Implicit Neural Representations

While deep learning has enabled language decoding from intracranial brain recordings, extending this capability to non-invasive recordings remains an unresolved challenge. Decoding individual words from non-invasive brain recordings is particularly difficult, as word-level neural evidence is weak, temporally distributed, and entangled with acoustic, lexical, and semantic structure. Existing retrieval pipelines often collapse these factors into a single representation, potentially discarding information available at intermediate temporal scales. Here, we introduce Hierarchical Dynamic Neural Decoding (HDND), a hierarchical dynamic decoding framework that treats word decoding as structured refinement rather than flat label retrieval. HDND combines intermediate neural representations, contextual semantic predictions, and, for selected reading conditions, an auxiliary character-form objective. We evaluate HDND across seven electroencephalography (EEG) and magnetoencephalography (MEG) datasets spanning English, Dutch, Mandarin, and Cantonese listening, reading, and reading-aloud conditions. Across the nine-condition word-retrieval benchmark, the proposed HDND yields a higher participant-averaged balanced Top-10 point estimate than the matched contextual word-decoding baseline in every condition and achieves the highest mean among all compared methods in eight of nine conditions. Across the same nine matched conditions, HDND also yields higher token-micro and pooled word-macro Top-10 point estimates in every setting. Sentence retrieval favors HDND in eight of nine conditions, while auditory speech-segment retrieval is mixed across the six listening conditions. These results show that hierarchical residual refinement can improve multilingual word retrieval from heterogeneous non-invasive brain recordings.

Generative models of neural activity could help characterize tissue dynamics, compare experimental conditions, and simulate population activity for applications ranging from disease and drug-response studies to closed-loop experimentation. Existing approaches, however, typically assume a fixed set of sorted neurons, whereas high-density microelectrode arrays produce extremely sparse, array-wide binary spike volumes in which the observed subset of electrodes varies across assays. We introduce a discrete generative model that represents this activity using a shared vocabulary of spatiotemporal motifs. A residual vector-quantized autoencoder learns the motif vocabulary, while a factorized masked transformer predicts where activity occurs and which motif appears at each active location. We evaluate the model on 31 assays spanning human brain organoids and acute \emph{ex vivo} human hippocampal tissue. The learned motifs are broadly reused: assay identity explains only $9$ of the entropy in motif use, and motif overlap across tissue types is comparable to overlap within them. When representation quality is evaluated independently of the generative prior, our approach achieves $5.2\times$ the voxel-level reconstruction average precision of a matched flat tokenizer. For masked completion and free generation, the full model achieves $1.4$--$2.6\times$ the site-level average precision of the matched generative baseline and outperforms it across all four families of generation metrics. These results establish a compact, reusable representation for array-wide spiking activity without learned assay-specific parameters, providing a scalable foundation for generative modeling across diverse neural preparations.

How neural representations preserve the structure of input changes connects representation analysis with internal intervention. We study operable representational content through compatible actions of reference transformations on neural features. We characterise when a transformation descends through an encoder, and give a linear setting in which the defect is governed by the transformation's demand for discarded information, measured in the metric the representation induces. On a rectifier the failure to realise a transformation has two distinguishable sources --- what the source region has already made unrecoverable, and what it costs to satisfy every region the transformation visits with one operator --- and for a \textit{measured} harmonic carrier the same question has a closed answer: a linear realisation exists exactly when the retained harmonic blocks are invariant under the action. Using colour as the in-depth instance, we find that hue orbits in frozen visual features concentrate 84--88% of their energy in the first two harmonics with rotation planes shared across shapes, that this organisation is substantially inherited from input and architecture and is reshaped by training and depth, and that the measured structure supports prediction, transport from new starting states, and composition --- with global and local realisations differing sharply in which they achieve. Guided by the measurements, we construct a compact interface whose rotation action is fixed by the structure and never fitted: it reads hue zero-shot at 3.4$^\circ$ median error on unseen shapes. Theory, structural measurement, and construction together establish transformation laws as a concrete object connecting the understanding of neural representations to their design.

EEG foundation models such as BIOT, LaBraM, and EEGMamba have achieved remarkable performance in neural signal decoding, but their black-box nature limits clinical trust and neuroscientific validation. We propose a unified attribution framework for interpreting EEG foundation models across heterogeneous architectures. The framework integrates gradient-, perturbation-, and activation-based explanation methods to analyze model behavior in spatial, temporal, and frequency dimensions. Spatially, it identifies critical EEG channels and visualizes their distributions using topographic maps. Temporally, it highlights decision-relevant signal segments through attribution heatmaps. In the frequency domain, it quantifies the contributions of canonical EEG rhythms via spectral perturbation analysis. To assess explanation reliability, we introduce a population-level evaluation combining Area Over the Perturbation Curve (AOPC) and cross-method consistency analysis. The framework further leverages Large Language Models (LLMs) to transform structured attribution outputs into natural-language reports, bridging low-level neural representations and high-level semantic reasoning. Experiments on benchmark datasets, including Mumtaz2016 and TUAB, demonstrate that the generated explanations are consistent with established neurophysiological markers, validating meaningful neural representations while exposing potential dependencies on artifacts and spurious patterns. The proposed framework provides a standardized approach for evaluating the interpretability, reliability, and physiological plausibility of EEG foundation models.

Most knowledge of graphical perception comes from behavioral studies. Understanding from a neural perspective is much more limited due in part to neuroimaging studies' expensiveness and difficulty to conduct. In this paper, we evaluate whether Meta's Tribe V2 neural encoding model can recover neural contrasts from a visualization fMRI study. Specifically, we evaluate Tribe V2 through a conceptual replication of the visualization-viewing component of a prior comparison of Bubble charts and three-dimensional Surface charts in color and grayscale. We generate TRIBE-predicted cortical responses for the original stimuli and compare the resulting contrasts with those reported in the human study. The model reproduced the direction of 11 of 14 reported cortical effects, with agreement concentrated in visual-processing regions. This agreement characterizes the model's alignment with the prior human-generated fMRI results rather than independently confirming them. We discuss the limitations encountered when working with this model for in-silico replication and hope to encourage future work exploring this new avenue for neuroimaging studies in visualization. Supplemental materials are available at https://osf.io/8a96x/.

