{"arxiv_id":"2603.08635","incoming":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"outgoing":{"papers":76,"sentences":108,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":4,"sentences":4,"quotes":[{"arxiv_id":"1804.03999","title":"Attention U-Net: Learning Where to Look for the Pancreas","url":"/paper/1804.03999","section":"Model Architecture","sentence":"Each block incorporates Group Normalization [ref] for stable training and 3D attention gates [ref] that allow the network to dynamically focus on salient regions of the mode space.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1607.06450","title":"Layer Normalization","url":"/paper/1607.06450","section":"Model Architecture","sentence":"Each block comprises a linear layer, Layer Normalization [ref] , and a Swish activation, distilling the features into a final latent vector $𝐳 ∈ℝ^256$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1604.06174","title":"Training Deep Nets with Sublinear Memory Cost","url":"/paper/1604.06174","section":"Training Strategy","sentence":"To accommodate the large memory footprint of our model architecture, we utilize gradient checkpointing [ref] , which trades computational time for reduced memory usage by re-computing intermediate activations during the backward pass.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1711.05101","title":"Decoupled Weight Decay Regularization","url":"/paper/1711.05101","section":"Training Strategy","sentence":"The network is trained by minimizing the composite loss function described above using the AdamW optimizer [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2111.05288","title":"Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach","url":"/paper/2111.05288","section":"Training Dataset and Preprocessing","sentence":"The foundational dataset for this work is provided by the BHPC [ref] , based on a semi-analytical solution of the Teukolsky equation.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1711.09607","title":"Gravitational self-force on generic bound geodesics in Kerr spacetime","url":"/paper/1711.09607","section":"Introduction","sentence":"The total computational effort also scales with orbital complexity; for reference, a full 1st order self-force calculation is estimated to cost $∼10^4$ CPU-hours for a single generic orbit [ref] .","intent_p":0.86,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0805.3337","title":"Two timescale analysis of extreme mass ratio inspirals in Kerr. 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Orbital Motion","url":"/paper/0805.3337","section":"Adiabatic inspiral waveform construction","sentence":"First, while accurate phase evolution ultimately requires PA corrections, the amplitudes themselves are only needed at this leading adiabatic order for EMRI data analysis [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2310.08927","title":"Accuracy Requirements: Assessing the Importance of First Post-Adiabatic Terms for Small-Mass-Ratio Binaries","url":"/paper/2310.08927","section":"Adiabatic inspiral waveform construction","sentence":"First, while accurate phase evolution ultimately requires PA corrections, the amplitudes themselves are only needed at this leading adiabatic order for EMRI data analysis [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":24,"sentences":26,"quotes":[{"arxiv_id":"gr-qc/0509101","title":"Gravitational wave snapshots of generic extreme mass ratio inspirals","url":"/paper/gr-qc/0509101","section":"Adiabatic inspiral waveform construction","sentence":"Each mode is indexed by integers $(ℓ, m, n, k)$, where $(ℓ, m)$ label the spin-weighted spheroidal harmonics, and the harmonic numbers $(n, k)$ correspond to the radial and polar motions [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"2102.02713","title":"Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency","url":"/paper/2102.02713","section":"Adiabatic inspiral waveform construction","sentence":"Each mode is indexed by integers $(ℓ, m, n, k)$, where $(ℓ, m)$ label the spin-weighted spheroidal harmonics, and the harmonic numbers $(n, k)$ correspond to the radial and polar motions [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"gr-qc/0202090","title":"Celestial mechanics in Kerr spacetime","url":"/paper/gr-qc/0202090","section":"Adiabatic inspiral waveform construction","sentence":"This motion is also characterized by three fundamental frequencies—$Ω_r$, $Ω_θ$, and $Ω_ϕ$—corresponding to the radial, polar, and azimuthal components of the orbit, respectively, as measured in Boyer-Lindquist coordinate time $t$ [ref] .","intent_p":0.85,"contests_p":null},{"arxiv_id":"gr-qc/9910091","title":"The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission","url":"/paper/gr-qc/9910091","section":"Orbital Geometry and Classification","sentence":"We adopt the convention where $x_I ∈[-1, 1]$ uniformly describes both prograde ($x_I > 0$) and retrograde ($x_I < 0$) orbits [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2506.09470","title":"The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes","url":"/paper/2506.09470","section":"Orbital Geometry and Classification","sentence":"We adopt the convention where $x_I ∈[-1, 1]$ uniformly describes both prograde ($x_I > 0$) and retrograde ($x_I < 0$) orbits [ref] .","intent_p":0.81,"contests_p":null}]}],"unlabelled_sentences":74},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2603.08635"}}