Paper Citation Record · LEDGER

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime

As of 12 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 2 inbound Pith citation observations for arXiv:2501.00429.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.00429 v2

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:12:16.206451Z

measured 69 of 69 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-12T03:10:43.367020Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-12T03:11:18.801254Z

Reference resolution

67 of 67 outbound references displayed

verified exact2
verified fuzzy46
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 86bdf315-528f-4777-b782-2613280e4124 · outbound

This paper cites Arrhenius.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Arrhenius

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.737917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 50ddc023-207f-421a-af3e-8ae338fad2d2 · outbound

This paper cites Diffusions hypercontractives.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Diffusions hypercontractives

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.718443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 80c69b26-e1e8-48fe-8606-68bfe5f9e193 · outbound

This paper cites A simple proof of the Poincaré inequality for a large class of probability measures.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A simple proof of the Poincaré inequality for a large class of probability measures

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:15.740008Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a84b997f-6a32-406e-8b13-c6f00342045c · outbound

This paper cites Rate of convergence for ergodic continuous markov processes: Lyapunov versus poincar \'e.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Rate of convergence for ergodic continuous markov processes: Lyapunov versus poincar \'e

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.699255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1df74a92-de1c-4b88-bf98-d40e1e628395 · outbound

This paper cites Analysis and geometry of Markov diffusion operators, volume 103.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Analysis and geometry of Markov diffusion operators, volume 103

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.676707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5726ea36-5bf4-4bb0-ba97-2f5bc7b569cb · outbound

This paper cites High-dimensional limit theorems for sgd: Effective dynamics and critical scaling.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime High-dimensional limit theorems for sgd: Effective dynamics and critical scaling

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.654978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation aa89633a-c039-43df-bc83-ba1c3abc93b4 · outbound

This paper cites B \'e rard.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime B \'e rard

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.631366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d972d41b-4abd-432f-a01b-7038b2ed8ed9 · outbound

This paper cites An Introduction to Optimization on Smooth Manifolds.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime An Introduction to Optimization on Smooth Manifolds

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:15.771290Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7550091d-4867-4b6b-914e-d9888a26f0b4 · outbound

This paper cites Metastability in reversible diffusion processes.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Metastability in reversible diffusion processes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.600374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 98a21497-d7fd-463a-9bb0-181d3bfd4b0d · outbound

This paper cites Hitting times, functional inequalities, lyapunov conditions and uniform ergodicity.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Hitting times, functional inequalities, lyapunov conditions and uniform ergodicity

Reference 10

Resolution: verified exact; doi, observed 2026-08-10T23:12:16.304762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e48fe83e-30d1-4fd8-aa33-9d96a5587b3b · outbound

This paper cites A note on talagrand’s transportation inequality and logarithmic sobolev inequality.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A note on talagrand’s transportation inequality and logarithmic sobolev inequality

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.580588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d407d5ce-2302-4df8-8db2-ccd6d1834247 · outbound

This paper cites A lower bound for the smallest eigenvalue of the laplacian.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A lower bound for the smallest eigenvalue of the laplacian

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.559245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4354ea52-c6d4-4e5e-87dc-68f93fedc126 · outbound

This paper cites An almost constant lower bound of the isoperimetric coefficient in the kls conjecture.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime An almost constant lower bound of the isoperimetric coefficient in the kls conjecture

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.534273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7bceaffc-97b9-46e6-91cb-722d7b54d3b1 · outbound

This paper cites An almost constant lower bound of the isoperimetric coefficient in the kls conjecture.

