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Daniel Baumann202216 min agoWhen I was younger, say between middle- and high-school, I was always in awe with the cosmos. Questions about where "all this" came from, where it was going, and what kept everything together were exc…
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Joshua Agterberg2023no dateIn situating our Cramer-Rao bound for dynamics parameters against existing static theory, Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities cites Agterberg et al. for two-to-infinity rates whose dependence on the spectral gap mirro…
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Minh Tang2022no dateWe cite the asymptotic efficiency of the spectral estimator for stochastic blockmodel parameters in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to clarify that block-level inference is well behaved even though individual late…
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Minh Tang2018no dateThe asymptotic normality of A's eigenvalues about those of P, with the O(1) Bernoulli-variance bias, is the result we lean on in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities when arguing that bias matters relative to spectral-…
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Avanti Athreya2016no dateWe rely on this limit theorem when summarising ASE consistency and the conditional Gaussian distribution of sqrt(n)(x_hat - Qx) in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities, which provides the per-vertex fluctuation scale t…
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Fangzheng Xie2023no dateXie and Xu's one-step procedure supplies the locally efficient per-vertex estimator we contrast with bare ASE in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities, where matching the oracle MLE covariance up to orthogonal transform…
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Fangzheng Xie2020no dateTo contrast our temporal Fisher information bound with static results, Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities cites Xie and Xu's Theta(d/n) minimax rate for latent position estimation under Frobenius loss, marking the pe…
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Barrett O'Neill1966no dateWe apply O'Neill's submersion formula in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to express the sectional curvature of the base via the A-tensor, which lets us attribute all base curvature to vertical components of Lie br…
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Michel Journée2010no dateJournee, Bach, Absil, and Sepulchre developed low-rank optimization on the PSD cone using the same R*^{n x d}/O(d) quotient that Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities inherits, and we cite them alongside Absil and Massa…
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Miles Cranmer2023no dateAfter UDE training, Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities suggests Cranmer's SymbolicRegression.jl to extract closed-form expressions N(P)X from sampled state-velocity pairs, while warning that gauge dependence of the l…
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Mark I Freidlin1998no dateWhen comparing smoothing priors with dynamically consistent alternatives, Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities invokes Freidlin-Wentzell theory to show that the small-noise rate function for an SDE coincides with a dyn…
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Christopher Rackauckas2020no dateOnce a trajectory has been recovered, Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities proposes fitting Universal Differential Equations from Rackauckas et al. so that the polynomial RDPG architecture supplies known mechanistic st…
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Markus Heinonen2018no dateIn our comparison table of trajectory models, we list Heinonen et al.'s GP-ODE (NPODE) as an example that achieves both C^1 smoothness and dynamical consistency by learning the vector field as a Gauss…
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Joshua Daniel Loyal2025no dateCited in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as an example of Bayesian hierarchical smoothing for RDPG trajectories that produces smooth interpolations but lacks dynamical consistency, since it does not enforce that v…
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Estelle Massart2020no dateMassart and Absil's quotient geometry with simple geodesics gives Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities the Procrustes distance as geodesic distance on the base manifold and the result that the injectivity radius at [X]…
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Estelle Massart2019no dateMassart, Hendrickx, and Absil compute sectional curvature on the fixed-rank PSD quotient, and Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities reuses their formulas to show that curvature on the base manifold blows up when the two…
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Shoshichi Kobayashi1963no dateKobayashi and Nomizu's treatise supplies the classical principal-bundle machinery we invoke in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities for existence and uniqueness of horizontal lifts and for the Ambrose-Singer theorem li…
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Timothée Poisot2015no dateWe invoke this work in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to motivate temporal networks scientifically, citing ecological food webs that vary across space and time as a driver for asking how latent dynamics generate…
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Tanya Strydom2022no dateCited in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as evidence that RDPG embeddings have been put to predictive use, specifically reconstructing trophic interactions, which strengthens the case that the latent representatio…
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Avanti Athreya2025no dateWe discuss this work at length in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as the closest prior approach: their gauge-invariant Procrustes distance and Euclidean mirror summarize network evolution well for change-point det…
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Marcelo Fiori2024no dateFiori and coauthors study Riemannian optimization on matrices with orthogonal columns, which we read in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as a gauge-fixing section of our principal bundle; their tangent-space dimens…
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Andrea Filippo Beretta2025no dateWe cite this work in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to draw the complementary contrast where geometry emerges from processes running on a network, whereas our setting has latent geometry generating the network an…
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Michael M Bronstein2021no dateCited in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities to flag gauge equivariance as a design principle in geometric deep learning, reinforcing that the differential-geometric vocabulary we deploy is shared across architectures…
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David M Rosen2019no datePose-graph optimization in SLAM is invoked in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as another setting that confronts analogous gauge freedom, supporting the claim that principal-bundle and holonomy ideas address phenom…
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Amit Singer2011no dateCryo-EM reconstruction from projection images related by unknown rotations is cited in Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities as a parallel domain where time-varying latent states must be estimated up to a symmetry group…
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Giulio Valentino Dalla Riva2026no dateLearning dynamics from time-varying latent representations is a goal shared across many domains, from neural connectomics to social network analysis, yet it is fundamentally complicated by the non-ide…
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Richard C. Lewontin1970no dateWe invoke Lewontin's three conditions (variation, differential reproduction, heredity) to anchor the definition of a Darwinian population, which Task ecologies and the evolution of world-tracking representations in large language models then applies at the level of whole tra…
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Marina Meilā2007no dateVariation of information from Meila supplies the metric we use in Task ecologies and the evolution of world-tracking representations in large language models to operationalize topological agreement between induced partitions in the model-organism experiments.
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Maithra Raghu2017no dateSVCCA appears in Task ecologies and the evolution of world-tracking representations in large language models within the cluster of cross-model representational comparison methods that quantify geometric similarity, against which our partition-level prediction is contrasted.
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Ari S. Morcos2018no dateTheir canonical-correlation analysis of representational similarity is grouped in Task ecologies and the evolution of world-tracking representations in large language models with related geometric comparison tools to set up the topological alternative we propose.