Wrapped loss function improves convergence and accuracy in multi-output models.
problem Nonconforming residual distributions in multi-output models.
method Proposes a 'Wrapped Loss Function' to regularize nonconforming residual distributions.
result Advanced properties of faster convergence, better accuracy, and improved handling of imbalanced data.
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
Adaptive PI by reweighting nonconformity scores improves model uncertainty reflection.
problem CP methods using a constant correction for all test points ignore individual uncertainties.
method QRF learns distribution of nonconformity scores and assigns weights to samples.
result PI lengths more aligned with model uncertainty and improved adaptiveness.
We investigate the issue of model selection and the use of the nonconformity (strangeness) measure in batch learning. Using the nonconformity measure we propose a new training algorithm that helps avoid the need for Cross-Validation or Leave-One-Out model selection strategies. We provide a new generalisation error boun…
Contrast uses normalizing flows to create precise prediction regions for multi-dimensional outputs.
problem Generating reliable prediction regions for multi-dimensional outputs in supervised and unsupervised learning.
method Contrast uses normalizing flows to define nonconformity scores based on distances in latent space, creating sharp prediction regions.
result Contrast maintains guaranteed coverage probability and outperforms existing methods in generating accurate prediction regions.
RR-GNN improves GNN prediction intervals by accounting for graph heteroscedasticity and structural biases.
problem Uncertainty quantification in GNNs for high-stakes domains.
method Graph-Structured Mondrian CP, Residual-Adaptive Nonconformity Scores, Cross-Training Protocol.
result Improved efficiency and no loss of coverage compared to CP baselines.
New method improves conformal prediction for machine learning models.
problem Improving the efficiency and informativeness of conformal prediction models.
method Introduces Penalized Inverse Probability (PIP) and Regularized PIP (RePIP) nonconformity score functions.
result PIP-based conformal classifiers strike a good balance between informativeness and efficiency.
Proposes a new method to minimize non-singleton predictions in conformal prediction.
problem Large prediction sets in conformal prediction are costly and inefficient.
method Introduces a new nonconformity score to minimize non-singleton sets and provides an algorithm to compute it efficiently.
result The proposed Singleton-Optimized Conformal Prediction (SOCOP) method increases singleton frequency by over 20% compared to standard scores, with minimal impact on average set size.
Python package 'nonconform' simplifies conformal anomaly detection.
problem Heuristic thresholding in anomaly detection systems.
method 'nonconform' package converts anomaly scores into calibrated p-values.
result Statistically principled anomaly detection is made accessible.
Optimizes minimum-volume prediction sets for multivariate regression.
problem Lack of efficient methods for multivariate conformal prediction.
method Optimization-driven framework for minimum-volume covering sets.
result Efficient and informative prediction sets with tight coverage.
SACP aggregates nonconformity scores from multiple predictors to create more efficient uncertainty sets.
problem Combining predictive uncertainties from multiple models for efficient and reliable uncertainty quantification.
method SACP (Symmetric Aggregated Conformal Prediction) aggregates nonconformity scores using a flexible symmetric aggregation function.
result SACP consistently improves efficiency and often outperforms state-of-the-art model aggregation baselines.
This work improves adaptive conformal prediction using self-supervised learning.
problem Improving the adaptability of conformal prediction intervals.
method Train an auxiliary model with a self-supervised pretext task on top of an existing predictive model and use the self-supervised error as an additional feature to estimate nonconformity scores.
result Empirically demonstrates the benefit of additional information in improving the efficiency (width), deficit, and excess of conformal prediction intervals.
Null-Calibrated Conformal Selection via Target-Membership Scores
problem Identifying test candidates whose unknown responses fall in a target region while controlling the false discovery rate
method Membership-score-based conformal selection
result Finite-sample valid null p-values
Proposes mCS for multivariate selection with FDR control.
problem Selecting high-quality candidates from multivariate datasets.
method Introduces regional monotonicity and multivariate nonconformity scores.
result Significantly improves selection power with FDR control.
ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.
problem The looseness in BCP's coverage guarantee due to Markov's inequality.
method Introduces a data-dependent transformation of nonconformity scores.
result Reduces the average coverage gap from 4.20% to 1.12% on benchmarks.
CoCP optimizes prediction intervals by jointly learning center and radius, improving efficiency and coverage.
problem Inefficient conformal prediction intervals under heteroscedasticity and skewness.
method Co-optimization framework that learns center and radius through alternating optimization steps.
result CoCP yields consistently shorter intervals and state-of-the-art conditional coverage diagnostics.
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.
Robust Bayes-Assisted Conformal Prediction improves prediction set sizes.
problem Misspecification of Bayesian working model and prior misalignment.
method RoBAS (Robust Bayes-Assisted Shrinkage) framework with two instantiations.
result Proposed scores adapt to prior quality, reducing interval widths in shifted settings.
A new method combines quantile regression, cross-conformalization, and out-of-bag predictions for valid prediction sets.
problem Valid prediction sets for classification and regression without distributional assumptions.
method Nested conformal prediction framework, combining quantile regression, cross-conformalization, and out-of-bag predictions.
result QOOB algorithm performs best or close to best on all simulated and real datasets.
This work approximates full conformal prediction for neural networks without sample splitting.
problem Uncertainty quantification for neural network regression models.
method Approximating full conformal prediction using Gauss-Newton influence for post-hoc uncertainty estimation.
result Locally-adaptive and often tighter prediction intervals compared to split-CP.
Link quandles are shown to be residually finite.
problem Residual finiteness of link quandles.
method Proving residual finiteness of free products of residually finite quandles with residually finite associated groups.
result Link quandles are residually finite.
