FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian pro…
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48 results for “FI modules”
Develops FI_G-modules for complex reflection groups and their applications.
problem Analyzing modules and configurations for complex reflection groups.
method Explores FI_G-modules, character polynomials, and representation stability.
result Extends representation stability to infinite groups and applies to various families of modules.
Extends methods to study polynomial roots over finite fields.
problem Stability of arithmetic statistics for polynomial roots.
method FI_G-modules, Grothendieck-Lefschetz trace formula, subexponential bounds.
result Average value of Gauss sums stabilizes as polynomial degree increases.
Homology of FI-modulesmath.RT
We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics a…
Unified approach to representation stability and character polynomials.
problem Generalizing representation stability across different groups.
method Axiomatic approach to categories of FI type.
result New types of categories (e.g. ) that exhibit stabilization.
In this paper we apply the theory of finitely generated FI-modules developed by Church, Ellenberg and Farb to certain sequences of rational cohomology groups. Our main examples are the cohomology of the moduli space of n-pointed curves, the cohomology of the pure mapping class group of surfaces and some manifolds of hi…
An FI-module over a commutative ring encodes a sequence of representations of the symmetric groups over . In this paper, we show that for a "finitely generated" FI-module over a field of characteristic , the cohomology groups $H^t(\mathfrak{S}…
New spectral sequence helps determine when cohomology of configuration spaces is finite.
problem Determining when cohomology of configuration spaces is finitely generated.
method Derived a spectral sequence from the homological algebra of the partition lattice.
result Criterion for finitely generated module .
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold - the diagonal coinvariant algebra on r sets of n variables - the cohomology and tau…
It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.
On the FI-module structure of math.AT
The groups are defined in terms of homotopy equivalences of certain graphs, and are natural generalisations of $\mbox{Out}(F_n)$ and $\mbox{Aut}(F_n)$. They have appeared frequently in the study of free group automorphisms, for example in proofs of homological stability in [8,9] and in the proof that Out$(F_n…
Representation Stabilitymath.GT
Representation stability is a phenomenon whereby the structure of certain sequences of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a framework, the theory of FI-modules, that explains the mechanism behind it.
Church-Ellenberg-Farb used the language of FI-modules to prove that the cohomology of certain sequences of hyperplane arrangements with S_n-actions satisfies representation stability. Here we lift their results to the level of the arrangements themselves, and define when a collection of arrangements is "finitely genera…
The Berkelmans-Pries Feature Importance Method: A Generic Measure of Informativeness of Featurescs.LG
New FI method accurately predicts feature importance.
problem Difficulty in evaluating feature importance in machine learning models.
method Combines Shapley values and Berkelmans-Pries dependency function.
result Proves accurate FI values for various cases.
The paper detects entrance positions using Wi-Fi and GPS signals.
problem Accurate detection of building entrance positions.
method Combines GPS signal drop and Wi-Fi RSS to detect entrances.
result The system's accuracy is one meter.
New method proves representation stability for linear groups, resolving homological questions.
problem Proving representation stability for linear groups over fields of characteristic zero.
method Introducing a technique for quantitative representation stability theorems.
result Vanishing result for higher syzygies of VIC- and SI-modules.
Deep neural networks predict walking, biking, and driving from Wi-Fi signals.
problem Predicting human mobility modes using Wi-Fi signals.
method Deployed Wi-Fi sensors at four locations, developed and tested multiple classifiers (MLP, Decision Tree, Bagged Decision Tree, Random Forest).
result Multilayer Perceptron achieved 86.52% correct predictions of mobility modes.
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include a proof of the Lannes--Schwartz Artinian conjecture in the generic representatio…
This paper provides a guide to feature importance methods for better scientific inference.
problem Limited understanding of data-generating process due to opaque ML model mechanisms.
method Comprehensive review and new proofs of global feature importance methods.
result Facilitates a thorough understanding and concrete recommendations for FI methods.
New method for mixed data FI controls type I error and achieves high power.
problem Statistical inadequacy of feature importance measures for mixed data.
method Combining CPI framework with sequential knockoffs for mixed data.
result Our method controls type I error and achieves high power for mixed data.
Study develops a semi-supervised deep ResNet for Wi-Fi mode detection.
problem Utilizing Wi-Fi signals for multimodal transportation mode detection with limited labeled data.
method Semi-supervised deep residual network (ResNet) framework.
result Framework achieves high prediction accuracy (81.8% for walking, 82.5% for biking, 86.0% for driving).
WiPIN uses Wi-Fi signals to identify people without requiring them to walk.
problem Identification requires walking and is unreliable with many users.
method Extracts body information from Wi-Fi signals without user movement.
result Achieves 92% accuracy with 30 users, robust to various settings.
Deep learning predicts user identity, activity, and location from Wi-Fi signals.
problem Privacy concerns and need for non-invasive user authentication, activity classification, and tracking.
method End-to-end deep learning framework using passive Wi-Fi signals.
result System autonomously predicts user identity, activity, and location without user intervention.
Paper proposes a SIMO DNN for indoor localization using Wi-Fi fingerprints.
problem Indoor localization with high accuracy and efficiency.
method Single-input and multi-output deep neural network architecture.
result SIMO-DNN scheme outperforms existing methods in floor detection and location accuracy.
The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.
problem Understanding the complexity of sampling non-log-concave distributions.
method Proves two lower bounds using Fisher information in the context of sampling.
result Lower bounds on the complexity of sampling non-log-concave distributions, ruling out high-accuracy algorithms.