We present a framework for tracking topological features directly within continuous implicit models. Such models, including implicit neural representations (INRs) and multivariate functional approximations (MFAs), are increasingly adopted to represent scientific data without the resolution constraints of discrete grids. They offer compact, smooth, and differentiable representations of complex fields, enabling new opportunities for high-performance data storage, reconstruction, and analysis. Given a continuous implicit model, our method tracks the evolution of critical points by querying the model and its derivatives, thereby eliminating the need to resample onto a grid. This approach enables faithful feature tracking while avoiding discretization-induced artifacts such as aliasing. We demonstrate the generality of our framework across a range of implicit representations, including analytic functions, MFAs, and INRs, and show that it produces smooth, coherent critical point trajectories. By enabling feature tracking directly on continuous representations, our method supports a new class of feature-driven visualization workflows centered on implicit models.

Implicit neural representation (INR) has achieved remarkable progress in novel view synthesis and image/video coding in recent years.Compared to conventional end-to-end image codecs, INR-based compressors demonstrate significant advantages in decoding complexity. However, their practical application has been hindered by the inferior encoding speed and underutilized decoding efficiency.In this work, we propose a feedforward INR image coding architecture, Practical INR Image Codec (PIC), that computes all the necessary information for INR network in a single forward pass, achieving an encoding speed of 20 FPS. Additionally, we implement a highly optimized decoder that reaches 2000 FPS decoding speed, significantly surpassing JPEG's performance at comparable rate-distortion (RD) performance. To the best of our knowledge, this work presents the first learning-based image codec that simultaneously outperforms or is comparable with JPEG in both RD performance and decoding speed while maintaining practical encoding speed. Code is available at https://github.com/actcwlf/PIC.

Class disentanglement (the separation of a representation's class-conditional point clouds along depth and over training) is usually read off descriptive curves. We measure it as certified topological interaction between labeled point clouds, using the recently introduced Intersection Euler Characteristic Profile: the Euler characteristic of the overlap of the clouds' ball unions as a function of scale, computed by one Alpha-complex sweep with no boundary-matrix reduction. Every number carries a test: exact permutation tests in both directions, a guarded separation certificate, and a paired test for the comparative claims applications make. Across 111 trained networks and 52,650 certified measurements, disentanglement is depth-graded and concentrated in the first epochs, and interaction quotients rank class pairs by confusability (Spearman rho=0.83), on par with cheap separability statistics. In a 96-model factorial population, augmentation is the one training choice that separates classes relative to chance; weight decay compresses the overlap without separating, and depth and width do nothing. The structural finding is one only a k-fold statistic can pose: the joint entanglement of a class triple sits below that of its strongest pair in 97% of triple-layer cells and 99.5% of deep cells, far below a measured null floor, in vision encoders and frozen language models alike. This pairwise dominance is a regularity, not a law: expected from the nesting of overlaps but not forced by geometry, present at initialization and in raw pixels, and manufactured in the last stage alone when a network memorizes random labels. The unnormalized profile mass predicts test accuracy (R^2=0.94), the quotient does not, and neither beats a linear probe. One lesson is reported in full: the paired test must use a scale-free statistic, or it certifies feature-norm dynamics as disentanglement.

Implicit neural representations (INRs) can model continuous 3D shapes with a shared coordinate decoder and per-instance latent codes. At test time, autodecoder-style models commonly freeze the decoder and optimize a new latent code from sparse off-grid SDF samples. When these samples underconstrain inference, the latent can drift toward regions that fit the observations but decode implausible unobserved geometry. We propose a post-hoc observation-conditioned latent energy prior for frozen INR decoders. The energy scores standardized latents conditioned on a permutation-invariant encoding of the sparse observation set and is used as a residual expert alongside an L2 latent prior selected on validation data. We evaluate on a controlled cell-nucleus SDF dataset and a public MedShapeNet-derived SDF completion dataset. The proposed L2 objective augmented with conditional energy improves consistently over a validation-selected L2 baseline in the sparsest cell-nucleus regimes and, on MedShapeNet, outperforms both L2 and a six-component GMM latent-density prior across all reported readouts. A shuffled-context ablation is consistently weaker than matched context, supporting an observation-specific contribution. These results suggest that lightweight conditional energies can make pretrained INR decoders more observation-aware without retraining.

Resolving complex fiber geometries in brain white matter requires high-resolution diffusion MRI at the cost of long acquisition times. This leads many clinical protocols to opt for low-resolution scans, making downstream microstructure estimation and tractography challenging. Implicit neural representations (INRs) can model the diffusion signal continuously, enabling native single-subject super-resolution by querying the network at arbitrary spatial coordinates, yet existing methods often suffer from long training times and lack a mechanism to incorporate anatomical priors to regularize super-resolution by constraining the space of plausible reconstructions. To address these limitations, we propose a novel transfer-learning framework that pre-trains an INR on a high-resolution template and then adapts it to subject-specific scans via registration and fine-tuning. For $4\times$ through-plane super-resolution from 5 mm to 1.25 mm on Human Connectome Project (HCP) data, our method reduces NRMSE by 36-49% and increases FSIM by 24-43% over a recent baseline with $6\times$ faster training, outperforming competing INR-based methods across both image quality and domain-specific metrics. Code is available on the project page at https://abdulkaderghandoura.github.io/research/msc-thesis/ .

Automatic neuron reconstruction from light microscopy images is a central problem in computational neuroanatomy. While recent methods have achieved encouraging results on local image blocks, it remains unclear whether such progress translates to reconstruction that is both structurally accurate and scalable to the whole-brain scale. We present CORAL, the first benchmark for structure-aware evaluation of automatic neuron reconstruction from light microscopy images at both local and whole-brain scales. Built on a high-quality whole-brain fMOST dataset with carefully curated annotations, CORAL establishes two progressive tasks: block-level reconstruction, which evaluates reconstruction methods under limited spatial context, and brain-wide reconstruction, which assesses complete neuron reconstruction at the whole-brain scale. To account for topological correctness beyond geometric distance similarity, we introduce a structure-aware metric based on fiber prediction. To further achieve complete neuron reconstruction across the entire brain, we develop a brain-wide neuron tracing framework that extends arbitrary local reconstruction methods to the whole-brain scale through an iterative local-to-global process. Using this benchmark, we provide the first structure-aware comparison of mainstream methods for local neuron reconstruction and further evaluate their performance in brain-wide reconstruction. Our results underscore the importance of structure-aware evaluation and the need for more robust methods for complete neuron reconstruction.

Age-related Macular Degeneration (AMD) is the major cause of blindness in the Western world. Its late dry phase is characterised by irreversible atrophic areas, namely Geographic Atrophy (GA). Longitudinal Fundus Autofluorescence (FAF) image acquisitions are currently the main tool for assessing lesion growth over time at the image level. However, due to its highly individualised progression, the evolution of late AMD remains poorly understood. In this work, we propose using Implicit Neural Representations (INRs) to model GA progression at the individual level in a low-data setting. Our approach generates both FAF and GA segmentation at both past and future time points. Among the comparison models, our method achieves competitive segmentation quality across different scenarios, yielding the lowest Mean Absolute Error (MAE) for the GA lesion area and the highest DICE score, without sacrificing FAF image quality. The code is available at https://github.com/SimoneSarrocco/ga-progression-with-inrs.

