Study on homological Dehn functions of groups of type FP2.
problem Understanding the homological Dehn functions of groups of type FP2. method Proved foundational results, studied homological Dehn functions of Leary's groups, and provided methods to obtain groups with specific homological Dehn functions.
result Found groups of type FP2 with quartic homological Dehn function and unsolvable word problem. Paper explores hyperbolic groups with unique subgroup properties.
problem Creating examples of hyperbolic groups with specific subgroup finiteness properties.
method Develops new examples of subgroups of hyperbolic groups with various finiteness properties.
result Uncountably many groups of type FP2 with similar properties to subgroups of hyperbolic groups. We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ2- and compactly-supported cohomology of these groups. For each n≥4 we construct a closed aspherical n-manifold that admit…
Previously one of the authors constructed uncountable families of groups of type FP and of n-dimensional Poincaré duality groups for each n≥4. We strengthen these results by showing that these groups comprise uncountably many quasi-isometry classes. We deduce that for each n≥4 there are uncountably many…
Formanek and Procesi have demonstrated that Aut(F_n) is not linear for n >2. Their technique is to construct nonlinear groups of a special form, which we call FP-groups, and then to embed a special type of automorphism group, which we call a poison group, in Aut(F_n), from which they build an FP-group. We first prove t…
Develops a neural network approach to solve inverse stochastic problems from particle observations.
problem Inference of Fokker-Planck equation coefficients from sparse particle data.
method Physics-informed neural networks (PINNs) with Kullback-Leibler divergence loss.
result Simultaneous inference of Fokker-Planck equation and multi-dimensional PDF from few particle observations.
Study of fixed points in large networks with random dependencies.
problem Systemic risk in large financial networks.
method Analysis of vector fixed point equations on random graphs, obtaining finite dimensional limits.
result Approximate solutions to random FP equations for large networks.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
If S is a subgroup of a direct product of two limit groups, and S is of type FP(2) over the rationals, then S has a subgroup of finite index that is a direct product of at most two limit groups.
FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.
problem Training neural networks without feedback from downstream layers.
method Forward Projection (FP) method that uses randomised nonlinear projections and closed-form regression.
result FP achieves comparable generalisation to backpropagation methods with a single forward pass, offering significant speedup.
We show that the Basilica Thompson group introduced by Belk and Forrest is not finitely presented, and in fact is not of type FP_2. The proof involves developing techniques for proving non-simple connectedness of certain subcomplexes of CAT(0) cube complexes.
We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups Gn<G of increasing finite index in a fixed finitely generated group G, assuming ⋂nGn=1. We focus in particular on finitely presented residually free groups, calculating thei…
GGFPS improves model performance by sampling molecules more efficiently.
problem Improving model performance and reducing data costs in chemistry problems.
method Gradient-Guided Furthest Point Sampling (GGFPS) that leverages molecular force norms.
result GGFPS leads to superior data efficiency and model robustness compared to other sampling methods.
The study examines geodesic orbit Finsler spaces with non-negative flag curvature and (FP) condition, proving they are compact.
problem Characterizing geodesic orbit Finsler spaces with specific curvature conditions.
method Analyzes the interaction between geodesic orbit property and flag curvature conditions.
result Compactness of geodesic orbit Finsler spaces with non-negative flag curvature and (FP) condition.
Hougthon's groups H_n is a family of groups where each H_n consists of `translations at infinity' on n rays of discrete points emanating from the origin on the plane. Brown shows H_n has type FP_n-1 but not FP_n by constructing infinite dimensional cell complex on which H_n acts with certain conditions. We modify his i…
If G1,...,Gn are limit groups and S⊂G1×...×Gn is of type $\FP_n(\mathbb Q)$ then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This settles a question of Sela.
Model uses HS-FP framework for South African asset allocation.
problem Develops a flexible non-parametric asset allocation model for South African markets.
method Historical Simulation with Flexible Probabilities (HS-FP) framework, using relative entropy for distribution estimation.
result HS-FP model outperforms classic MVO and EW benchmarks in out-of-sample performance.
FP-UCB algorithm achieves bounded regret for finitely parameterized multi-armed bandits.
problem Finitely parameterized multi-armed bandits with unknown but known parameter set.
method FP-UCB algorithm using structural information about the parameter set.
result FP-UCB achieves bounded regret under structural condition, logarithmic otherwise.
New method improves feature selection by integrating stability paths.
problem Improving feature selection with tighter false positive control.
method Integrating stability paths to strengthen theoretical bounds on E(FP).
result Significantly more true positives with same E(FP) control.
Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, the performance gain is at the expense of a reduction in float…
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
problem Approximating gauge actions with lattice artifacts.
method Lattice gauge-equivariant convolutional neural networks (L-CNNs).
result L-CNNs provide fixed point actions with no lattice artifacts.
We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups containing finitely presented subgroups which are not of type FP3, and h…
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
Since machine learning models have been applied to neuroimaging data, researchers have drawn conclusions from the derived weight maps. In particular, weight maps of classifiers between two conditions are often described as a proxy for the underlying signal differences between the conditions. Recent studies have however…
In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact …
New activation networks improve model efficiency and performance.
problem Creating hardware-efficient deep learning models.
method Restructurable Activation Networks (RANs) with RAN-explicit and RAN-implicit methods.
result RANs achieve state-of-the-art results with improved hardware efficiency.
GAN-FP uses GANs to predict equipment failures from imbalanced data.
problem Accurately predicting equipment failures with limited data and high imbalance.
method GAN-FP employs two GAN networks to generate and classify imbalanced data, optimizing a weighted loss objective and a consistency GAN.
result GAN-FP outperforms traditional methods in imbalanced failure prediction.