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.515743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5d1fdc55-1ec7-4ba5-a08f-e62f1a71c778 · outbound

This paper cites The ballistic limit of the log-sobolev constant equals the Polyak- ojasiewicz constant.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The ballistic limit of the log-sobolev constant equals the Polyak- ojasiewicz constant

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.493755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 77fc56ab-a5c1-4855-8a2c-6cab9504cee5 · outbound

This paper cites Analysis of langevin monte carlo from poincare to log-sobolev.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Analysis of langevin monte carlo from poincare to log-sobolev

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.463293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1aa9c012-d0a2-494c-a51a-f7d8b2aaacae · outbound

This paper cites The critical locus of overparameterized neural networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The critical locus of overparameterized neural networks

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:12:16.525072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9fa2b51f-7b79-403b-ac7d-598bf66741f6 · outbound

This paper cites The loss landscape of overparameterized neural networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The loss landscape of overparameterized neural networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:15.835454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8aebff4-08f2-4740-8657-08ed58434f2e · outbound

This paper cites Brian Davies.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Brian Davies

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.439555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 76c96393-a8a3-4c20-91d8-09719a45a431 · outbound

This paper cites Essentially no barriers in neural network energy landscape.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Essentially no barriers in neural network energy landscape

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.417945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 78c2b450-38f9-4fc4-afd7-d17b8e99a504 · outbound

This paper cites Thin shell implies spectral gap up to polylog via a stochastic localization scheme.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Thin shell implies spectral gap up to polylog via a stochastic localization scheme

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.395685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e330d163-92d0-4fac-a54a-3a61d7e8c44b · outbound

This paper cites On the convergence of langevin monte carlo: The interplay between tail growth and smoothness.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime On the convergence of langevin monte carlo: The interplay between tail growth and smoothness

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.374134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1234de19-648e-443a-8521-29da26829cc6 · outbound

This paper cites an unresolved cited work.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:12:17.351944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9af14195-6a2c-45fa-a805-12ad640d5730 · outbound

This paper cites The activated complex in chemical reactions.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The activated complex in chemical reactions

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.328683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2beb9c41-e728-443a-a4a9-d49184ec351b · outbound

This paper cites Convergence rates for the stochastic gradient descent method for non-convex objective functions.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Convergence rates for the stochastic gradient descent method for non-convex objective functions

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.306564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1b3b7cc2-1caf-4933-a215-ff0c41520afb · outbound

This paper cites Topology and geometry of half-rectified network optimization.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Topology and geometry of half-rectified network optimization

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.280344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4ad82b0a-a43a-402e-8e20-bb1b07e07c46 · outbound

This paper cites Random Perturbations of Dynamical Systems, volume 260.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Random Perturbations of Dynamical Systems, volume 260

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.255343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ddc89815-0d80-4e03-b96f-bc6fd498c35c · outbound

This paper cites Loss surfaces, mode connectivity, and fast ensembling of dnns.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Loss surfaces, mode connectivity, and fast ensembling of dnns

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:15.899208Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fdf878d-b818-4912-8ccf-64e29866a1cf · outbound

This paper cites Metastability in reversible diffusion processes ii: Precise asymptotics for small eigenvalues.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Metastability in reversible diffusion processes ii: Precise asymptotics for small eigenvalues

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.215235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fc1fff18-a073-4a7d-8e3e-c0e9e3747ebb · outbound

This paper cites Differential Topology.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Differential Topology

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.195956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d9d920f6-b273-4003-bef1-518932dd3d6d · outbound

This paper cites Nonlinear analysis on manifolds: Sobolev spaces and inequalities.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Nonlinear analysis on manifolds: Sobolev spaces and inequalities

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.176548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 698fbce7-d690-4881-b4b3-520461f8832a · outbound

This paper cites Isoperimetric problems for convex bodies and a localization lemma.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Isoperimetric problems for convex bodies and a localization lemma

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.158053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8b7da718-d42a-4dd2-85fb-2f3d1c398bd7 · outbound

This paper cites Linear convergence of gradient and proximal-gradient methods under the polyak- ojasiewicz condition.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Linear convergence of gradient and proximal-gradient methods under the polyak- ojasiewicz condition

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.138985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8c0549c4-3b33-46d5-b673-222a8bce3142 · outbound