Quantifying myocardial perfusion from cardiac magnetic resonance (CMR) can be achieved by fitting tracer-kinetic models to the dynamic contrast-enhanced MR data. However, fitting the observed data with multi-compartment exchange models, which describe the evolution of the contrast agent in the tissue, to estimate perfusion parameters is a challenging inverse problem that is sensitive to noise and acquisition variability. Previously, physics-informed neural networks (PINNs) have been proposed as an alternative to conventional non-linear least squares fitting methods with promising results for quantitative perfusion CMR. In this work, we extend the previously proposed PINN framework with spatiotemporal implicit neural representations (INRs) to represent the MR signal as a continuous spatiotemporal function and to improve the accuracy, smoothness, and physical consistency of the PINN model. In realistic simulated CMR datasets, our proposed PINN with INRs demonstrates improved robustness and parameter estimation accuracy over the previously established methods. The code is available at https://github.com/q-cardIA/pinn-inr.

How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank. We show that both quantities can change under an information-preserving invertible reparameterization, so neither is intrinsically a concept dimension. We distinguish model-defined population quantities (generating dimension, sufficient linear dimension, and minimum guarding rank) from procedure-defined quantities such as stopping count and cumulative edit rank. In a population Gaussian construction, an invertible shear preserves the prediction problem and all three quantities, yet changes the cumulative Euclidean erasure count from one to two. The separation holds for Moore--Penrose ordinary least squares and every finite nonnegative ridge weight. For a two-output full-QR procedure matching our motivating video analysis, cumulative edit rank similarly changes from two to the ambient dimension four. Conversely, the complete cumulative metric-QR trajectory is affine-equivariant when its positive-definite metric, probe, regularizer, and tie-breaking are transported consistently; exact covariance is one corollary, not a canonical semantic metric. In a known-rank finite-sample Adam/QR calibration, identity mixing stops after one accepted update in all 20 large-sample runs, whereas each tested shear $a\in\{.5,.75,1,1.25,2\}$ accepts at least two updates in all 20 runs. Controlled reparameterizations of frozen V-JEPA2 features preserve rank-zero predictions yet alter later Euclidean trajectories under practical optimization. These visual contact experiments are stress tests, not estimates of contact dimension. Iterative erasure therefore returns a procedure-relative estimand jointly determined by representation geometry and the full measurement procedure, not a semantic dimension by itself.

Gravimetry images subsurface density contrasts associated with geological structures, geothermal systems, and intrusive bodies. Recovering a three-dimensional density model from gravity observations is highly ill-posed because of its non-uniqueness, limited data coverage, and the attenuation of the gravity field with depth. Classical inversion methods rely on explicit regularization and parameter tuning, whereas supervised deep-learning approaches require representative gravity--density pairs that are rarely available. This paper proposes an unsupervised depth-aware implicit neural representation for 3D gravity inversion. The density volume is represented by multiple coordinate-based neural networks assigned to overlapping depth slabs and optimized directly from the observed gravity measurements through the sensitivity matrix. Slab-specific Fourier features, physics-based depth gains, and scheduled regularization provide structural priors without requiring labeled density models. Experiments on four synthetic scenarios show that the proposed method provides better overall performance in terms of RMSE, PSNR, and SSIM than the evaluated conventional and neural baselines. It also recovers more compact and spatially coherent density bodies, improves the separation of nearby anomalies, preserves internal structures, and reconstructs their vertical extent better. These results indicate that the proposed depth-aware formulation helps to mitigate the depth ambiguity inherent in gravity inversion. In the field experiment, where no ground-truth density model was available, the method produced compact, separated, and vertically coherent anomalies consistent with the observed gravity pattern.

Continuous parameterization of medical data has emerged as a powerful paradigm for resolution-independent image representation. While Implicit Neural Representations offer high fidelity and compact storage, their reliance on global Multi-Layer Perceptrons incurs sizeable computational costs, large memory requirements, and extensive optimization times. As medical imaging trends towards ever-more detailed, high-resolution volumes, these costs impose significant bottlenecks in the applicability of implicit approaches. Recently, explicit Gaussian-based primitives have revolutionized the representation learning paradigm by trading deep network evaluations for localized, rasterization-friendly primitives. In this paper, we present a comprehensive, cross-dimensional evaluation of Gaussian representations against implicit approaches for medical imaging applications. First, we outline a theoretical overview on the mathematical properties offered by explicit primitives beyond what is capable under the implicit neural paradigm. Subsequently, we benchmark the computational performance on two demanding image datasets: 2D microscopy histology and 3D lung Computed Tomography (CT). Our experiments demonstrate that Gaussian representations consistently match or surpass reconstruction metrics compared to implicit methods across all compression factors, while displaying significantly lower optimization times, and memory requirements. Together with the compelling mathematical properties offered by explicit primitives, these findings motivate the wider adoption of Gaussian representations and position them as an attractive direction for future research in medical imaging.

The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry. Current message-passing Graph Neural Networks (GNNs) are bounded by the 1-Weisfeiler-Lehman (1-WL) test, limiting their ability to capture cycles induced by spatial proximities. To address this, we propose a training-free geometric prior based on tropical algebraic geometry. We apply the recently established tropical Abel-Jacobi transform and polarization distances to machine learning on tree-structured data. We introduce a structural transformation pipeline, comprising cycle space augmentation and quotient space construction, to convert spatial trees into cyclic metric graphs suitable for embedding into the Tropical Jacobian. Computing exact tropical polarization distances requires solving the NP-Hard Closest Vector Problem (CVP) on integer lattices. Instead of relying on explicit approximations with quantization errors (e.g., Babai's rounding), we adopt a continuous relaxation on the universal cover of the Albanese torus. We show that the discrete Arakelov-Green measure, computed in closed form via the graph Laplacian's generalized inverse, decomposes exactly into the intrinsic path metric minus the unquantized polarization distance on this cover, avoiding integer lattice searches. This metric yields two descriptors: eigenvectors provide node-level structural coordinates, and the permutation-invariant eigenvalue spectrum provides a graph-level signature. On the BREC benchmark, the eigenvector formulation demonstrates expressivity beyond the 1-WL limit. On 3D morphology datasets (ACT-4, JML-4, BIL-6), the spectrum seamlessly integrates into standard architectures (VAEs, GNNs, Tree-LSTMs) without additional trainable parameters, outperforming explicit lattice approximations and improving classification accuracy over existing spatial models.

