Amir Mallak, Alaa Maalouf, Lior Wolf +2cs.LG cs.CV
Neural fields (NFs) map continuous coordinates to signals such as color or density, but fast high-quality reconstruction from sparse observations remains difficult. Classical Neural Tangent Kernel (NTK) regression gives closed-form fits, yet it is fundamentally linear and cannot accumulate reusable task priors. We develop three algorithms that address these gaps. NTK-KIP learns a distilled support set of coordinates (and optional labels) so that a finite NTK can inpaint large missing regions from little observed data, yielding a compact non-linear representation instead of a raw kernel solve. MetaQuill meta-learns a shared initialization for an INR so that new scenes can be adapted by updating only a small task-specific weight offset, which provides true feature learning and a reusable prior. Finally, MetaQuill-KIP fuses both ideas: it seeds the task with a KIP-style non-linear warm start, then refines only that small offset around the meta-learned initialization. MetaQuill-KIP achieves high-PSNR reconstructions and semantically plausible inpainting under very sparse observations, while requiring only lightweight per-instance adaptation, whereas diffusion-style baselines typically depend on large pretrained generative priors and costly per-image tuning. This shows that NTK-driven neural fields can be made both non-linear and meta-learnable, narrowing the gap between analytic kernels and practical few-shot reconstruction.
Tobias Djuren, Markus Worchel, Ugo Finnendahl +1cs.GR cs.CV
Implicit surface representations have regained popularity because of their use in machine learning. A common component in optimization is regularization, penalizing the deviation of the surface from its original shape. The popular as-rigid-aspossible (ARAP) energy strikes a good compromise between realistic deformation behavior and efficient computation, at least for piecewise linear meshes. We develop an approach for computing the ARAP energy of a deformation function based on point sampling of the surface. The implicit representation is exploited to provide differentials in each sample. The evaluation is efficient and exact in each sample (up to numerical precision). We demonstrate the general applicability of the method to neural shape processing in several applications and contrast its properties with alternatives from the literature.
Neural representations for videos (NeRV) have shown strong reconstruction fidelity by storing video-specific information in network weights. However, existing formulations typically require either costly per-video optimization or video-specific weight generation, making it difficult to scale to efficient amortized video representation. We propose CoANeRV, a coordinate-aware token-space framework that adapts the broader token-conditioned neural-field paradigm to amortized video representation. CoANeRV forms compact video tokens in one feed-forward pass and uses a shared coordinate-conditioned decoder to reconstruct continuous spatio-temporal queries, avoiding per-video decoder optimization or generation while retaining coordinate-level reconstruction flexibility. To make token-space reconstruction effective, CoANeRV introduces a coordinate-aware decoding architecture that aligns spatio-temporal queries with video tokens through axis-adaptive positional encoding and temperature-modulated cross-attention. Block-wise coordinate querying further reduces peak attention memory, making high-resolution reconstruction practical. Experiments on diverse video datasets show that CoANeRV consistently improves reconstruction quality over prior feed-forward NeRV and INR baselines, reduces peak memory compared with attention-based coordinate decoders, and provides efficient amortized encoding without per-video optimization. These results support the proposed video-specific combination of feed-forward token formation, spatio-temporal coordinate retrieval, and memory-bounded dense querying. The code is available at https://github.com/jialong2023/CoANeRV.
The Minkowski functionals of a field's excursion sets -- area, boundary measure, and Euler characteristic -- describe its level-set morphology; the Euler characteristic is the cheapest handle on topology. We derive smooth Monte-Carlo estimators for all three of a continuous neural field, evaluated at scattered points via the co-area formula and Gauss-Bonnet, using only autodiff: no grid, no complex, no persistence. The estimator is accurate to 1-3% against exact topology in 2D and 3D, and costs about 3 ms per iteration where a persistent-homology (PH) loss on a cubical grid costs 650-1000 ms -- a 250x gap. We establish four design rules without which these losses silently fail: a dense level ladder (invariants are flat in the parameters away from transitions), a $C^2$ backbone (ReLU nets hide curvature in kinks), the full Minkowski vector (Euler characteristic alone is an alternating sum, gamed by debris-hole cancellation; pricing perimeter closes the channel), and sampling-scale coverage. In 2D the vector-valued cap is the only method in a controlled comparison that both repairs topology (3/3 seeds) and preserves fidelity -- uniform smoothing repairs at 11-17x the fidelity cost, and the Euler term alone repairs nothing. In 3D neural-SDF fitting, however, a failure mode we believe general to any sampled soft topology objective appears: gradient descent adversarially hides topological noise below the sampling density, where the estimator is blind -- spurious-feature counts are invariant to 4x more samples, and closing the window needs cubically many points, erasing the cost advantage. A grid-based PH baseline, whose complex is the evaluation resolution, solves the same benchmark ($4/9$ exact; median $b_1$ error 1 vs. ours above $10^4$). The 250x cost of persistence is, at present, the price of having no null space. We release estimators, receipts, and benchmarks.
