Implicit Neural Representations

The rapid adoption of data-driven methods in biomedicine has intensified concerns over privacy, governance, and regulation, limiting raw data sharing and hindering the assembly of representative cohorts for clinically relevant AI. This landscape necessitates practical, efficient privacy solutions, as cryptographic defenses often impose heavy overhead and differential privacy can degrade performance, leading to sub-optimal outcomes in real-world settings. Here, we present a lightweight federated learning method, INFL, based on Implicit Neural Representations that addresses these challenges. Our approach integrates plug-and-play, coordinate-conditioned modules into client models, embeds a secret key directly into the architecture, and supports seamless aggregation across heterogeneous sites. Across diverse biomedical omics tasks, including cohort-scale classification in bulk proteomics, regression for perturbation prediction in single-cell transcriptomics, and clustering in spatial transcriptomics and multi-omics with both public and private data, we demonstrate that INFL achieves strong, controllable privacy while maintaining utility, preserving the performance necessary for downstream scientific and clinical applications.

Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of constructing the diagram combinatorially, VoroFields learns a continuous, differentiable surrogate whose maximizer structure induces the partition implicitly. The Voronoi cells correspond to maximizer regions of the field, with boundaries defined by equal responses between competing sites. A hierarchical decomposition reduces the combinatorial complexity by refining only near envelope transition strata. Experiments across site families and metrics demonstrate accurate recovery of cells and boundary geometry without shape-specific constructions.

Implicit neural representations (INRs) have emerged as a powerful framework for continuous image representation learning. In Functa-based approaches, each image is encoded as a latent modulation vector that conditions a shared INR, enabling strong reconstruction performance. However, the structure and interpretability of the corresponding latent spaces remain largely unexplored. In this work, we investigate the latent space of Functa-based models for ultrasound videos and propose Low-Rank-Modulated Functa (LRM-Functa), a novel architecture that enforces a low-rank adaptation of modulation vectors in the time-resolved latent space. When applied to cardiac ultrasound, the resulting latent space exhibits clearly structured periodic trajectories, facilitating visualization and interpretability of temporal patterns. The latent space can be traversed to sample novel frames, revealing smooth transitions along the cardiac cycle, and enabling direct readout of end-diastolic (ED) and end-systolic (ES) frames without additional model training. We show that LRM-Functa outperforms prior methods in unsupervised ED and ES frame detection, while compressing each video frame to as low as rank k=2 without sacrificing competitive downstream performance on ejection fraction prediction. Evaluations on out-of-distribution frame selection in a cardiac point-of-care dataset, as well as on lung ultrasound for B-line classification, demonstrate the generalizability of our approach. Overall, LRM-Functa provides a compact, interpretable, and generalizable framework for ultrasound video analysis. The code is available at https://github.com/JuliaWolleb/LRM_Functa.

Robust scene representation is essential for autonomous systems to safely operate in challenging low-visibility environments. In these conditions, radar has a clear advantage over cameras and lidars due to its resilience to environmental factors such as fog, smoke, or dust. However, radar data is inherently sparse and noisy, making reliable 3D surface reconstruction challenging. To address this, we propose a neural implicit approach for 3D mapping from radar point clouds that jointly models scene geometry and view-dependent radar intensities. Our method leverages a memory-efficient hybrid feature encoding to learn a continuous Signed Distance Field (SDF) for surface reconstruction, while also capturing radar-specific reflective properties. We show that our approach produces smoother, more accurate 3D surface reconstructions compared to existing lidar-based reconstruction methods applied to radar data and can reconstruct view-dependent radar intensities. We also show that, in general, as input point clouds get sparser, neural implicit representations render more faithful surfaces than traditional explicit SDFs and meshing techniques.