Decoding continuous motor trajectories from neural activity is essential for developing practical brain-computer interfaces (BCIs). However, current neural decoders are constrained by the limited scale and heterogeneity of neural recordings. In contrast, behavioral data can be collected more readily and at substantially larger scale from humans, animals, simulations, and robotic systems. Here, we introduce NeuroPB, a framework that scales neural decoding by transferring knowledge from pretrained behavioral representations. NeuroPB first pretrains a motor encoder on large-scale motor behavior data and then aligns neural activity with the resulting behavioral representation space using a limited set of paired neural-behavioral recordings. A neural encoder and lightweight motor decoder are subsequently optimized to reconstruct continuous movement from the aligned neural representations. Across multiple macaque motor datasets, behavioral pretraining improves trajectory decoding, including an 11% $R^2$ increase on center-out and 8% on random-target compared with training the motor encoder from scratch. Notably, pretraining on robotic trajectories achieves performance comparable to pretraining on macaque trajectories, demonstrating that transferable kinematic structure is shared across biological and artificial models. Moreover, decoding performance improves as the scale and diversity of robotic pretraining data increase, when the amount of neural data is fixed. Pretraining also enhances generalization across recording sessions, subjects, and motor tasks, with only 10% calibration needed to match training from scratch. Overall, these results establish behavioral pretraining as a scalable source for neural decoding and provide a promising route toward high-performance and calibration-efficient BCIs under limited neural data.

Longitudinal multiparametric MRI is central to follow-up imaging in oncology, yet real-world clinical data are characterised by missing sequences, heterogeneous acquisition protocols, and varying spatial resolutions across time points. We propose a patient-specific conditional implicit neural representation (INR) that models multimodal longitudinal MRI as a continuous function of world coordinates, time, and modality conditioning. The model is trained with stochastic modality dropout to handle incomplete data, and its continuous coordinate-space formulation enables both spatial and temporal interpolation without resampling to a fixed voxel grid. A self-consistency-based confidence estimator is derived from cross-modal reconstruction performance at inference time. We evaluate the framework on longitudinal MRI from paediatric brain tumour patients, demonstrating statistically significant improvements over linear interpolation for T1CE and FLAIR (p < 0.05), with mean MS-SSIM of 0.95 $\pm$ 0.02 for T1CE. Predicted confidence correlates strongly with true reconstruction quality (Pearson r up to 0.996), suggesting reliable deployment potential in heterogeneous clinical settings.

Decoders of anesthetic state from cortical activity fail across drug classes, most notoriously ketamine, but reported accuracy cannot say whether the neural representation or only the decision threshold has failed; we separate the two in a controlled preparation with ground-truth labels. We decoded awake versus anesthetized from mouse electrocorticography (the 250-Hz-bandlimited local field potential, sampled at 1875 Hz) under leave-one-anesthetic-out evaluation across five mechanistically distinct anesthetics (isoflurane, dexmedetomidine, ketamine, propofol, and midazolam), comparing a spatially blind band-power decoder, covariance/Riemannian representations, and Riemannian domain adaptation, with all statistics at the session level and mouse-level cluster bootstrapping for the ketamine fold. The representation transfers: band-power ranks awake versus anesthetized at a session AUROC of at least 0.96 on every held-out drug, ketamine included (0.980, cluster confidence interval 0.821 to 1.000). The failure is confined to the threshold: across three representations the ketamine ranking is near-invariant while its balanced accuracy swings from chance to high, and a permutation test is significant for ranking (p = 0.0025) but not for fixed-threshold accuracy (p = 0.3795). Riemannian domain adaptation is net-negative. A causal, label-free threshold anchored to the subject's own pre-induction baseline fixes ketamine (balanced accuracy 0.50 to 0.85) and dominates domain adaptation. Because the ketamine test sessions come from three mice that also contribute training drugs, this is within-subject cross-drug transfer; we do not claim population-level transfer across subjects. In cross-drug state decoding the actionable failure is calibration, not representation.

Implicit Neural Representations (INRs) encode signals as the weights of a coordinate-based neural network and have recently been proposed as an alternative domain for downstream learning. While promising, classification directly in weight space remains challenging due to the high dimensionality and complex structure of INR parameters. Furthermore, the way discriminative information is distributed across INR weights remains poorly understood. We propose a hierarchical Mixture-of-Experts (HMoE) Transformer that processes INR weights using conditional computation aligned with the structure of the underlying implicit network. Coupled with a meta-learning framework that shapes INR parameters for downstream tasks, our model achieves state-of-the-art accuracy across standard benchmarks, ranging from low-resolution datasets to high-resolution ImageNet-1K. To gain insight into how INRs encode discriminative information, we develop weight-space attribution and pruning methods that identify parameters most relevant for classification. These analyses reveal how class-specific structure emerges within INR layers and support the suitability of MoE architectures for weight-space learning. Our approach advances both the performance and interpretability of weight-space classifiers.

Many learning problems require representations that reconcile direct input, nearby structure, and broader context. In implicit neural layers, these influences are usually absorbed into a single fixed-point update, making it hard to identify what enters from the stimulus, what propagates locally, what comes from global context, and what is produced by solver dynamics. Here we introduce SILVA Networks, Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields. SILVA separates stimulus, local interaction, global interaction, damping, and readout inside one fixed-point architecture. The same template is instantiated for images, molecules, citation networks, and long-range graph benchmarks through domain-specific definitions of nodes, neighborhoods, and global summaries. Experiments and ablations show task-dependent roles for these terms: local interactions are load-bearing in the graph tasks, MNIST gains little from recurrence at the tested capacity, and the clearest global benefit appears in a long-range node-classification benchmark. SILVA therefore provides an implicit representation whose internal interaction dynamics can be trained, ablated, visualized, and diagnosed.

Time-varying implicit neural representations (INRs) provide a compact representation of scientific volumes and, for modalities such as dynamic X-ray computed tomography (CT), are often the only practical way to represent the data. However, interactive volume rendering of INRs is challenging, as cheap memory lookups are replaced by expensive neural inferences, hindering the performance. Therefore, conventional volume rendering methods such as ray marching with dense sampling are often impractical. While resampling, caching, and retraining can mitigate this cost, they compromise convenience and accuracy and become impractical for time-varying data. We tackle these challenges using a query-efficient stochastic volume rendering framework based on delta tracking. Our system employs a four-stage pipeline that exploits heterogeneous parallelism, using ray tracing cores for traversal and tensor cores for batched neural evaluation. Furthermore, we present strategies to reduce INR queries via ray budgeting and query pruning, thereby increasing per-frame performance. Using our renderer, many time-varying INRs can be rendered directly from their original representation. The system achieves ~30-40 FPS at 1024x1024 resolution on an RTX 4090 GPU and converges to high-fidelity images. Moreover, the system enables interactive temporal exploration of the continuous domain, with timestep updates taking approximately 1-2 ms.