This paper cites Mountain pass theorems and global homeomorphism theorems.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Mountain pass theorems and global homeomorphism theorems

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.117583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6fb74091-bb74-4bbe-a32a-844ddae87bde · outbound

This paper cites Elimination of all bad local minima in deep learning.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Elimination of all bad local minima in deep learning

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.089514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ab62030-901b-4d6e-8cb0-1155cd311439 · outbound

This paper cites Brownian motion in a field of force and the diffusion model of chemical reactions.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Brownian motion in a field of force and the diffusion model of chemical reactions

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.064020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation adb7d748-5894-4f48-89dc-e1143757ede4 · outbound

This paper cites Explaining landscape connectivity of low-cost solutions for multilayer nets.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Explaining landscape connectivity of low-cost solutions for multilayer nets

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:17.041747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6c6a07de-09a0-43aa-9d5f-3877caebbedf · outbound

This paper cites an unresolved cited work.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:12:17.019885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 957c7bb3-8a47-4d6c-868b-eb723b688821 · outbound

This paper cites The Kannan-Lov\'asz-Simonovits Conjecture.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The Kannan-Lov\'asz-Simonovits Conjecture

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:15.976365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6289222-bce9-4a90-9eec-4dd5e9dd5578 · outbound

This paper cites Eldan's stochastic localization and the kls conjecture: Isoperimetry, concentration and mixing.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Eldan's stochastic localization and the kls conjecture: Isoperimetry, concentration and mixing

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.996818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d94b7bd7-551b-4ebb-b49f-cf142c2145a1 · outbound

This paper cites The effect of smooth parametrizations on nonconvex optimization landscapes.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime The effect of smooth parametrizations on nonconvex optimization landscapes

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.972468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fe646964-d14e-4697-92ed-9fa88a98a6e7 · outbound

This paper cites Stochastic modified equations and adaptive stochastic gradient algorithms.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Stochastic modified equations and adaptive stochastic gradient algorithms

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.951990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ec20132-c4d7-4553-94fd-df887b7ddbe1 · outbound

This paper cites A Hessian-Aware Stochastic Differential Equation for Modelling SGD.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A Hessian-Aware Stochastic Differential Equation for Modelling SGD

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.019830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 216c97a5-f0ea-4b06-8ff8-593df10d4b5e · outbound

This paper cites What happens after sgd reaches zero loss?-a mathematical framework.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime What happens after sgd reaches zero loss?-a mathematical framework

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.933061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 589dc516-4f0a-43b1-997b-c096cdc40f75 · outbound

This paper cites Adding one neuron can eliminate all bad local minima.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Adding one neuron can eliminate all bad local minima

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.911561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 08e806f3-6da1-499c-ab9f-e0eda692f389 · outbound

This paper cites Understanding the loss surface of neural networks for binary classification.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Understanding the loss surface of neural networks for binary classification

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.885770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1ed93642-5cea-432c-b0de-b462718b438c · outbound

This paper cites Exploring Neural Network Landscapes: Star-Shaped and Geodesic Connectivity.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Exploring Neural Network Landscapes: Star-Shaped and Geodesic Connectivity

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.052346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9a0627c-075c-4d0e-95da-e80325b4def2 · outbound

This paper cites Loss landscapes and optimization in over-parameterized non-linear systems and neural networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Loss landscapes and optimization in over-parameterized non-linear systems and neural networks

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.857828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3906c2f4-a294-4829-bff1-c3a352a9d7e5 · outbound

This paper cites A topological property of real analytic subsets.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A topological property of real analytic subsets

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.835827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8802d012-818e-4cd0-8f7e-5343d6d04432 · outbound

This paper cites Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.076795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 855ff917-e39c-4a3b-b7c7-0a0567adf557 · outbound

This paper cites Stasheff.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Stasheff

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.085667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13813026-74e1-476d-81bb-af274c904968 · outbound