Implicit neural representations (INRs) offer continuous coordinate-based encodings for atlas registration, cross-modality resampling, sparse-view completion, and compact sharing of neuroanatomical data. Yet reproducible evaluation is lacking for high-resolution larval zebrafish microscopy, where preserving neuropil boundaries and fine neuronal processes is critical. We present a reproducible INR benchmark for the MapZebrain larval zebrafish brain atlas. Using a unified, seed-controlled protocol, we compare SIREN, Fourier features, Haar positional encoding, and a multi-resolution grid on 950 grayscale microscopy images, including atlas slices and single-neuron projections. Images are normalized with per-image (1,99) percentiles estimated from 10% of pixels in non-held-out columns, and spatial generalization is tested with a deterministic 40% column-wise hold-out along the X-axis. Haar and Fourier achieve the strongest macro-averaged reconstruction fidelity on held-out columns (about 26 dB), while the grid is moderately behind. SIREN performs worse in macro averages but remains competitive on area-weighted micro averages in the all-in-one regime. SSIM and edge-focused error further show that Haar and Fourier preserve boundaries more accurately. These results indicate that explicit spectral and multiscale encodings better capture high-frequency neuroanatomical detail than smoother-bias alternatives. For MapZebrain workflows, Haar and Fourier are best suited to boundary-sensitive tasks such as atlas registration, label transfer, and morphology-preserving sharing, while SIREN remains a lightweight baseline for background modelling or denoising.

Satellite Earth observation has accumulated massive spatiotemporal archives essential for monitoring environmental change, yet these remain organized as discrete raster files, making them costly to store, transmit, and query. We present GeoNDC, a queryable neural data cube that encodes planetary-scale Earth observation data as a continuous spatiotemporal implicit neural field, enabling on-demand queries and continuous-time reconstruction without full decompression. Experiments on a 20-year global MODIS MCD43A4 reflectance record ($8016 \times 4008$ pixels, 7 bands, 915 temporal frames) show that the learned representation supports direct spatiotemporal queries on consumer hardware. On Sentinel-2 imagery (10 m), continuous temporal parameterization recovers cloud-free dynamics with high fidelity ($R^2 > 0.85$) under simulated 2-km cloud occlusion. On HiGLASS biophysical products (LAI and FPAR), GeoNDC attains near-perfect accuracy ($R^2 > 0.98$). The representation compresses the 20-year MODIS archive to 0.44,GB -- approximately 95:1 relative to an optimized Int16 baseline -- with high spectral fidelity (mean $R^2 > 0.98$, mean RMSE $= 0.021$). These results suggest GeoNDC offers a unified AI-native representation for planetary-scale Earth observation, complementing raw archives with a compact, analysis-ready data layer integrating query, reconstruction, and compression in a single framework.

A precise spatial delivery of the radiation dose is crucial for the treatment success in radiotherapy. In the lung and upper abdominal region, respiratory motion introduces significant treatment uncertainties, requiring special motion management techniques. To address this, respiratory motion models are commonly used to infer the patient-specific respiratory motion and target the dose more efficiently. In this work, we investigate the possibility of using implicit neural representations (INR) for surrogate-based motion modeling. Therefore, we propose physics-regularized implicit surrogate-based modeling for respiratory motion (PRISM-RM). Our new integrated respiratory motion model is free of a fixed reference breathing state. Unlike conventional pairwise registration techniques, our approach provides a trajectory-aware spatio-temporally continuous and diffeomorphic motion representation, improving generalization to extrapolation scenarios. We introduce biophysical constraints, ensuring physiologically plausible motion estimation across time beyond the training data. Our results show that our trajectory-aware approach performs on par in interpolation and improves the extrapolation ability compared to our initially proposed INR-based approach. Compared to sequential registration-based approaches both our approaches perform equally well in interpolation, but underperform in extrapolation scenarios. However, the methodical features of INRs make them particularly effective for respiratory motion modeling, and with their performance steadily improving, they demonstrate strong potential for advancing this field.

Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

Previous multi-view normal integration methods typically sample a single ray per pixel, without considering the spatial area covered by each pixel, which varies with camera intrinsics and the camera-to-object distance. Consequently, when the target object is captured at different distances, the normals at corresponding pixels may differ across views. This multi-view surface normal inconsistency results in the blurring of high-frequency details in the reconstructed surface. To address this issue, we propose a scale-encoded neural surface representation that incorporates the pixel coverage area into the neural representation. By associating each 3D point with a spatial scale and calculating its normal from a hybrid grid-based encoding, our method effectively represents multi-scale surface normals captured at varying distances. Furthermore, to enable scale-aware surface reconstruction, we introduce a mesh extraction module that assigns an optimal local scale to each vertex based on the training observations. Experimental results demonstrate that our approach consistently yields high-fidelity surface reconstruction from normals observed at varying distances, outperforming existing multi-view normal integration methods.