Early warning of extreme weather is essential for mitigating the societal, economic, and environmental risks posed by hazardous weather events. However, expert-centered warning workflows are costly, labor-intensive, and difficult to scale throughout the warning-to-action process. Although recent advances in Large Language Model (LLM) agents have enabled the automation of weather-related tasks, existing studies remain centered on isolated scientific tasks and overlook the chain of interdependent processes required for operational extreme-weather early warning. To bridge this gap, this study investigates automated end-to-end extreme-weather early warning through LLM agents. We first develop SIREN-Bench, a comprehensive benchmark comprising 600 question-answer instances across 19 tasks, and covering four individual warning procedures and an end-to-end warning chain. Evaluation on SIREN-Bench reveals substantial capability gaps in existing weather agent frameworks. This motivates us to develop SIREN, an experience-grounded agent framework inspired by experts' use of historical cases, which combines an agentic execution environment integrating heterogeneous weather evidence and tools with a family of agent harnesses that exploit historical cases through retrieval, skill distillation, and predictive modeling. Extensive experiments demonstrate that SIREN outperforms weather-agent baselines on both individual warning procedures and end-to-end warning chains.

We propose a neural representation for minimal surfaces. Unlike prior approaches based on discretization or Physics-Informed Neural Networks (PINNs), where meshes or neural fields are optimized to approximate the governing equations, our method builds on an exact representation, similar to the classical Weierstrass--Enneper parameterization, yielding minimal surfaces up to negligible quadrature error in evaluation. We formulate a training objective for the Plateau problem that optimizes over this representation.

The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

We study sinusoidal recurrence as an iterative mechanism for harmonic spectral enrichment in implicit neural representations (INRs). Our analysis reveals that sinusoidal activations induce a harmonic line spectrum, providing a spectral account of how recurrent unrolling enriches the effective spectral support. We realize this principle with a shared sinusoidal block that iteratively refines the latent representation. We empirically validate the resulting spectral behavior against feed-forward INRs, non-sinusoidal recurrent variants, and equilibrium-style sinusoidal models. Complementing this analysis, we evaluate the proposed architecture across image and 3D representation tasks. On RGB image benchmarks, our method achieves higher fidelity than feed-forward baselines with fewer parameters and fewer optimization steps, and it further transfers favorably to super-resolution, NeRF, and SDF tasks.

Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.

Diffusion Magnetic Resonance Imaging (dMRI) is a powerful tool for probing brain microstructure, but clinical acquisitions are often limited by low out-of-plane resolution, resulting in degraded structural information and reduced utility for advanced analysis. We introduce SIINR (Structurally Informed Implicit Neural Representations), a general framework for super-resoltion of clinical dMRI datasets while quantifying uncertainty in the reconstructed outputs. SIINR utilizes a supervised 3D U-net as a prior and combines it with a self-supervised implicit neural representation (INR) that fuses the high-resolution prior and the original low-resolution data. The INR enables joint modeling across spatial and angular domains, enforces data consistency, and provides analytic approximate posterior distributions for downstream uncertainty quantification. We validate the framework on a diverse set of open-access dMRI datasets, demonstrating that SIINR outperforms standard interpolation methods in both quantitative error metrics and qualitative anatomical fidelity. Experiments on clinical cases, including subjects with multiple sclerosis and brain lesions, illustrate the framework its ability to propagate intensity changes and flag uncertain regions in challenging scenarios. SIINR is flexible, modular, and can be adapted to different upsampling ratios and downstream tasks, providing a principled approach for enhancing clinical dMRI and supporting robust interpretation of derived neuroimaging metrics.

Functional magnetic resonance imaging (fMRI)-based visual decoding aims to recover visual information from measured brain activity, commonly by mapping fMRI responses into latent visual features for downstream decoding tasks. Most existing methods learn mappings from fMRI responses to visual features extracted by artificial neural networks (ANNs), yet it remains unclear whether ANN-derived features provide suitable targets for brain decoding. In this study, we investigate spiking neural network (SNN)-derived visual features as alternative targets for fMRI-based visual decoding. We compare an ANN baseline with four SNN variants from the same architectural family, which differ in their spiking dynamics. To isolate the effect of the target features, all models use the same L2-regularized linear fMRI-to-feature decoder, while only the feature vectors used as regression targets are varied. Compared with the ANN baseline, SNN-derived features exhibit stronger alignment with fMRI responses and improve visual semantic decoding performance. For instance, on the GoD dataset, SNN-derived features reduce feature-prediction error from 0.7707 to 0.0282 and improve top-1 semantic decoding accuracy from 0.1800 to 0.4400. Ablation results further indicate that both spiking neural dynamics and temporal simulation steps contribute to the observed advantage. These findings support SNN-derived features as effective brain-decodable visual representations and highlight target feature design as an important component of fMRI-based visual decoding.

Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function. By replacing traditional multi-layer perceptrons (MLPs) with a parameterized primitive engine, Fluid-SDF reconstructs complex, non-convex topologies using strictly under 100 parameters, achieving comparable or superior intersection-over-union (mIoU) to standard neural baselines. Furthermore, we demonstrate that Fluid-SDF acts as a powerful geometric prior, inherently resisting high-frequency dataset noise where capacity-matched neural networks catastrophically overfit. Finally, unlike standard INRs, Fluid-SDF's explicit parameter space allows for direct, zero-shot user editing of local and global shape features without retraining. By bypassing expensive on-device gradient updates entirely, Fluid-SDF is uniquely suited for mobile AI, augmented reality, and resource-constrained embedded environments

Implicit neural representation (INR) methods provide continuous coordinate-to-value mappings and integrate naturally with direct volume rendering, making them attractive for representing volumetric data. However, existing INR-based approaches for volumetric data are inherently lossy, and even small reconstruction errors can propagate through rendering and downstream analysis. In this work, we explore Lossless-INR, a lossless INR framework for 3D scientific volumetric data based on bit-plane decomposition. By decomposing each voxel value into binary bit-planes, we reformulate reconstruction as per-bit binary classification, so that exact recovery reduces to predicting every bit correctly. To make this optimization tractable while keeping the representation compact, we combine an octree block-partitioning strategy that adaptively subdivides complex regions with a ternary feature-grid network whose grid entries are parameterized by a ternary set of values. Experiments on diverse volumetric datasets show that this design can achieve zero bit-error rate and bit-exact reconstruction, enabling faithful rendering and downstream analysis with a compact representation. The code is available at https://github.com/TouKaienn/Lossless-INR.

Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.

Within Explainable Artificial Intelligence, mechanistic interpretability uses Sparse Autoencoders (SAEs) to extract more interpretable features from neural representations. However, assessing their monosemanticity, and thus explanation quality, remains challenging. Existing metrics require external concept labels or depend on pretrained embedding models, making them sensitive to encoder's geometry. We introduce the Tversky Monosemanticity Score (TMS), a label-free metric that operationalizes monosemanticity as activation-set coherence of binarized SAE latents, and does not require external embedding encoders. We evaluate TMS on SAEs trained on features from pretrained vision and vision-language models (DINOv3, CLIP, BLIP2), two common SAE regimes (TopK, BatchTopK), multiple sparsity levels, and expansion factors. Our results show that TMS is less affected by encoder anisotropy than its embedding-based alternative, while remaining aligned with established monosemanticity indicators. TMS also reveals distinct SAE training dynamics across base models. Moreover, under encoder anisotropy, TMS provides a stronger indication of probe-based concept deletion effectiveness, while being competitive otherwise.

Deep neural networks trained on natural images are shown to produce outputs consistent with human observers for brightness illusions. While this phenomenon has been documented across architectures, all evidence, to date, is measured at the output level: restored pixels, decoded trajectories, or classification decisions. Whether these models actually represent illusions internally, and if so where and how, remains unknown. We show that denoising models develop illusion-sensitive representations at specific internal layers, across varied architectures. Specifically, we identify the layers and channels that discriminate illusory from physically matched control regions. We show that the denoising objective is a more important driver of the effect than the architecture. On domain-appropriate stimuli, these activations track a validated psychophysical model of human brightness perception (FLODOG; Spearman $ρ\geq 0.70$) and scale monotonically with parametric illusion strength. Leveraging these findings, we provide causal evidence via channel ablation showing that illusion-sensitive channels specifically and substantially affect the internal signal. Yet injecting these representations into the generation pipeline produces no measurable pixel shift across all tested architectures; we term such representations perceptual phantoms: active in internal processing yet invisible to any output-based evaluation. While related internal-output dissociations have been characterized in language models, this is the first such characterization for perceptual representations in denoising vision models.

Style transfer remains a fundamental and highly important task across various data modalities, enabling creative manipulation conditioned by both reference images and textual descriptions. Recently, methods utilizing Gaussian Splatting have emerged as a unified representation for 2D images, video, 3D scenes, and 4D dynamics. However, representing videos and 2D images with Gaussian Splatting is structurally sub-optimal for dense continuous domains. The number of required Gaussians often approaches the total number of pixels, raising questions about the actual utility of such a representation for these specific modalities. In contrast, Implicit Neural Representations have established themselves as a much more popular and natural choice across all these data domains. Implicit Neural Representations naturally provide significant advantages, including data compression, inherent capabilities for super resolution, and seamless integration with deep generative models. To this end, we introduce OmniStyle-INR, a novel framework that leverages network-based continuous representations as a truly universal domain. Our approach successfully performs high-quality style transfer across all visual modalities, guided seamlessly by both text prompts and visual exemplars.

We describe a model of perceptual inference in primary visual cortex (V1) equivalent to a minimal diffusion model whose function can be readily understood from its parameters. The model is based on sparse coding with a non-factorial prior over latent variables in the form of an unconstrained, pairwise interaction matrix, extending standard sparse coding inference to a general recurrent dynamical system. We efficiently train these recurrent dynamics using a denoising score-matching objective and implicit differentiation. After training on natural images, the learned interaction matrix mirrors the structure of horizontal connections in superficial layers of V1 that link neurons of similar orientation tuning. This model exhibits exceptionally good denoising performance, restoring image features such as extended contours amid extreme visual ambiguity, nearly matching the behavior of standard, black-box diffusion architectures in generalization regime. Owing to the model's simplicity, the network's Jacobian can be decomposed directly in terms of the interaction matrix between latent variables, revealing mechanistically how the recurrent dynamics assign high probability over a continuous family of natural structural deformations. Intriguingly, within this circuit, a large fraction of latent variables learn to disconnect from visual input altogether, essentially forming a hierarchical representation that appears to enforce global consistency among image features. Together, the model and results bridge two distinct domains: for neuroscience, it generates concrete, testable hypotheses regarding functional connectivity in recurrent neural circuits during perceptual inference tasks; for machine learning, it elucidates the internal mechanisms learned by diffusion models that allow them to generate infinitely many novel images from a finite training set.

Decoding continuous three-dimensional (3D) motor imagery (MI) using non-invasive electroencephalography (EEG)-based brain--computer interfaces (BCIs) remains challenging due to signal variability and residual decoding errors. Deep learning architectures such as convolutional neural network--long short-term memory (CNN--LSTM) models can capture spatial and temporal dynamics for continuous kinematic decoding; however, systematic residual errors persist in predicted trajectories. We propose a two-stage decoding framework that applies reinforcement learning (RL) to perform residual kinematic correction on the outputs of a CNN--LSTM decoder (CNN--LSTM--RL). The RL agent is trained offline without direct EEG input and instead operates on predicted kinematic trajectories to optimize movement accuracy relative to target trajectories. Decoding performance was quantified using Pearson correlation coefficients ($r$) and Root Mean Square Errors (RMSE) along the $x, y$, and $z$ axes. Compared to CNN--LSTM applied alone, CNN--LSTM--RL improved the mean correlation from $0.5076$ to $0.7181$ ($p = 0.0005$) in 2D and from $0.6420$ to $0.7780$ ($p = 0.0059$) in VR, with relative gains of $41.5\%$ and $21.2\%$, respectively. Correspondingly, RMSE was reduced from $0.0890$ to $0.0532$ (2D, $p < 0.0001$) and from $0.0714$ to $0.0441$ (VR, $p < 0.0001$), representing relative reductions of $40.2\%$ and $38.2\%$. These findings demonstrate that this scalable framework enhances 3D BCI MI decoding by correcting kinematic errors via offline residual RL without extra neural data, advancing neurorehabilitation, prosthetics, and virtual interaction.

