[Paper] Pruning AMR: Efficient Visualization of Implicit Neural Representations via Weight Matrix Analysis

Source: arXiv - 2512.02967v1

Overview

The paper introduces PruningAMR, a technique that turns a pre‑trained implicit neural representation (INR) into a memory‑efficient, adaptively refined mesh. By analyzing the weight matrices of the INR and pruning redundant components, the method automatically generates a variable‑resolution grid that concentrates detail where the underlying function changes most—crucial for visualizing large 4‑D medical scans, scientific simulations, and other data‑intensive domains.

Key Contributions

• Weight‑matrix‑based feature detection: Uses an interpolative decomposition (ID) to prune the INR’s weight matrices, exposing the geometric features encoded in the network.
• Adaptive Mesh Refinement (AMR) driven by the pruned network: The pruned INR guides a mesh‑generation process that refines only where needed, producing a non‑uniform grid aligned with the function’s complexity.
• Data‑agnostic workflow: Works directly on a trained INR without requiring access to the original training samples, making it applicable to black‑box models.
• Substantial memory savings: Demonstrates up to an order‑of‑magnitude reduction in storage compared to naïve uniform discretization, while preserving visual fidelity.
• Open‑source reference implementation: Provides code and scripts for reproducing the experiments on 2‑D and 4‑D CT datasets.

Methodology

1. Start with a pre‑trained INR (typically a small multilayer perceptron that maps coordinates → signal values).
2. Apply Interpolative Decomposition (ID) to each weight matrix:
   • ID selects a subset of columns (or rows) that span the column space within a user‑defined tolerance.
   • The selected columns correspond to “important” basis functions; the rest are deemed redundant and can be pruned.
3. Construct a pruned network that retains only the essential basis functions. Because the pruning is performed per‑layer, the resulting network is much smaller but still approximates the original function accurately.
4. Extract a feature map from the pruned network by evaluating its Jacobian or gradient magnitude across a coarse sampling of the domain. Peaks in this map indicate regions of high geometric complexity (edges, surfaces, rapid intensity changes).
5. Drive Adaptive Mesh Refinement:
   • Begin with a coarse regular grid.
   • Subdivide cells whose feature‑map values exceed a threshold, recursively, until a target error or maximum depth is reached.
   • The final mesh has fine cells only where the INR’s underlying function varies sharply.
6. Render or export the adaptively refined grid for downstream visualization, analysis, or downstream tasks (e.g., finite‑element simulation).

Results & Findings

• 2‑D synthetic functions: Pruning reduced the number of network parameters by ~70 % while keeping L₂ error below 1 e‑3. The AMR grid achieved comparable visual quality to a uniform grid that was 8× denser.
• 4‑D CT scan (time‑resolved): Starting from a 4‑D INR (≈ 1 M parameters), PruningAMR produced a mesh with ~0.12 M voxels—a ≈ 85 % memory reduction—yet preserved clinically relevant structures (e.g., vessel walls) within a 2 % relative error.
• Speed: Mesh generation time scaled linearly with the number of pruned basis functions, enabling interactive refinement for volumes up to 256³ × 64 time steps on a single GPU.

Overall, the experiments confirm that the weight‑matrix analysis reliably identifies where the INR stores high‑frequency information, and that the subsequent AMR yields a compact, high‑fidelity discretization.

Practical Implications

• Medical imaging pipelines: Radiology systems that already store scans as INRs can now produce on‑the‑fly, high‑resolution visualizations without loading the full dense volume into RAM, enabling faster diagnosis on edge devices.
• Scientific simulation post‑processing: Large‑scale fluid or climate simulations that output INRs can be visualized or converted to meshes for downstream analysis (e.g., vortex detection) with dramatically lower storage footprints.
• Game and AR/VR content creation: Artists using neural‑based texture or geometry representations can export adaptive meshes that keep detail where the viewer focuses, reducing bandwidth for streaming or mobile rendering.
• Model‑agnostic compression: Because PruningAMR works without training data, it can be integrated into model‑serving stacks to compress any black‑box INR before archiving or transmitting it.

Limitations & Future Work

• Dependence on ID tolerance: Selecting the pruning tolerance is still heuristic; overly aggressive pruning can miss subtle features, while conservative settings reduce memory gains.
• Scalability to extremely deep networks: The current pipeline assumes relatively shallow MLPs (≤ 8 layers). Extending the method to deeper, transformer‑style INRs will require more sophisticated matrix factorization techniques.
• Dynamic scenes: For time‑varying INRs where the underlying function changes rapidly, a single static mesh may become outdated; future work could explore incremental mesh updates driven by temporal feature tracking.
• Quantitative visual perception studies: The paper reports numerical errors but lacks user studies on perceived quality; evaluating how clinicians or designers perceive the adaptively refined visualizations would strengthen the claim of “visual fidelity.”

PruningAMR opens a practical path from compact neural representations to adaptive, memory‑aware visualizations—bridging the gap between the elegance of INRs and the concrete needs of developers building real‑world visualization tools.

Authors

• Jennifer Zvonek
• Andrew Gillette

Paper Information

• arXiv ID: 2512.02967v1
• Categories: cs.LG, math.NA
• Published: December 2, 2025
• PDF: Download PDF