Establishing dense volumetric correspondences across anatomical shapes is essential for group-level analysis but remains challenging for implicit neural representations. Most existing implicit registration methods rely on supervision near the zero-level set and thus capture only surface correspondences, leaving interior deformations under-constrained. We introduce a volumetrically consistent implicit model that couples reconstruction of signed distance functions (SDFs) with neural diffeomorphic flow to learn a shared canonical template of the placenta. Volumetric regularization, including Jacobian-determinant and biharmonic penalties, suppresses local folding and promotes globally coherent deformations. In the motivating application to placenta MRI, our formulation jointly reconstructs individual placentas, aligns them to a population-derived implicit template, and enables voxel-wise intensity mapping in a unified canonical space. Experiments on in-vivo placenta MRI scans demonstrate improved geometric fidelity and volumetric alignment over surface-based implicit baseline methods, yielding anatomically interpretable and topologically consistent flattening suitable for group analysis.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing continuous signals independently of grid resolution. In this paper, we propose a high-fidelity neural compression framework based on a SIREN (Sinusoidal Representation Networks) auto-decoder to represent multi-structural seismic velocity models from the OpenFWI benchmark. Our method compresses each 70x70 velocity map (4,900 points) into a compact 256-dimensional latent vector, achieving a compression ratio of 19:1. We evaluate the framework on 1,000 samples across five diverse geological families: FlatVel, CurveVel, FlatFault, CurveFault, and Style. Experimental results demonstrate an average PSNR of 32.47 dB and SSIM of 0.956, indicating high-quality reconstruction. Furthermore, we showcase two key advantages of our implicit representation: (1) smooth latent space interpolation that generates plausible intermediate velocity structures, and (2) zero-shot super-resolution capability that reconstructs velocity fields at arbitrary resolutions up to 280x280 without additional training. The results highlight the potential of INR-based auto-decoders for efficient storage, multi-scale analysis, and downstream geophysical applications such as full waveform inversion.

This paper presents NOIR, a framework that reframes core medical imaging tasks as operator learning between continuous function spaces, challenging the prevailing paradigm of discrete grid-based deep learning. Instead of operating on fixed pixel or voxel grids, NOIR embeds discrete medical signals into shared Implicit Neural Representations and learns a Neural Operator that maps between their latent modulations, enabling resolution-independent function-to-function transformations. We evaluate NOIR across multiple 2D and 3D downstream tasks, including segmentation, shape completion, image-to-image translation, and image synthesis, on several public datasets such as Shenzhen, OASIS-4, SkullBreak, fastMRI, as well as an in-house clinical dataset. It achieves competitive performance at native resolution while demonstrating strong robustness to unseen discretizations, and empirically satisfies key theoretical properties of neural operators. The project page is available here: https://github.com/Sidaty1/NOIR-io.

Implicit Neural Representations (INRs) provide compact models of geometry, but it is unclear when their learned shapes can be edited without retraining. We show that the Gram operator induced by the INR's penultimate features admits deformation eigenmodes that parameterize a family of realizable edits of the SDF zero level set. A key finding is that these modes are not intrinsic to the geometry alone: they are reliably recoverable only when the Gram operator is estimated from sufficiently rich sampling distributions. We derive a single closed-form update that performs geometric edits to the INR without optimization by leveraging the deformation modes. We characterize theoretically the precise set of deformations that are feasible under this one-shot update, and show that editing is well-posed exactly within the span of these deformation modes.

Existing 3D editing methods often produce unrealistic and unrefined results due to the deeply integrated nature of their reconstruction networks. To address the challenge, this paper introduces CEI-3D, an editing-oriented reconstruction pipeline designed to facilitate realistic and fine-grained editing. Specifically, we propose a collaborative explicit-implicit reconstruction approach, which represents the target object using an implicit SDF network and a differentially sampled, locally controllable set of handler points. The implicit network provides a smooth and continuous geometry prior, while the explicit handler points offer localized control, enabling mutual guidance between the global 3D structure and user-specified local editing regions. To independently control each attribute of the handler points, we design a physical properties disentangling module to decouple the color of the handler points into separate physical properties. We also propose a dual-diffuse-albedo network in this module to process the edited and non-edited regions through separate branches, thereby preventing undesired interference from editing operations. Building on the reconstructed collaborative explicit-implicit representation with disentangled properties, we introduce a spatial-aware editing module that enables part-wise adjustment of relevant handler points. This module employs a cross-view propagation-based 3D segmentation strategy, which helps users to edit the specified physical attributes of a target part efficiently. Extensive experiments on both real and synthetic datasets demonstrate that our approach achieves more realistic and fine-grained editing results than the state-of-the-art (SOTA) methods while requiring less editing time. Our code is available on https://github.com/shiyue001/CEI-3D.

Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the boundary. Soft-constrained physics-informed neural networks (PINNs), which embed the PDE as a residual penalty, suffer from gradient pathology in this regime and tend to fit boundary measurements while leaving the interior field essentially untouched. We propose Neural Field Thermal Tomography (NeFTY), a hard-constrained neural field framework for label-free three-dimensional inverse heat conduction. NeFTY represents the unknown diffusivity as a continuous coordinate-based neural network, and at every optimization step passes the candidate field through a differentiable implicit-Euler heat solver with harmonic-mean interface flux, so that the governing PDE holds exactly on the discretization rather than as a soft penalty. Adjoint gradients propagate the surface reconstruction error back to the network weights at solver-level memory cost, making test-time inversion tractable on a single GPU. Across synthetic 3D benchmarks, NeFTY substantially outperforms soft-constrained PINN variants and a voxel-grid baseline on label-free volumetric recovery, and it transfers to real thermography data, surpassing classical signal-processing baselines in both defect segmentation and depth estimation. Additional details at https://cab-lab-princeton.github.io/nefty/

A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available, such systems often reside in high-dimensional state spaces and exhibit nonlinear dynamics, making traditional numerical solvers computationally expensive and ill-suited for real-time analysis and control. Consider the problem of learning a parametric flow of a dynamical system: with an initial field and a set of physical parameters, we aim to predict the system's evolution over time in a way that supports long-horizon rollouts, generalization to unseen parameters, and spectral analysis. We propose a physics-coded neural field parameterization of the Koopman operator's spectral decomposition. Unlike a physics-constrained neural field, which fits a single solution surface, and neural operators, which directly approximate the solution operator at fixed time horizons, our model learns a factorized flow operator that decouples spatial modes and temporal evolution. This structure exposes underlying eigenvalues, modes, and stability of the underlying physical process to enable stable long-term rollouts, interpolation across parameter spaces, and spectral analysis. We demonstrate the efficacy of our method on a range of dynamics problems, showcasing its ability to accurately predict complex spatiotemporal phenomena while providing insights into the system's dynamic behavior.

Accurate 3D reconstruction of vertebral anatomy from ultrasound is important for guiding minimally invasive spine interventions, but it remains challenging due to acoustic shadowing and view-dependent signal variations. We propose an occupancy-based shape completion method that reconstructs complete 3D anatomical geometry from partial ultrasound observations. Crucially for intra-operative applications, our approach extracts the anatomical surface directly from the image, avoiding the need for anatomical labels during inference. This label-free completion relies on a coupled latent space representing both the image appearance and the underlying anatomical shape. By leveraging a Neural Implicit Representation (NIR) that jointly models both spatial occupancy and acoustic interactions, the method uses acoustic parameters to become implicitly aware of the unseen regions without explicit shadowing labels through tracking acoustic signal transmission. We show that this method outperforms state-of-the-art shape completion for B-mode ultrasound by 80% in HD95 score. We validate our approach both in-silico and on phantom US images with registered mesh models from CT labels, demonstrating accurate reconstruction of occluded anatomy and robust generalization across diverse imaging conditions. Code and data will be released on publication.

Implicit Neural Representations (INRs) have emerged as a promising paradigm for video representation and compression. However, existing multi-scale INR generators often suffer from significant parameter redundancy by stacking independent processing blocks for each scale. Inspired by the principle of scale self-similarity in the generation process, we propose SRNeRV, a novel scale-wise recursive framework that replaces this stacked design with a parameter-efficient shared architecture. The core of our approach is a hybrid sharing scheme derived from decoupling the processing block into a scale-specific spatial mixing module and a scale-invariant channel mixing module. We recursively apply the same shared channel mixing module, which contains the majority of the parameters, across all scales, significantly reducing the model size while preserving the crucial capacity to learn scale-specific spatial patterns. Extensive experiments demonstrate that SRNeRV achieves a significant rate-distortion performance boost, especially in INR-friendly scenarios, validating that our sharing scheme successfully amplifies the core strengths of the INR paradigm.