In this paper, we investigate preprocessing techniques aimed at improving the efficiency of accessing models of propositional formulas represented in conjunctive normal form (CNF). We focus on three fundamental tasks: uniform sampling, direct model access, and model enumeration. Our analysis reveals that most state-of-the-art preprocessors, when they do not preserve formula equivalence, are generally unsuitable for these tasks. In contrast, we demonstrate that preprocessors which preserve model counts can be effectively leveraged, provided relevant preprocessing information is maintained. To validate our approach, we perform extensive experiments on a diverse suite of benchmarks from multiple domains. The experimental results show that our preprocessing methods are both efficient and robust, yielding significant performance improvements for model access queries when CNF formulas are compiled into d-DNNF representations.

Neural networks increasingly guide decisions in high-stakes domains such as medical diagnosis, credit approval, and energy bidding. Audit in these settings requires case-level evidence: which training cases support an action and what outcomes they carried. Case-based decision theory (CBDT) formalizes this reasoning by aggregating outcome support from remembered cases. We show that an OLS action readout fitted on a fixed neural representation admits an exact case-based decomposition. Each action score is a weighted sum of training-case returns, with coefficients determined by empirical Gram geometry. We identify a sufficient regime for CBDT similarity semantics; outside it, the coefficients should generally be treated as signed Gram-geometric influence. The decomposition yields audit signals that trace scores to training cases, measure action coherence, and identify weak support. Across synthetic CBDT, PJM, Adult Income, and Default Credit tasks, the method recovers case-level preference structure and achieves the highest mean Top-30 consistency among compared attribution baselines, while remaining competitive on support reconstruction. The audit requires only fitting an OLS top-layer probe, without retraining the representation or accessing the original optimization trajectory; probe fidelity is measured by score reconstruction.

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

Implicit neural representations (INRs) offer compact encoding of volumes, but as lossy approximators, inevitably have prediction errors. We consider INRs that can simultaneously encode relative error scales by predicting distributions using tools from uncertainty estimation. Typically, uncertainty estimation relies on computationally expensive approaches or on predefined parametric assumptions about the predictive distribution (e.g., Gaussian). In this study, we propose a lightweight method that reformulates regression-based INR training as a classification task by discretizing continuous targets into bins, enabling flexible distribution modeling to capture complex multimodal behaviors. We analyze the trade-off between regression and classification for INR training and demonstrate that the classification setting tends to achieve high reconstruction quality and competitive error awareness through uncertainty estimation, compared to regression-based approaches.

Compositionality, by organizing complex behavior as combinations of simpler elements, enables robot learning that is scalable and data efficient. Leveraging this principle, we propose a generative learning-from-demonstration framework that enables compositional modeling of robotic behavior by connecting perception and motion through shared object-level representations. We render scenes from object-centric neural representations that integrate canonical neural fields with latent-conditioned deformations, capturing positional and geometric variations in a smooth, consistent, and interpretable way. For motion generation, a temporal mixture-of-experts (MoE) employs a gating mechanism to combine object-conditioned movement primitives over time, producing complete trajectories. This spatial-temporal compositionality maintains the data efficiency of movement primitives while grounding motion in visual structure, enabling systematic generalization across diverse scene configurations. In simulation, long-horizon manipulation tasks are successfully completed using the proposed model, which requires significantly less training data than other image-based baselines. Real-world experiments further demonstrate the method's robustness to noise, its ability to generalize at the category level through language-based segmentation models, and its capacity to operate directly on 3D scene representations.

A learning-based physics-constrained neural kernel for sound field estimation is proposed. Sound field estimation aims to estimate the spatial distribution of an acoustic field from a discrete set of microphone measurements, which have a wide range of applications. Among existing sound field estimation methods, kernel-regression-based methods offer a flexible and principled framework for incorporating physical constraints and allow inference through linear operation. It is also possible to adapt the kernel function to the target acoustic environment by representing the directional weighting function as an implicit neural representation (INR) and optimizing hyperparameters using measurements. However, the kernel function is generally optimized for single snapshot measurements of the microphones, which can lead to strong overfitting and poor generalization. We propose a source-position-dependent INR for the directional weighting function, enabling the kernel function to capture common directional patterns and to generalize to unseen source positions in the target acoustic environment. Experimental results indicate that our proposed method outperforms the snapshot-based method by estimating a directional weighting function that matches the directivity of the target sound field.

Multi-Pool Chemical Exchange Saturation Transfer (CEST) MRI provides valuable metabolic information but is clinically limited by long acquisition times. Although sparse sampling reduces scanning time, reconstructing high-resolution Z-spectra from limited data remains an ill-posed inverse problem. Conventional interpolation and generic Implicit Neural Rep-resentations (INRs) often lack physical constraints, leading to spectral artifacts and physically invalid signals. To address this, we propose Lorentz Encoding (LE), a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning. Unlike generic positional encodings, LE regularizes the continuous spectral mapping by projecting sparse coordinates into a physically constrained space governed by a combination of parametric Lorentzian profiles with learnable basis functions. This mechanism effectively reduces noise and enforces consistency with physical models. Experiments on in vivo human brain data demonstrate that LE significantly outperforms state-of-the-art methods. Specifically, under a 39-point sampling strategy, LE achieves a PSNR of 57.58 dB and an SSIM of 0.9994. Furthermore, the learned physics-informed encodings form a continuous, geometrically ordered trajectory in the latent space, ensuring accurate quantitative metabo-lite mapping (APT, NOE, MT).

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.

Establishing large-scale, high-resolution neural connectivity maps is fundamental to elucidating the structural basis of brain function. However, when processing terabyte- or petabyte-scale electron microscopy data, over-segmentation inherent in automated reconstruction algorithms remains a critical bottleneck, requiring extensive manual proofreading spanning person-years. To alleviate the heavy reliance on annotated data and the limited flexibility of conventional tracing methods, we propose a training-free, targeted neuron tracing framework. Specifically, we introduce a skeleton-guided Heuristic Spatial Search paradigm that leverages geometric priors to iteratively reconstruct neuronal morphologies through a probing-verification cycle. To achieve robust zero-shot semantic verification, we further develop a Dimension-Aware Semantic Verification strategy built upon the foundation model NeuroSAM 2. This strategy resolves intra-slice splits via Planar Ensemble Consensus and inter-slice splits via Axial Spatio-Temporal Propagation. Notably, we integrate the proposed workflow into the Neuroglancer visualization platform, enabling an interactive human-in-the-loop proofreading system. Experimental results demonstrate that the proposed method outperforms supervised baselines and reduces manual proofreading time by 33.4%. The source code is publicly available at https://github.com/HeadLiuYun/Probe-EM.