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.
problem Establishing a precise mathematical relationship between statistical physics and polynomial estimators limits.
method Analyzing Gaussian additive models (GAMs) to show FP potential monotonicity equals low-degree polynomial estimators limits.
result For a broad family of Gaussian additive models, the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential.
AI agent plays CSGO deathmatch with human-like style.
problem Lack of API for CSGO limits data for reinforcement learning.
method Behavioural cloning on large noisy and expert datasets.
result Matches human difficulty level in deathmatch mode.
This paper extends FP's method to complex hyperbolic branched covers to find Einstein metrics.
problem Finding Einstein metrics on non-locally symmetric manifolds.
method Generalized FP's construction to complex hyperbolic branched covers.
result Yields a negatively curved Einstein metric that asymptotically approaches GH's metric.
The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the r…
WILD-SCAV benchmarks AI in complex 3D FPS environments.
problem Lack of complexity and diversity in RL environments.
method Developed a 3D open-world FPS game environment.
result Demonstrates effectiveness in benchmarking RL algorithms.
FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.
problem Lack of flat posterior in approximate Bayesian inference methods hinders effective Bayesian Model Averaging.
method Proposes Flat Posterior-aware Bayesian Model Averaging (FP-BMA) and Flat Posterior-aware Bayesian Transfer Learning schemes.
result FP-BMA successfully captures flat posteriors, improving generalization performance.
Let G be a Chevalley group scheme and B<=G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O_S be the corresponding S-arithmetic ring. Then, the S-arithmetic group B(O_S) is of type F_{|S|-1} but not of type FP_{|S|}. Moreover one can der…
We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups. We prove that if G1,...,Gn are in E then a subgroup Γ⊂G1×...×Gn is of type $\…
The study generalizes cohomology results for hyperbolic groups.
problem Understanding cohomology of hyperbolic groups and their subgroups.
method Generalizing Gersten's theorem on ℓ∞-cohomology and applying it to hyperbolic groups. result Obtained hyperbolicity criteria for specific groups.
The paper classifies PD_4-complexes based on their fundamental group properties.
problem Understanding the structure of PD_4-complexes based on their fundamental group properties.
method Analyzing the fundamental group and its modules to classify PD_4-complexes.
result The classification of PD_4-complexes based on their fundamental group properties.
Meta-learning improves image segmentation performance.
problem Improving image segmentation accuracy using meta-learning.
method Extending FOMAML and Reptile to image segmentation, using EfficientLab architecture, and leveraging test error definition.
result Meta-learned initializations provide value for few-shot image segmentation but are quickly matched by conventional transfer learning.
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…
Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.
problem Understanding computational hardness in statistical inference.
method Proposed and refined Franz-Parisi criterion, established equivalence with SQ lower bounds.
result Optimized Franz-Parisi criterion is equivalent to Statistical Query (SQ) lower bounds.
Unified model predicts equipment failure and remaining useful life.
problem Predicting equipment failure and remaining useful life separately is sub-optimal.
method Two methods: Deep Weibull model (DW-RNN) and multi-task learning (MTL-RNN).
result Our methods consistently outperform baseline RUL methods and produce consistent results for RUL and FP.
Study presentations of groups that can be generalised over continuous open group monomorphisms.
problem Investigate presentations of groups that can be generalised over continuous open group monomorphisms.
method Systematic study of presentations with generalisation properties, focusing on right-angled Artin groups (RAAGs).
result Establish high connectivity properties for universal Salvetti-type complexes and novel examples of LC groups with prescribed compactness properties.
Scalable subspace clustering for high-dimensional data.
problem Finding clusters in non-disjoint subspaces and scaling to large data.
method Bottom-up strategy using FP-trees for frequent pattern mining.
result The proposed algorithm produces clusters with high accuracy and scales well to large data.
A novel score-based method solves high-dimensional Fokker-Planck equations with improved accuracy and speed.
problem High-dimensional Fokker-Planck equations suffer from the curse of dimensionality, leading to numerical errors and slow sampling.
method Score-based Physics-Informed Neural Networks (PINNs) that fit the score function in SDEs, using three methods: Score Matching, Sliced Score Matching, and Score-PINN.
result The score-based method outperforms traditional Monte Carlo and vanilla PINNs in high-dimensional settings, offering faster sampling and reduced errors.
Surface Houghton groups are studied for their mapping class properties.
problem Understanding the mapping class properties of surface Houghton groups.
method Analyzing the asymptotic rigidity and monodromy homeomorphisms of fibered components.
result Surface Houghton groups are of type Fn−1 but not of type FPn. The study of PD3-pairs extends results for aspherical 3-manifolds.
problem Understanding PD3-pairs with aspherical ambient spaces. method Attaching 1-handles to PD3-pairs with aspherical ambient space and π1-injective boundary. result There are only finitely many PD3-pairs with a specific group property. Enhanced ontology learning from text improves question-answering systems.
problem Improving ontology learning from unstructured text for better question-answering systems.
method Heuristically modified FP-Tree with DFA for concept extraction and frequent pattern mining for ontology learning.
result Our approach significantly improves question-answering system performance, answering 80% of questions compared to 28.4% with Text2Onto.
PS^2 selects assets then weights for high-dimensional investing.
problem High-dimensional mean--variance investing challenges.
method Two-step framework: Lasso screening followed by standard portfolio estimation.
result FPS^2 with defactored returns improves performance.