2D Gaussian Splatting has emerged as a novel image representation technique that can support efficient rendering on low-end devices. However, scaling to high-resolution images requires optimizing and storing millions of unstructured Gaussian primitives independently, leading to slow convergence and redundant parameters. To address this, we propose Structured Gaussian Image (SGI), a compact and efficient framework for representing high-resolution images. SGI decomposes a complex image into multi-scale local spaces defined by a set of seeds. Each seed corresponds to a spatially coherent region and, together with lightweight multi-layer perceptrons (MLPs), generates structured implicit 2D neural Gaussians. This seed-based formulation imposes structural regularity on otherwise unstructured Gaussian primitives, which facilitates entropy-based compression at the seed level to reduce the total storage. However, optimizing seed parameters directly on high-resolution images is a challenging and non-trivial task. Therefore, we designed a multi-scale fitting strategy that refines the seed representation in a coarse-to-fine manner, substantially accelerating convergence. Quantitative and qualitative evaluations demonstrate that SGI achieves up to 7.5x compression over prior non-quantized 2D Gaussian methods and 1.6x over quantized ones, while also delivering 1.6x and 6.5x faster optimization, respectively, without degrading, and often improving, image fidelity. Code is available at https://github.com/zx-pan/SGI.

Modern visual generative models acquire rich visual knowledge through large-scale training, yet existing visual representations (such as pixels, latents, or tokens) remain external to the model and cannot directly exploit this knowledge for compact storage or reuse. In this work, we introduce a new visual representation framework that encodes a signal as a function, which is parametrized by low-rank adaptations attached to a frozen visual generative model. Such implicit representations of visual signals, e.g., an 81-frame video, can further be hashed into a single compact vector, achieving strong perceptual video compression at extremely low bitrates. Beyond basic compression, the functional nature of this representation enables inference-time scaling and control, allowing additional refinement on the compression performance. More broadly, as the implicit representations directly act as a function of the generation process, this suggests a unified framework bridging visual compression and generation.

Recent Super-Resolution~(SR) methods mainly adopt Transformers for their strong long-range modeling capability and exceptional representational capacity. However, most SR Transformers rely heavily on relative positional bias~(RPB), which prevents them from leveraging hardware-efficient attention kernels such as FlashAttention. This limitation imposes a prohibitive computational burden during both training and inference, severely restricting attempts to scale SR Transformers by enlarging the training patch size or the self-attention window. Consequently, unlike other domains that actively exploit the inherent scalability of Transformers, SR Transformers remain heavily focused on effectively utilizing limited receptive fields. In this paper, we propose Rank-factorized Implicit Neural Bias~(RIB), an alternative to RPB that enables FlashAttention in SR Transformers. Specifically, RIB approximates positional bias using low-rank implicit neural representations and concatenates them with pixel content tokens in a channel-wise manner, turning the element-wise bias addition in attention score computation into a dot-product operation. Further, we introduce a convolutional local attention and a cyclic window strategy to fully leverage the advantages of long-range interactions enabled by RIB and FlashAttention. We enlarge the window size up to \textbf{96$\times$96} while jointly scaling the training patch size and the dataset size, maximizing the benefits of Transformers in the SR task. As a result, our network achieves 35.63,dB PSNR on Urban100$\times$2, while reducing training and inference time by \textbf{2.1$\times$} and \textbf{2.9$\times$}, respectively, compared to the RPB-based SR Transformer~(PFT).

Whole-slide images (WSIs) are fundamental for computational pathology, where accurate lesion segmentation is critical for clinical decision making. Existing methods partition WSIs into discrete patches, disrupting spatial continuity and treating multi-resolution views as independent samples, which leads to spatially fragmented segmentation and reduced robustness to resolution variations. To address the issues, we propose WSI-INR, a novel patch-free framework based on Implicit Neural Representations (INRs). WSI-INR models the WSI as a continuous implicit function mapping spatial coordinates directly to tissue semantics features, outputting segmentation results while preserving intrinsic spatial information across the entire slide. In the WSI-INR, we incorporate multi-resolution hash grid encoding to regard different resolution levels as varying sampling densities of the same continuous tissue, achieving a consistent feature representation across resolutions. In addition, by jointly training a shared INR decoder, WSI-INR can capture general priors across different cases. Experimental results showed that WSI-INR maintains robust segmentation performance across resolutions; at Base/4, our resolution-specific optimization improves Dice score by +26.11%, while U-Net and TransUNet decrease by 54.28% and 36.18%, respectively. Crucially, this work enables INRs to segment highly heterogeneous pathological lesions beyond structurally consistent anatomical tissues, offering a fresh perspective for pathological analysis.

