Manifold Projection
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Related Articles from SNS
IRIS: time-structured manifold projections
Announce Type: new Abstract: High-dimensional biomedical data, such as cell-by-gene matrices, are increasingly generated temporally. However, Manifold Learning algorithms, like t-SNE and UMAP, cannot incorporate time-ordering in their layouts, obfuscating the dynamics of cell types or other classes. As a solution, we present IRIS, a new Manifold Learning algorithm that structures layouts both chronologically and by manifold topology.
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
On Out-of-sample Embedding in UMAP
Announce Type: new Abstract: Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space. An increasingly popular algorithm is Uniform Manifold Learning and Projection (UMAP), which uses algebraic topology to map distances between the two spaces. While it works well on many types of data sets, UMAP has trouble adding out-of-sample points to a pre-existing mapping.
KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices
Announce Type: replace Abstract: The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to training instability and restricted scalability. The Manifold-Constrained Hyper-Connections (mHC) mitigate these challenges by projecting the residual connection space onto a Birkhoff polytope, however, it faces two issues: 1) its iterative Sinkhorn-Knopp (SK) algorithm does not always yield exactly doubly stochastic residual matrices; 2) mHC incurs a...
Learned Subspace Compression for Communication-Efficient Pipeline Parallelism
Announce Type: new Abstract: Pipeline parallelism enables training of large language models that exceed single-device memory, yet inter-stage activation communication becomes the dominant bottleneck when trained on low-bandwidth networks. Recent work in this area has proposed using fixed orthogonal projections to compress activations. However, this still results in a significant performance degradation and requires a number of non-standard adaptations to constrain the optimization.
Balanced LoRA: Removing Parameter Invariance to Accelerate Convergence
Announce Type: new Abstract: Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models. Notably, LoRA is inherently overparameterized: multiple pairs of low-rank factors can yield the same adapted weight matrix. We show--both theoretically and empirically--that these pairs exhibit significantly different condition numbers.
Routing on the Stiefel Manifold: When Does Adaptive Subspace Selection Help for Cross-Domain EEG Decoding?
arXiv:2605.31043v1 Announce Type: cross Abstract: Cross-domain EEG decoding remains challenging despite advances in Riemannian deep learning: covariance matrices from different subjects occupy systematically distinct regions of the SPD manifold, yet existing domain adaptation methods either require target-domain calibration data or learn subject-specific components that cannot generalise across domains. We propose dynamic Stiefel routing: a pool of $K$ expert projection filters on the...
Deep-learning-based low-energy trigger algorithms for the Hyper-Kamiokande experiment
arXiv:2605.31391v1 Announce Type: cross Abstract: Modern machine learning techniques have become increasingly important in particle physics because of their powerful pattern-recognition capabilities, including in real-time data acquisition where stringent runtime constraints apply. This paper details the performance of deep-learning-based trigger algorithms for a large water Cherenkov detector such as Hyper-Kamiokande aimed at low-energy neutrino events (below 7 MeV). The performance of...
Deep-learning-based low-energy trigger algorithms for the Hyper-Kamiokande experiment
arXiv:2605.31391v1 Announce Type: new Abstract: Modern machine learning techniques have become increasingly important in particle physics because of their powerful pattern-recognition capabilities, including in real-time data acquisition where stringent runtime constraints apply. This paper details the performance of deep-learning-based trigger algorithms for a large water Cherenkov detector such as Hyper-Kamiokande aimed at low-energy neutrino events (below 7 MeV). The performance of custom...
FlatVPR: Plug-and-play Geo-linear Residual Adapter for Geometric Rectification of Foundation Model Feature Manifolds
Announce Type: new Abstract: This paper proposes ``FlatVPR,'' a novel geometric rectification paradigm that effectively bridges the trade-off between map lightweightness and localization accuracy in visual place recognition (VPR) by enforcing a feature manifold structure where any descriptor between two adjacent anchors $\mathbf{z}_A$ and $\mathbf{z}_B$ can be accurately reconstructed via linear interpolation $\hat{\mathbf{z}}_{pseudo} = (1-t)\mathbf{z}_A + t\mathbf{z}_B$, where $t \in...