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Architecture Shapes Transfer Specificity in Implicit Neural Representations
Authors:
D Yang Eng
Abstract:
Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solu…
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Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solution suites for heat, viscous Burgers, and focusing cubic NLS. The analytic tests use independent-seed random controls, while the PDE benchmarks use alternate same-family source controls and auxiliary ablations.
Across settings, transfer magnitude and transfer specificity separate clearly. In a 10-seed controlled 1D geometric test, Fourier Features show the largest structured transfer ($33.1\times$), followed by SIREN ($23.0\times$) and ReLU ($10.7\times$), but ReLU is far more selective: random-control transfer is $0.41\times$ for ReLU versus $14.24\times$ for SIREN. On a controlled two-parameter 1D family, the ranking changes: ReLU gives the clearest structured-versus-control separation at default settings, whereas Fourier Features improve only after bandwidth retuning. In Navier--Stokes and the broader 1D PDE suite, no single architecture dominates every equation, yet the same pattern remains: SIREN often reuses weights broadly, whereas ReLU and, in some equations, Fourier Features are more source-selective. Static diagnostics remain weak, and the heuristic scaling law $A_{\text{transfer}} \propto 1/Δt^2$ is rejected in the implemented 1D audit.
These results position transfer specificity as a useful diagnostic for coordinate networks and suggest that architecture selection in scientific machine learning should be evaluated under explicit control conditions, not by transfer magnitude alone.
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Submitted 4 June, 2026;
originally announced June 2026.
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Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation
Authors:
D Yang Eng
Abstract:
The pointwise determinant ratio \[ R_ψ(z)\equiv \log\!\left(\frac{\det g_{\mathrm{RF}}(z;ψ)}{\det g_{\mathrm{FS}}(z)}\right) \] measures how the Ricci-flat metric on the Dwork quintic departs from the Fubini--Study baseline. We ask whether this scalar observable can be described compactly in terms of a small number of projective invariants, and whether the same scaffold remains usable across compl…
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The pointwise determinant ratio \[ R_ψ(z)\equiv \log\!\left(\frac{\det g_{\mathrm{RF}}(z;ψ)}{\det g_{\mathrm{FS}}(z)}\right) \] measures how the Ricci-flat metric on the Dwork quintic departs from the Fubini--Study baseline. We ask whether this scalar observable can be described compactly in terms of a small number of projective invariants, and whether the same scaffold remains usable across complex-structure moduli. Using Donaldson's $k=10$ balanced metric as an algebraic teacher and symbolic regression on sampled points, we find that, within the restricted moduli-only feature class studied here, two low-order symmetric features, the power sum $p_2=\sum_i |z_i|^4$ and the cubic elementary symmetric polynomial $σ_3=e_3$, already capture most of the teacher variation. A degree-3 polynomial in $(p_2,σ_3)$ achieves held-out test $R^2=0.946$, while adding the remaining low-order symmetric generators changes this by less than $10^{-3}$. Within the same two-feature space, symbolic regression identifies a five-term rational-polynomial expression that matches the $k=10$ teacher with $R^2=0.9994$. Refitting the same functional scaffold across $ψ\in[0,0.8]$ keeps the mean determinant-ratio proxy $\langle R_ψ\rangle$ within $0.01\%$ of the local teachers on the sampled point clouds and yields smoothly varying fitted coefficients over the studied range. The holomorphic Yukawa coupling $κ_{111}=5$ is reproduced as a normalization check only. Taken together, these results provide a compact symbolic description of one metric-derived scalar observable on the Dwork family, while remaining bounded by the finite-$k$ teacher used for distillation rather than establishing a closed-form Ricci-flat metric.
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Submitted 4 June, 2026; v1 submitted 8 February, 2026;
originally announced February 2026.
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A Generalizable Deep Learning System for Cardiac MRI
Authors:
Rohan Shad,
Cyril Zakka,
Dhamanpreet Kaur,
Mrudang Mathur,
Robyn Fong,
Joseph Cho,
Ross Warren Filice,
John Mongan,
Kimberly Kalianos,
Nishith Khandwala,
David Eng,
Matthew Leipzig,
Walter R. Witschey,
Alejandro de Feria,
Victor A. Ferrari,
Euan A. Ashley,
Michael A. Acker,
Curtis Langlotz,
William Hiesinger
Abstract:
Cardiac MRI allows for a comprehensive assessment of myocardial structure, function and tissue characteristics. Here we describe a foundational vision system for cardiac MRI, capable of representing the breadth of human cardiovascular disease and health. Our deep-learning model is trained via self-supervised contrastive learning, in which visual concepts in cine-sequence cardiac MRI scans are lear…
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Cardiac MRI allows for a comprehensive assessment of myocardial structure, function and tissue characteristics. Here we describe a foundational vision system for cardiac MRI, capable of representing the breadth of human cardiovascular disease and health. Our deep-learning model is trained via self-supervised contrastive learning, in which visual concepts in cine-sequence cardiac MRI scans are learned from the raw text of the accompanying radiology reports. We train and evaluate our model on data from four large academic clinical institutions in the United States. We additionally showcase the performance of our models on the UK BioBank and two additional publicly available external datasets. We explore emergent capabilities of our system and demonstrate remarkable performance across a range of tasks, including the problem of left-ventricular ejection fraction regression and the diagnosis of 39 different conditions such as cardiac amyloidosis and hypertrophic cardiomyopathy. We show that our deep-learning system is capable of not only contextualizing the staggering complexity of human cardiovascular disease but can be directed towards clinical problems of interest, yielding impressive, clinical-grade diagnostic accuracy with a fraction of the training data typically required for such tasks.