Despite the rapid progress of vision-language-action (VLA) models, the prevailing practice of predicting action chunks as discrete waypoints remains structurally misaligned with the intrinsic continuity of physical motion. This discretization arises naturally from fixed-rate robot data collection and the token-by-token prediction paradigm of large language models, but ties actions to rigid sampling rates, does not naturally support analytically consistent higher-order derivatives, and introduces quantization artifacts that hinder precise, compliant interaction. We propose Neural Implicit Action Fields (NIAF), which reformulates chunk-level action representation from discrete waypoints to continuous action functions. Using a vision-language model as a hierarchical spectral modulator over a learnable motion prior, NIAF synthesizes continuous-time action manifolds with arbitrary temporal resolution. This formulation enables analytical differentiation, allowing explicit supervision of velocity and regularization of higher-order derivative signals to promote mathematical consistency, physical plausibility, and control smoothness. Our approach achieves strong results on CALVIN and LIBERO across diverse backbones. Real-world experiments further confirm that NIAF supports stable impedance control, bridging policy-side action generation and execution-side smooth control.

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the input space to the solution space with a weighted residual formulation based on the finite element method, enabling discretization-independent prediction beyond the training resolution without relying on labeled simulation data. The present framework for multiphysics problems is implemented in Folax, a JAX-based operator learning platform, and is verified on nonlinear coupled thermo-mechanical problems. Two- and three-dimensional representative volume elements with varying heterogeneous microstructures, and a close-to-reality industrial casting example under varying boundary conditions are investigated as the example problems. We investigate the potential of several neural operators combined with the proposed finite element-guided approach, including Fourier neural operators (FNOs), deep operator networks (DeepONets), and a newly proposed implicit finite operator learning (iFOL) approach based on conditional neural fields. The results demonstrate that FNOs yield highly accurate solution operators on regular domains, where the global features can be efficiently learned in the spectral domain, and iFOL offers efficient parametric operator learning capabilities for complex and irregular geometries. Furthermore, studies on training strategies, network decomposition, and training sample quality reveal that a monolithic training strategy using a single network is sufficient for accurate predictions, while training sample quality strongly influences performance. Overall, the present approach highlights the potential of physics-informed operator learning with a finite element-based loss as a unified and scalable approach for coupled multiphysics simulations.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for various signal processing tasks, but their inherent spectral bias limits the ability to capture high-frequency details. Existing methods partially mitigate this issue by using Fourier-based features, which usually rely on fixed frequency bases. This forces multi-layer perceptrons (MLPs) to inefficiently compose the required frequencies, thereby constraining their representational capacity. To address this limitation, we propose Content-Aware Frequency Encoding (CAFE), which builds upon Fourier features through multiple parallel linear layers combined via a Hadamard product. CAFE can explicitly and efficiently synthesize a broader range of frequency bases, while the learned weights enable the selection of task-relevant frequencies. Furthermore, we extend this framework to CAFE+, which incorporates Chebyshev features as a complementary component to Fourier bases. This combination provides a stronger and more stable frequency representation. Extensive experiments across multiple benchmarks validate the effectiveness and efficiency of our approach, consistently achieving superior performance over existing methods. Our code is available at https://github.com/JunboKe0619/CAFE.