This paper cites On connected sublevel sets in deep learning.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime On connected sublevel sets in deep learning

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.807835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1ea9f38e-66c4-42e1-87c3-bff0c9e8e5b3 · outbound

This paper cites Toward moderate overparameterization: Global convergence guarantees for training shallow neural networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Toward moderate overparameterization: Global convergence guarantees for training shallow neural networks

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.784655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 24292958-bdc0-4b55-8148-8f80f2591fdd · outbound

This paper cites Homogenization of SGD in high-dimensions: Exact dynamics and generalization properties.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Homogenization of SGD in high-dimensions: Exact dynamics and generalization properties

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.106038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ce45f0e-d0e1-4d82-89d2-123264b84e75 · outbound

This paper cites Gradient methods for minimizing functionals.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Gradient methods for minimizing functionals

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.761460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 210d5f6b-4bc9-4c10-8227-b4c9c6c9bc5c · outbound

This paper cites Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.119333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d56b85c-2a10-42e1-a718-3485c368dd50 · outbound

This paper cites Fast convergence to non-isolated minima: four equivalent conditions for c 2 functions.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Fast convergence to non-isolated minima: four equivalent conditions for c 2 functions

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.125786Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95296e62-0e87-401b-b37f-81a4a253cd17 · outbound

This paper cites On the quality of the initial basin in overspecified neural networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime On the quality of the initial basin in overspecified neural networks

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.701454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9be140d7-6e39-4cbe-9ac6-58f0ad974746 · outbound

This paper cites Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.139515Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cc2b628-b54d-4c78-b1d5-925f34b0da4e · outbound

This paper cites Empirical Analysis of the Hessian of Over-Parametrized Neural Networks.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Empirical Analysis of the Hessian of Over-Parametrized Neural Networks

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.150579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7e60787-5c0b-4381-a5c2-dffbe0c0b416 · outbound

This paper cites an unresolved cited work.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:12:16.678264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation da2a9499-7722-4f92-9785-2677b00bbee3 · outbound

This paper cites Spurious Valleys in Two-layer Neural Network Optimization Landscapes.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Spurious Valleys in Two-layer Neural Network Optimization Landscapes

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.165512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16c7a15b-3bf6-47ec-8f9f-22190f2e67ce · outbound

This paper cites On the volume of tubes.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime On the volume of tubes

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.653369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 31be22b7-93ad-4877-b548-146af09fb9a5 · outbound

This paper cites Sampling as optimization in the space of measures: The langevin dynamics as a composite optimization problem.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Sampling as optimization in the space of measures: The langevin dynamics as a composite optimization problem

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.627571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 98d47f59-f85a-4d5b-a42a-0bfde04766f0 · outbound

This paper cites Stochastic gradient descent with noise of machine learning type part ii: Continuous time analysis.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Stochastic gradient descent with noise of machine learning type part ii: Continuous time analysis

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.604535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b53a91d2-12d6-4efa-ac95-d503a9bf388e · outbound

This paper cites Global convergence and variance reduction for a class of nonconvex-nonconcave minimax problems.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime Global convergence and variance reduction for a class of nonconvex-nonconcave minimax problems

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-10T23:12:16.196878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab6c6a72-4043-4a47-8191-7adaf4c5a924 · outbound

This paper cites A hitting time analysis of stochastic gradient langevin dynamics.

Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime A hitting time analysis of stochastic gradient langevin dynamics

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:12:16.551900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 9ac769cb-0a34-410c-abb1-8dc1469ec257 · inbound

On the Connectedness of Sublevel Sets in Invex Optimization cites this paper.

On the Connectedness of Sublevel Sets in Invex Optimization Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T10:56:05.496899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7b1cbf33-563c-4132-a353-4c0964aa1f0c · inbound

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets cites this paper.

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets Poincare Inequality for Local Log-Polyak-\L ojasiewicz Measures: Non-asymptotic Analysis in Low-temperature Regime

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:11:18.802745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.