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Submitted 25 March, 2026; v1 submitted 1 December, 2023;
originally announced December 2023.
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Autonomous Driving in the Lung using Deep Learning for Localization
Authors:
Jake Sganga,
David Eng,
Chauncey Graetzel,
David B. Camarillo
Abstract:
Lung cancer is the leading cause of cancer-related death worldwide, and early diagnosis is critical to improving patient outcomes. To diagnose cancer, a highly trained pulmonologist must navigate a flexible bronchoscope deep into the branched structure of the lung for biopsy. The biopsy fails to sample the target tissue in 26-33% of cases largely because of poor registration with the preoperative…
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Lung cancer is the leading cause of cancer-related death worldwide, and early diagnosis is critical to improving patient outcomes. To diagnose cancer, a highly trained pulmonologist must navigate a flexible bronchoscope deep into the branched structure of the lung for biopsy. The biopsy fails to sample the target tissue in 26-33% of cases largely because of poor registration with the preoperative CT map. To improve intraoperative registration, we develop two deep learning approaches to localize the bronchoscope in the preoperative CT map based on the bronchoscopic video in real-time, called AirwayNet and BifurcationNet. The networks are trained entirely on simulated images derived from the patient-specific CT. When evaluated on recorded bronchoscopy videos in a phantom lung, AirwayNet outperforms other deep learning localization algorithms with an area under the precision-recall curve of 0.97. Using AirwayNet, we demonstrate autonomous driving in the phantom lung based on video feedback alone. The robot reaches four targets in the left and right lungs in 95% of the trials. On recorded videos in eight human cadaver lungs, AirwayNet achieves areas under the precision-recall curve ranging from 0.82 to 0.997.
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Submitted 16 July, 2019;
originally announced July 2019.
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Deep Learning for Localization in the Lung
Authors:
Jake Sganga,
David Eng,
Chauncey Graetzel,
David B. Camarillo
Abstract:
Lung cancer is the leading cause of cancer-related death worldwide, and early diagnosis is critical to improving patient outcomes. To diagnose cancer, a highly trained pulmonologist must navigate a flexible bronchoscope deep into the branched structure of the lung for biopsy. The biopsy fails to sample the target tissue in 26-33% of cases largely because of poor registration with the preoperative…
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Lung cancer is the leading cause of cancer-related death worldwide, and early diagnosis is critical to improving patient outcomes. To diagnose cancer, a highly trained pulmonologist must navigate a flexible bronchoscope deep into the branched structure of the lung for biopsy. The biopsy fails to sample the target tissue in 26-33% of cases largely because of poor registration with the preoperative CT map. We developed two deep learning approaches to localize the bronchoscope in the preoperative CT map in real time and tested the algorithms across 13 trajectories in a lung phantom and 68 trajectories in 11 human cadaver lungs. In the lung phantom, we observe performance reaching 95% precision and recall of visible airways and 3 mm average position error. On a successful cadaver lung sequence, the algorithms trained on simulation alone achieved 77%-94% precision and recall of visible airways and 4-6 mm average position error. We also compare the effect of GAN-stylizing images and we look at aggregate statistics over the entire set of trajectories.
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Submitted 25 March, 2019;
originally announced March 2019.
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OffsetNet: Deep Learning for Localization in the Lung using Rendered Images
Authors:
Jake Sganga,
David Eng,
Chauncey Graetzel,
David Camarillo
Abstract:
Navigating surgical tools in the dynamic and tortuous anatomy of the lung's airways requires accurate, real-time localization of the tools with respect to the preoperative scan of the anatomy. Such localization can inform human operators or enable closed-loop control by autonomous agents, which would require accuracy not yet reported in the literature. In this paper, we introduce a deep learning a…
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Navigating surgical tools in the dynamic and tortuous anatomy of the lung's airways requires accurate, real-time localization of the tools with respect to the preoperative scan of the anatomy. Such localization can inform human operators or enable closed-loop control by autonomous agents, which would require accuracy not yet reported in the literature. In this paper, we introduce a deep learning architecture, called OffsetNet, to accurately localize a bronchoscope in the lung in real-time. After training on only 30 minutes of recorded camera images in conserved regions of a lung phantom, OffsetNet tracks the bronchoscope's motion on a held-out recording through these same regions at an update rate of 47 Hz and an average position error of 1.4 mm. Because this model performs poorly in less conserved regions, we augment the training dataset with simulated images from these regions. To bridge the gap between camera and simulated domains, we implement domain randomization and a generative adversarial network (GAN). After training on simulated images, OffsetNet tracks the bronchoscope's motion in less conserved regions at an average position error of 2.4 mm, which meets conservative thresholds required for successful tracking.
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Submitted 15 September, 2018;
originally announced September 2018.