FILTR: Extracting Topological Features from Pretrained 3D Models

3D point cloud-language models (3D-LLMs) enable 3D understanding by pairing point cloud encoders with large language models, but existing methods rely on costly multi-modal encoders (e.g., ULIP-2) that require image-text-point cloud alignment on 8x A100-scale compute, creating high barriers for research and deployment. In this work, we systematically investigate whether low-cost self-supervised point cloud encoders, specifically PCP-MAE and Point-MAE, can serve as effective alternatives. Using MiniGPT-3D as our testbed, we evaluate 7 encoder initialization/pre-training setups (1 multi-modal baseline, 5 self-supervised, 1 random init) under frozen and unfrozen fine-tuning (12 total groups), across 2 architectures (MaskTransformer, PointTransformer), 3 objectives (PCP-MAE, Point-MAE, random init), and 2 datasets (Objaverse 660K, ShapeNet55-34 approximately 50K). Our experiments reveal three key findings: (1) The four-stage MiniGPT-3D pipeline can effectively train a 3D encoder from random initialization: an end-to-end trained random init encoder reaches 52.50% open-vocabulary accuracy and 44.45 captioning score, approaching top pre-trained variants; (2) Architecture and pre-training objective show strong crossover interaction: PCP-MAE + MaskTransformer achieves 59.00% accuracy (best self-supervised), while Point-MAE + MaskTransformer drops to 46.50%, with the pattern reversed for PointTransformer; (3) Closed-set ModelNet40 classification remains a core weakness of purely geometric encoders, reaching only ~13-18% accuracy vs. ~62% for the multi-modal baseline, even after end-to-end fine-tuning. Our results offer practical guidelines for cost-effective 3D-LLM design and reveal interaction patterns between self-supervised objectives and encoder architectures.

When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the computation of PH of large 3D images, and any analysis of PH that incorporates the number of generators. As such, it is often necessary to denoise the data before computing its PH. We analyze the PH of synthetic 3D images of porous media in the presence of spatially uncorrelated noise, and perform a comparative analysis of various topological measures (e.g. bottleneck distance, Wasserstein distance, persistence statistics and persistence images) to assess their robustness to both noise and the denoising process (i.e. adding spatially uncorrelated Gaussian noise, and denoising by either a Gaussian convolution or a machine learning approach).

The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Characteristic Transform (ECT) is the injective shape descriptor obtained by collecting ECCs over many directions. How the ECT is encoded for a neural network is itself an inductive bias, conventionally fixed by discretizing each ECC. We introduce a continuous encoding: for each direction and each vertex it records the net Euler-characteristic change attributed to that vertex, producing a per-direction token sequence that a small transformer maps to a feature vector. We separate the resulting pipeline into two stages on orthogonal axes: an ECC encoder that acts within each direction, mapping its curve to a fixed-length vector, and an ECT representation that acts across directions, aggregating the per-direction vectors into one. We study six ECT representation architectures spanning a range of inductive biases, from a structure-agnostic feedforward baseline to convolutional and complex-valued models that preserve equivariance under planar rotations. Across six classification benchmarks covering point clouds, graphs, cubical complexes, and meshes, the continuous encoding improves accuracy on five of six datasets, and control experiments attribute the gain to the tokenization itself rather than to the added transformer capacity. The representation architecture matters less than the encoding, and the payoff from its inductive biases depends on the encoding: a feedforward network performs best under continuous encoding but is less robust under discretization than convolutional architectures.