Free and knot quandles are residually finite.
problem Residual finiteness of quandles.
method Definition and investigation of residual finiteness; proof for free and knot quandles; discussion on automorphism groups.
result Free and knot quandles are residually finite and Hopfian.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Residues theorem for flags of holomorphic foliations proved.
problem Proving residue theorems for flags of holomorphic foliations.
method Defining Nash residue and proving relations between residues of flags and foliations.
result Partial answer to the rationality conjecture in this context.
Every non-trivial knot group is fully residually perfect.
problem Understanding the residual properties of knot groups.
method Analyzing the residual properties of knot groups using group theory.
result Every non-trivial knot group is fully residually perfect.
Residual algorithms improve reinforcement learning performance.
problem Distribution mismatch in model-based planning.
method Bidirectional target network technique for residual algorithms.
result Residual reinforcement learning significantly outperforms vanilla methods.
A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.
problem Lack of principled uncertainty quantification for graph-valued supervised prediction.
method Proposes a conformal prediction framework using Z-Gromov-Wasserstein distances for graph-valued outputs.
result Provides distribution-free coverage guarantees for graph-valued outputs.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
Formula calculates residues for maps near holomorphic distributions.
problem Calculating residues for maps near holomorphic distributions.
method Residues formula for maps generically transversal to regular holomorphic distributions.
result Established a residues formula for maps near holomorphic distributions.
Let p be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually p. Let M=M3 be a virtually fibered 3-manifold. It is well-known that G=π1(M) is residually solvable and even residually finite solvable. We prove that G is always virtually residually p…
Researchers identify critical protein residues using advanced graph theory.
problem Identifying essential residues in proteins for function.
method Learning Random Geometric Graphs (RGG) with Cramer's V correlation and organic thresholding.
result Advanced RGG methods accurately identify critical residues compared to existing techniques.
Defines Wodzicki residue using groupoids and fibered distributions.
problem Defining and understanding the Wodzicki residue in noncommutative geometry.
method Using groupoid language and filtered manifolds, defining the residue and showing its properties.
result The groupoidal residue is a trace on pseudodifferential operators and matches the usual residue in certain cases.
Holomorphic residue formula for complex supermanifolds.
problem Residue localization on complex supermanifolds.
method Holomorphic residue localization formula for odd vector fields.
result Explicit local residue formula under isolated non-degeneracy hypotheses.
Wide residual networks generalize well with uniform convergence to RNTK as width increases.
problem Understanding the generalization ability of wide residual networks.
method Uniform convergence of residual network kernel to residual neural tangent kernel (RNTK).
result Generalization error converges to kernel regression error with respect to RNTK.
The paper studies residues of manifolds and their applications in geometry.
problem Understanding the residues of manifolds and their geometric implications.
method Analytic continuation and Möbius invariance of residues, introduction of relative and weighted residues.
result Scalar curvature, mean curvature, and Euler characteristic can be expressed in terms of residues.
Given a prime p, a group is called residually p if the intersection of its p-power index normal subgroups is trivial. A group is called virtually residually p if it has a finite index subgroup which is residually p. It is well-known that finitely generated linear groups over fields of characteristic zero are …
Analysis shows BN prevents gradient vanishing/explosion in residual networks.
problem Gradient vanishing/explosion problem in residual networks.
method Mathematical analysis of BN and residual network training.
result BN confounds gradient variance, preventing vanishing/explosion.
We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
Study on endomorphism and automorphism groups of specific quandles.
problem Characterizing endomorphism and automorphism groups of residually finite and profinite quandles.
method Proved properties of endomorphism monoids and automorphism groups for residually finite and profinite quandles.
result Endomorphism and automorphism groups of residually finite quandles are residually finite.
Unified ODE model explains residual and non-residual networks.
problem Unclear relationship between residual and non-residual networks.
method Introducing a damping term in an ODE model to interpolate between ResNet and CNN architectures.
result Unified framework for understanding residual and non-residual networks.
Defines and proves generalized noncommutative residue theorems for specific dimensions.
problem Defining and proving residue theorems for noncommutative geometry.
method Defined generalized noncommutative residue of Dirac operator; proved Kastler-Kalau-Walze type theorems.
result Validated Kastler-Kalau-Walze type theorems for 4D and 6D compact manifolds.
Paper proposes continuous residual layers for graph neural networks.
problem Low-pass filtering effect in GCN-based models.
method Integrates Ordinary Differential Equations (ODE) to produce outputs of continuous residual layers.
result Continuous residual layers achieve better results than non-residual modules in multiple layers.
Batch normalization makes deep residual networks train faster.
problem Training deep residual networks with large depths.
method Downscaling the residual branch by a normalizing factor early in training.
result Normalized residual blocks compute functions close to the identity function early in training.
Proves Singer conjecture for graph manifolds with residually finite groups.
problem Proving the Singer conjecture for graph manifolds with specific properties.
method Used residual finiteness and graph manifold properties to prove the conjecture.
result Proved the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.
Fair market valuations ignore future worker profits in employee-owned firms.
problem Ignoring future worker profits in fair market valuations for employee-owned firms.
method Analyzing property rights and residual claimants in employee-owned firms.
result Fair market valuations are inappropriate for employee-owned firms.
Researchers determine Baum-Bott residues for foliations without generic hypothesis.
problem Determining Baum-Bott residues for singular foliations without generic assumptions.
method Express residues in terms of Grothendieck residue and apply Cenkl's algorithm.
result Residues can be expressed in terms of a simpler foliation and algorithm holds without regularity assumption.