Dynamic Trace Estimation

Authors: Prathamesh Dharangutte, Christopher Musco

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We support our theory with empirical results, showing significant computational improvements on three applications in machine learning and network science: tracking moments of the Hessian spectral density during neural network optimization, counting triangles, and estimating natural connectivity in a dynamically changing graph.
Researcher Affiliation Academia Prathamesh Dharangutte Dept.of Computer Science & Engineering New York University ptd244@nyu.edu Christopher Musco Dept.of Computer Science & Engineering New York University cmusco@nyu.edu
Pseudocode Yes Algorithm 1 Delta Shift Input: Implicit matrix-vector multiplication access to A1, ..., Am Rn n, positive integers ℓ0, ℓ, damping factor γ [0, 1]. Output: t1, . . . , tm approximating tr(A1), . . . , tr(Am). Initialize t1 1 ℓ0 Pℓ0 i=1 g T i A1gi, where g1, . . . , gℓ0 Rn are random 1 vectors for j 2 to m do Draw ℓrandom 1 vectors g1, . . . , gℓ Rn z1 Aj 1g1, . . . , zℓ Aj 1gℓ, w1 Ajg1, . . . , wℓ Ajgℓ tj (1 γ)tj 1 + 1 ℓ Pℓ i=1 g T i (wi (1 γ)zi) end for
Open Source Code No The paper does not contain an explicit statement offering access to its source code or a link to a code repository.
Open Datasets Yes The graph dataset we use is the Wikipedia vote network dataset with 7115 nodes [25, 24]. We use the road network data Gleich/minnesota (available at https://sparse.tamu.edu/Gleich/ minnesota).
Dataset Splits No The paper does not explicitly provide training/test/validation dataset splits or cross-validation setup details.
Hardware Specification No The paper does not explicitly describe the specific hardware (e.g., GPU/CPU models, memory) used for running its experiments.
Software Dependencies Yes We implement matrix vector products with H using the Py Hessian library [47]
Experiment Setup No The paper does not explicitly provide specific hyperparameter values or detailed system-level training settings in the main text.