem.
result MAPCA provides a unified geometric language for various self-supervised learning objectives.
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if …
Transfer learning aims to improve learning in target domain by borrowing knowledge from a related but different source domain. To reduce the distribution shift between source and target domains, recent methods have focused on exploring invariant representations that have similar distributions across domains. However, w…
Medical imaging models may encode demographic attributes without violating fairness, depending on the approach.
problem Discrimination in medical imaging models due to encoding demographic attributes.
method Examined marginal and class-conditional representation invariance, traditional fairness notions, and counterfactual fairness.
result Demographically invariant models may not necessarily be fair, and encoding demographic attributes can be advantageous.
Researchers compute quantum invariant for four-puncture sphere, verifying volume conjecture.
problem Verifying the Bonahon-Wong-Yang volume conjecture for a specific case.
method Representation theory of the Checkov-Fock algebra to compute quantum invariant.
result Verification of the volume conjecture for four-puncture sphere bundles with technical conditions.
New approach to disentangled representations using mutual information.
problem Disentangled representations lack sufficient inductive biases.
method Formulate disentanglement through mutual information and conditional independence.
result Violation of mutual information assumption leads to loss of disentanglement.
DISCoVeR learns disentangled representations by separating shared and condition-specific factors.
problem Learning disentangled representations for multi-condition data.
method Dual-latent architecture, parallel reconstructions, max-min objective.
result DISCoVeR achieves improved disentanglement on various datasets.
New method improves domain generalization by matching object representations.
problem Existing domain generalization methods fail to generalize to unseen domains.
method Proposes matching-based algorithms to match object representations across domains.
result MatchDG algorithm matches ground-truth object representations and improves out-of-domain accuracy.
Let X be a compact toric Kähler manifold with −KX nef. Let L⊂X be a regular fiber of the moment map of the Hamiltonian torus action on X. Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of X as virtual counts of holomorphic discs with Lagrangian boundary condition L. We prove a formula…
New invariant for spin 3-manifolds using super 3-cocycles.
problem Constructing an invariant for spin 3-manifolds.
method State sum construction based on super 3-cocycles and combinatorial representation.
result The invariant is sensitive to the spin structure.
Using the L^2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p,q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p,q). A key step is the identification of the function's local minima as moduli spaces of holomorph…
Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces…
The paper explores how to make machine learning models robust to domain shifts.
problem Machine learning models are unreliable in domains different from training.
method Introducing a broad formal notion of invariance and causal structures.
result The true underlying causal structure of the data plays a critical role in robustness.
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
This paper calculates Dijkgraaf-Witten invariants from Chern classes.
problem Computing Dijkgraaf-Witten invariants from specific 3-cocycles.
method Defines and computes invariants from second Chern classes of representations.
result Clarifies topological interpretation under certain conditions.
We construct unitary modular categories for a general class of coset conformal field theories based on our previous study of these theories in the algebraic quantum field theory framework using subfactor theory. We also consider the calculations of the corresponding 3-manifold invariants. It is shown that under certain…
Paper calculates Donaldson-Thomas invariants for a specific category.
problem Relating quadratic differentials to stability conditions and invariants.
method Uses string and band techniques from representation theory.
result Agrees with physics predictions for degenerate ring domains.
Direct formula found for ADO invariants from homological representations.
problem Computing ADO invariants from quantum group representations.
method Direct homological formula for ADO invariants using partial traces of homological representations.
result Direct formula for ADO invariants without further truncations.
New approach tackles domain adaptation without assuming domain invariant representations.
problem Learning models on source domains for target domains with labeled and unlabeled data.
method Hidden Covariate Shift hypothesis; learning representation to match joint distributions.
result State-of-the-art performance on Amazon Reviews dataset.
NICE learns a representation to avoid bad controls in causal inference.
problem Avoiding bad controls in causal inference from observational data.
method Uses invariant risk minimization (IRM) to learn a representation of covariates that avoids bad controls.
result NICE outperforms adjusting for all covariates in cases with unknown collider variables and bad controls.
New theory defines invariants for framed 3-manifolds using trivalent graphs with self-loops.
problem Defining invariants for framed 3-manifolds with semi-simple Lie groups.
method Constructing graph complexes and cocycles, including self-loops, to define invariants.
result Higher-loop invariants can be defined by graph cocycles with or without self-loops.
Study irreducible SU(2) representations for knots in 3D.
problem Existence of irreducible SU(2) representations for cyclic branched covers of knots.
method Combining covering space techniques, SICUP matrices, and instanton Floer homology.
result Irreducible SU(2) representations exist for certain knots and branched covers.
The study analyzes neural network predictions of knot invariants and finds that braid representations work best.
problem Understanding and predicting knot invariants using neural networks.
method Investigated different knot representations and invariants, proposed a cosine similarity score.
result Braid representations are best for predicting knot invariants, and some invariants are easier to learn than others.
We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariance…
New representation connects two link invariants.
problem Link invariants of different types.
method Augmentation representation of link group.
result Connects two types of link invariants.
Convex learning for diverse invariances in semi-inner-product space.
problem Efficiently learning invariant representations for a wide range of invariances.
method Developed a convex representation learning algorithm for generalized invariances modeled as semi-norms, introducing Euclidean embeddings for kernel representers in a semi-inner-product space.
result Accurate invariant representations learned efficiently and effectively, validated by experiments.