Efficient point cloud geometry compression (PCGC) is essential for 3D sensing applications such as autonomous driving and digital twins. Hybrid methods combine the generalization of learned models with the adaptability of Implicit Neural Representations (INRs), but existing schemes often use complex architectures, rigid update strategies, and post-training weight compression, limiting adaptation efficiency and increasing bitstream overhead. This paper proposes Hybrid-PCGC, which formulates hybrid compression as a joint geometry-and-model bitrate allocation problem and optimizes instance-specific weight offsets as rate-constrained transmitted variables. It separates dataset-agnostic prior modeling from instance-specific adaptation through four components: a Frozen General Module (FGM), a Dual Trainable Adaptive Module (DTAM), an Adaptive Scope Controller (ASC), and a Supervised Offset Compression Module (SOCM). FGM captures global geometric regularities, while the parameter-efficient DTAM adapts to individual point clouds. ASC selects the update scope based on coding difficulty, and SOCM jointly optimizes and compresses weight offsets through differentiable entropy supervision during training. Experiments show that Hybrid-PCGC balances fidelity and bitrate, reducing bitrate by 13.96% and 16.33% over G-PCC on lossless and lossy benchmarks, respectively, and saving up to 12.33% bitrate over the state-of-the-art hybrid method on challenging dense point clouds.

Learning neural implicit fields of 3D shapes is a rapidly emerging field that enables shape representation at arbitrary resolutions. Due to the flexibility, neural implicit fields have succeeded in many research areas, including shape reconstruction, novel view image synthesis, and more recently, object pose estimation. Neural implicit fields enable learning dense correspondences between the camera space and the object's canonical space-including unobserved regions in camera space-significantly boosting object pose estimation performance in challenging scenarios like highly occluded objects and novel shapes. Despite progress, predicting canonical coordinates for unobserved camera-space regions remains challenging due to the lack of direct observational signals. This necessitates heavy reliance on the model's generalization ability, resulting in high uncertainty. Consequently, densely sampling points across the entire camera space may yield inaccurate estimations that hinder the learning process and compromise performance. To alleviate this problem, we propose a method combining an SO(3)-equivariant convolutional implicit network and a positive-incentive point sampling (PIPS) strategy. The SO(3)-equivariant convolutional implicit network estimates point-level attributes with SO(3)-equivariance at arbitrary query locations, demonstrating superior performance compared to most existing baselines. The PIPS strategy dynamically determines sampling locations based on the input, thereby boosting the network's accuracy and training efficiency. Our method outperforms the state-of-the-art on three pose estimation datasets. Notably, it demonstrates significant improvements in challenging scenarios, such as objects captured with unseen pose, high occlusion, novel geometry, and severe noise.

Synthetic aperture radar (SAR) is a tomographic sensor that measures 2D slices of the 3D spatial Fourier transform of the scene. In many operational scenarios, the measured set of 2D slices does not fill the 3D space in the Fourier domain, resulting in significant artifacts in the reconstructed imagery. Traditionally, simple priors, such as sparsity in the image domain, are used to regularize the inverse problem. In this paper, we review our recent work that achieves state-of-the-art results in 3D SAR imaging employing neural structures to model the surface scattering that dominates SAR returns. These neural structures encode the surface of the objects in the form of a signed distance function learned from the sparse scattering data. Since estimating a smooth surface from a sparse and noisy point cloud is an ill-posed problem, we regularize the surface estimation by sampling points from the implicit surface representation during the training step. We demonstrate the model's ability to represent target scattering using measured and simulated data from single vehicles and a larger scene with a large number of vehicles. We conclude with future research directions calling for methods to learn complex-valued neural representations to enable synthesizing new collections from the volumetric neural implicit representation.

Implicit Neural Representations (INRs) have recently demonstrated impressive performance for video compression. However, since a separate INR must be overfit for each video, scaling to high-resolution videos while maintaining encoding efficiency remains a significant challenge. Hypernetwork-based approaches predict INR weights (hyponetworks) for unseen videos at high speeds, but with low quality, large compressed size, and prohibitive memory needs at higher resolutions. We address these fundamental limitations through three key contributions: (1) an approach that decomposes the weight prediction task spatially and temporally, by breaking short video segments into patch tubelets, to reduce the pretraining memory overhead by 20$\times$; (2) a residual-based storage scheme that captures only differences between consecutive segment representations, significantly reducing bitstream size; and (3) a temporal coherence regularization framework that encourages changes in the weight space to be correlated with video content. Our proposed method, TeCoNeRV, achieves substantial improvements of 2.47dB and 5.35dB PSNR over the baseline at 480p and 720p on UVG, with 36% lower bitrates and 1.5-3$\times$ faster encoding speeds. With our low memory usage, we are the first hypernetwork approach to demonstrate results at 480p, 720p and 1080p on UVG, HEVC and MCL-JCV. Our project page is available at https://namithap10.github.io/teconerv/ .