Signed pairwise interactions conflate uniqueness, redundancy, and synergy
problem Signed pairwise interactions conflate uniqueness, redundancy, and synergy
method Stochastic Hi-Fi
result Stochastic Hi-Fi recovers structure missed by scalar baselines
Losaw improves FI scores by decorrelating features in ML models.
problem Feature correlation distorts feature importance scores in ML models.
method Losaw uses local sample weighting to decorrelate features.
result Losaw consistently improves feature importance scores and prediction accuracy.
Adaptive PINNs improve accuracy by adding points where solutions are uncertain.
problem Inadequate sampling in PINNs leads to inaccurate solutions, especially near singularities.
method FI-PINNs use failure probability to dynamically add points, improving numerical accuracy.
result FI-PINNs achieve better accuracy through adaptive sampling, as proven by rigorous error bounds.
Paper presents a new Wi-Fi RSS and geomagnetic field database for indoor localization and trajectory estimation.
problem Indoor localization and trajectory estimation challenges.
method Convolutional neural network (CNN) for RSS data and LSTM network for geomagnetic field intensity.
result CNN and LSTM networks show feasibility for localization and trajectory estimation.
For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated by elements which are supported on subsurfaces whose genus is at most G_k. We a…
FI-GNNs learn expressive node representations from sparse features.
problem Sparse and high-dimensional node features limit GNN performance.
method Plug-and-play GNN framework that highlights informative feature interactions.
result FI-GNNs learn highly expressive node representations on feature-sparse graphs.
A method for concept-based learning using probabilistic inference and expert rules.
problem Concept-based learning with limited training data.
method Divide images into patches, transform into embeddings, cluster, and use frequentist inference to find concepts.
result FI-CBL outperforms concept bottleneck model in small data scenarios.
New DNN architecture for indoor localization in multi-story buildings.
problem Scalable indoor localization in complex multi-story buildings.
method Stacked autoencoder and feed-forward classifier for multi-label classification.
result Near state-of-the-art performance with lower complexity and energy consumption.
The study predicts solar flare productivity using magnetic data from SDO/HMI.
problem Forecasting solar flares, especially M- and X-class, to mitigate space weather effects.
method Statistical and machine learning methods applied to 563 ARs' magnetic data.
result Improved accuracy in predicting AR's Flare Index, especially for large values.
Feature bagging improves stability through random feature subsampling.
problem Improving the stability of ensemble learning methods.
method Introducing feature instability (FI) and analyzing feature bagging in parametric and model-free settings.
result Feature bagging provides stronger stability than non-bagged methods, especially with aggressive subsampling.
Investigates optimal trading strategies for illiquid assets using a modified market impact model.
problem Optimizing investment behavior in a large unregulated financial institution with illiquid assets.
method Extension of Almgren-Chriss model to account for market illiquidity and expected utility optimization.
result Explicit closed-form solution for optimal trading strategy with interesting properties.
New method handles missing data in multimodal brain imaging.
problem Missing data in multimodal brain imaging.
method Full Information Linked ICA (FI-LICA) algorithm.
result FI-LICA outperforms current practices in classification and prediction.
New method corrects bias in feature importance measures of GBM.
problem Bias in feature importance measures of GBM.
method Cross-validated unbiased base learners.
result Significant improvement in feature importance measures with minimal computational cost.
A new risk measure (FRM) for EM FI returns helps investors protect against volatility and policy instability.
problem Systemic risk in EM FI returns due to external shocks and domestic policy instability.
method Daily FRM-EM measure applied to 25 largest EM FI returns, incorporating Macro factors.
result FRM-EM captures systemic risk behavior in EM FI returns, reaching maximum during crises.
FI-GRL learns graph node representations efficiently and generalizes to unseen nodes.
problem Transductive graph representation learning requires all nodes to be known, limiting generalization.
method FI-GRL uses random projection to preserve graph structure and feature extraction via SVD.
result FI-GRL achieves accurate representations for seen nodes and generalizes to unseen nodes.
Deep learning model classifies concurrent human interactions from WiFi data with high accuracy.
problem Classifying concurrent human interactions from WiFi data with high accuracy.
method Attention-BiGRU deep learning model using Multiple Input Multiple Output radio link.
result Maximum benchmark accuracy of 94% for a single subject-pair, 88% for ten subject pairs.
Improves FI-PINNs by combining re-sampling and subset simulation for better failure probability estimation.
problem Estimating failure probability in physics-informed neural networks (PINNs).
method Adaptive sampling with re-sampling and subset simulation, using cosine-annealing for uniform to adaptive transition.
result Significant improvement in estimating failure probability and generating new training points in the failure region.
FIS-GAN uses importance sampling in GANs to speed up training.
problem Efficiency in GAN training by focusing on hard-to-generate examples.
method Adapting importance sampling into GANs using normalizing flows.
result Significant acceleration in GAN optimization with improved fidelity.
Hi-fi priors enhance BNNs by learning flexible activations.
problem Challenging to impose function-space priors on BNNs.
method Optimization techniques to learn flexible activations.
result BNNs with flexible activations can achieve desired priors.
This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compacti- fied moduli spaces, orientation formulas, and CW structures of the underlying manifolds.
Paper categorifies Vassiliev skein relation for Khovanov homology.
problem Clarifying the relation between Vassiliev invariants and Khovanov homology.
method Developed a categorified version of Vassiliev skein relation on Khovanov homology.
result Khovanov homology's genus-one operation leads to a crossing change, enabling invariance under Reidemeister moves and extending to singular links.
Study identifies key parameters and input dimensions making LLMs and VLMs brittle.
problem Vulnerability of large language and vision-language models to perturbations.
method Proposed FI measure based on information geometry to quantify sensitivity.
result Small subset of high FI parameters significantly contribute to brittleness.
Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It requires to identify all itemsets appearing in at least a fraction of a transactional dataset . Often though, the ultimate goal of mining is not an analysis of the dataset \emph{per se}, but the understanding of …