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John Nicholson

Publications and source records attributed to John Nicholson.

23 records · Page 2Linked to original sources

Robust Computer Vision in an Ever-Changing World: A Survey of Techniques for Tackling Distribution Shifts

AI applications are becoming increasingly visible to the general public. There is a notable gap between the theoretical assumptions researchers make about computer vision models and the reality those models face when deployed in the real world. One of the critical reasons for this gap is a challenging problem known as distribution shift. Distribution shifts tend to vary with complexity of the data, dataset size, and application type. In our paper, we discuss the identification of such a prominent gap, exploring the concept of distribution shift and its critical significance. We provide an in-depth overview of various types of distribution shifts, elucidate their distinctions, and explore techniques within the realm of the data-centric domain employed to address them. Distribution shifts can occur during every phase of the machine learning pipeline, from the data collection stage to the stage of training a machine learning model to the stage of final model deployment. As a result, it raises concerns about the overall robustness of the machine learning techniques for computer vision applications that are deployed publicly for consumers. Different deep learning models each tailored for specific type of data and tasks, architectural pipelines; highlighting how variations in data preprocessing and feature extraction can impact robustness., data augmentation strategies (e.g. geometric, synthetic and learning-based); demonstrating their role in enhancing model generalization, and training mechanisms (e.g. transfer learning, zero-shot) fall under the umbrella of data-centric methods. Each of these components form an integral part of the neural-network we analyze contributing uniquely to strengthening model robustness against distribution shifts. We compare and contrast numerous AI models that are built for mitigating shifts in hidden stratification and spurious correlations, ...

cs.CV↗

Projective modules and the homotopy classification of $(G,n)$-complexes

A $(G,n)$-complex is an $n$-dimensional CW-complex with fundamental group $G$ and whose universal cover is $(n-1)$-connected. If $G$ has periodic cohomology then, for appropriate $n$, we show that there is a one-to-one correspondence between the homotopy types of finite $(G,n)$-complexes and the orbits of the stable class of a certain projective $\mathbb{Z} G$-module under the action of $\text{Aut}(G)$. We develop techniques to compute this action explicitly and use this to give an example where the action is non-trivial.

math.AT↗

Homotopy classification of 4-manifolds whose fundamental group is dihedral

We show that the homotopy type of a finite oriented Poincaré 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck and Bauer, this applies in the case of smooth oriented 4-manifolds whose fundamental group is a finite subgroup of SO(3). An important class of examples are elliptic surfaces with finite fundamental group.

math.GT↗

On CW-complexes over groups with periodic cohomology

If $G$ has $4$-periodic cohomology, then D2 complexes over $G$ are determined up to polarised homotopy by their Euler characteristic if and only if $G$ has at most two one-dimensional quaternionic representations. We use this to solve Wall's D2 problem for several infinite families of non-abelian groups and, in these cases, also show that any finite Poincaré $3$-complex $X$ with $π_1(X)=G$ admits a cell structure with a single $3$-cell. The proof involves cancellation theorems for $\mathbb{Z} G$ modules where $G$ has periodic cohomology.

math.AT↗

A cancellation theorem for modules over integral group rings

A long standing problem, which has its roots in low-dimensional homotopy theory, is to classify all finite groups $G$ for which the integral group ring $\mathbb{Z}G$ has stably free cancellation (SFC). We extend results of R. G. Swan by giving a condition for SFC and use this to show that $\mathbb{Z}G$ has SFC provided at most one copy of the quaternions $\mathbb{H}$ occurs in the Wedderburn decomposition of the real group ring $\mathbb{R}G$. This generalises the Eichler condition in the case of integral group rings.

math.KT↗