Variational inference (VI) is a powerful method for principled posterior inference for scientific inverse imaging. VI learns the posterior distribution, often with a flow-based network, which can cheaply generate posterior samples upon optimization, and can flexibly incorporate score-based or classic priors. However, its application to large-scale image reconstruction is severely hindered by the poor scalability of the flow-based networks. In this work, we introduce ShuffleFlow, a scalable VI framework to address this challenge. Our method breaks down the problem into three parts: a pixel-unshuffling-based image coordinate sampler, a neural field as feature encoder, and a conditional normalizing flow (CNF) as posterior estimator. Specifically, our framework partitions an image into a stack of sub-images with pixel-unshuffling and uses a shared CNF to model the joint distribution of the sub-image stack. We condition the CNF on the output of a neural field, which embeds feature vectors corresponding to pixel-unshuffling sample locations to capture spatial structures, and share the flow's latent variable across the channels to model their correlations. We demonstrate our method's effectiveness and efficiency on both linear and nonlinear imaging inverse problems, and show its ability to more rapidly generate a high-sample-count posterior than diffusion samplers.
Alonso Urbano, David W. Romero, Max Zimmer +1cs.LG cs.CV
Neural fields parameterize data as functions from coordinates to values, providing a unified framework for representation learning across modalities. Existing approaches are dominated by per-sample meta-learning, which scales poorly due to memory-intensive inner-loop optimization. The natural alternative -- feed-forward encoding -- typically introduces modality-specific assumptions, sacrificing the generality that makes learning with neural fields attractive. We argue that locality and hierarchy are useful priors for learning field representations that can be injected without compromising modality-agnosticism. We propose LH-NeF, a framework to learn general-purpose tokenized representations of continuous signals. A locality-preserving hierarchical encoder maps raw coordinate-value field observations to structured tokens, from which the field is reconstructed during training. By replacing meta-learning's inner loop with a single forward pass, LH-NeF uses 42$\times$ less memory and supports 133$\times$ larger batches than the strongest modality-agnostic baseline. Across images, 3D shapes, and climate fields, our learned representations match or exceed performance of modality-agnostic, modality-specific, and specialized generative neural field baselines on both reconstruction and downstream tasks.
3D representations are fundamental to scene rendering, understanding, and interaction. Recent approaches, such as 3D Gaussian Splatting and Neural Radiance Fields, achieve impressive photorealistic novel-view synthesis, but lack the ability to easily decompose scene elements into a few primitives, requiring additional segmentation or grouping for object-level manipulation. We present MLP-Splatting, a method that enables scene decomposition via a few expressive light-field primitives while providing photorealistic novel-view synthesis. MLP-Splatting models each primitive as an independent compact MLP with localized spatial support that predicts radiance and opacity. In contrast to low-level Gaussian primitives or a single global radiance field, our neural primitives provide greater expressive capacity while remaining spatially localized. Rendering is performed through efficient sparse volumetric compositing over ray-primitive interactions. Our primitives are supervised using RGB supervision alone, which yields primitives that represent local scene regions often corresponding to objects or object parts, enabling interactive object-level editing without segmentation masks by selecting a handful of primitives. Our method, augmented with optional semantic feature distillation, enables open-vocabulary scene interaction and open-set instant segmentation. Compared to state-of-the-art methods, we achieve substantially lower memory usage (1/15$\times$) and faster rendering (3$\times$), as we show in our experiments compared to semantic 3DGS methods. Project Page: https://shinjeongkim.com/mlp-splatting