Inverse design of mechanical metamaterials seeks a periodic unit cell whose homogenized elastic properties meet a prescribed target, but current learning-based methods are data-hungry, mostly interpolative, and provide no guarantee that the generated design satisfies the specification. We introduce CertMix, a data-efficient framework that represents each exemplar unit cell as a small periodic neural implicit field, specifically a SIREN signed-distance decoder overfit from a shared anchor, so that exemplar weight vectors become aligned and directly comparable. The key observation is that, in this aligned weight space, the homogenized elasticity tensor is approximately linear in the mixing coefficients. Targeted design therefore reduces to a small constrained affine-mixing problem solved with a differentiable periodic homogenizer in the loop. Negative coefficients enable extrapolation beyond the exemplar range, a linearity-mismatch trust region keeps blends valid, and split-conformal calibration converts the mismatch signal into a distribution-free certificate on achieved-property error. From as few as 50 exemplars, CertMix attains a scaled property error of $10^{-4}$, roughly two to three orders of magnitude below conditional generative baselines trained on 1000 cells. It remains accurate far outside the exemplar range, is $57\times$ faster than per-target topology optimization while avoiding checkerboards and enclosed voids, and extends to spatially graded fields, 3D triply periodic surfaces, and a certified running-shoe midsole application.

Cardiac cine Magnetic Resonance Imaging (MRI) is a critical diagnostic tool that provides dynamic insights for radiologists. To accelerate acquisition, under-sampled k-space data is often used, requiring reconstruction methods that combine coil sensitivity encoding with prior information to recover missing data. Deep learning approaches have gained more attention for leveraging data-adaptive priors. While supervised learning approaches are a common choice, they depend on fully sampled reference data, which is not always available. Unsupervised methods eliminate the need for fully sampled reference data, which can be advantageous in cardiac cine MRI reconstruction. Among them, implicit neural representations (INRs) have shown great potential due to their simple architecture and good quality reconstructions. In this work, we propose an image-domain dual-branch INR framework, termed I-FP-INR, which extends the original INR design by introducing an additional feature-processing branch. This design aims to extract complementary feature embeddings to enhance the overall representation, thereby benefiting reconstruction. Extensive evaluations on both public datasets and in-house data show consistent improvements over baseline methods in reconstruction quality, with strong robustness across varied scenarios.

Standard machine learning training presents data as discrete endpoint pairs, omitting the structure of the space between them. This paper introduces Transition Information Density (TID) -- the information content recoverable from structured intermediate states between categorically distinct training endpoints -- and Positional Identity, the defined location of an intermediate state on the A-to-B continuum. Both constructs are grounded in three empirical contexts: grapheme-color synesthesia, the Synesthesia Grid (a boundary-contour morphing algorithm instantiating TID in visual morphological space), and a four-condition training experiment across four representational mediums. Probes trained on structured interpolation at defined Positional Identities (C3) exhibit substantially lower intrinsic dimensionality than volume-matched controls (C2) in Phonetic/Linguistic (C3: 3.33 vs. C2: 10.81) and Semantic Description (C3: 4.59 vs. C2: 8.67) mediums. Visual and cross-modal mediums do not show this effect, establishing a modality boundary condition. A fixed-N=50 comparison confirms that Positional Identity structure, not sample count, drives the effect. Resolution N scales monotonically with representational richness. Pooled TwoNN analysis reveals globally collapsed representations in visual space (0.075) and globally consistent representations in phonetic space (0.977). The paper contributes a formal definition of TID and Positional Identity, a nine-metric shape characterization framework, and a four-condition experimental design isolating trajectory structure, data volume, and Positional Identity as distinct factors.

The rapid advancements in using neural networks as implicit data representations have attracted significant interest in developing machine learning methods that analyze and process the weight spaces of other neural networks. However, efficiently handling these highdimensional weight spaces remains challenging. Existing methods often overlook the sequential nature of layer-by-layer processing in neural network inference. In this work, we propose a novel approach using dynamic graphs to represent neural network parameters, capturing the temporal dynamics of inference. Our Dynamic Neural Graph Encoder (DNG-Encoder) processes these graphs, preserving the sequential nature of neural processing. Additionally, we also leverage DNG-Encoder to develop INR2JLS (Implicit Neural Representation to Joint Latent Space) for facilitate downstream applications, such as classifying Implicit Neural Representations (INRs). Our approach demonstrates significant improvements across multiple tasks, surpassing the state-of-the-art INR classification accuracy by approximately 10% on the CIFAR-100-INR.

Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint. However, as existing INRs for unstructured volumes do not encode geometry, they require partial mesh storage for later sampling, limiting achievable compression. At the same time, novel view synthesis methods have shown that explicit collections of 3D Gaussians can be used to accurately visualize volume data. In this work, we introduce an explicit model for volume data compression based on 3D Gaussian primitives. We reinterpret collections of 3D Gaussians as an explicit representation of a scalar field and use a sampling strategy that reconstructs scalar values at spatial locations through weighted aggregation of intersecting Gaussians. We develop optimized CUDA-accelerated pipelines for structured and unstructured model sampling, loss functions that encourage accurate domain encoding by our models, and a novel sampling-error based densification strategy. Our explicit formulation naturally encodes domain geometry, eliminating the need for mesh storage in unstructured volumes and introducing significantly higher compression opportunities. Compared to existing INRs, we demonstrate that our explicit model achieves competitive reconstruction quality with significant training speedups on structured volumes, while markedly outperforming in all metrics on unstructured volumes.

Implicit neural representations (INRs) are well suited to cardiac motion estimation, providing continuous, compact representations of motion fields. However, fitting an INR to each image sequence is time-consuming and sensitive to the optimisation trajectory. Learned priors can help guide optimisation towards plausible motion fields and enable faster adaptation, but learning priors for cardiac motion INRs remains under-explored. In this work, we compare four strategies for learning cardiac motion priors, including a population prior learned by joint optimisation, a consensus prior obtained by weight averaging, auto-decoders, and meta-learning. Using short-axis tagged cardiac magnetic resonance images from the UK Biobank, we evaluate their impact on tracking accuracy, motion behaviour, and adaptation trajectory. All learned priors substantially improved early adaptation performance compared with random initialisation. While the simple consensus prior was effective, auto-decoders recovered large deformations faster during early adaptation. Meta-learning achieved strong early performance and maintained the best adaptation trajectory over 50 iterations.

Diffusion MRI probes brain microstructure with particular sensitivity to early cerebrovascular and neurodegenerative changes. Neurite Orientation Dispersion and Density Imaging (NODDI) decomposes the diffusion signal into three biophysically interpretable maps: neurite density index (NDI), orientation dispersion index (ODI), and free water fraction (FWF), capturing neurite packing, fiber coherence, and extracellular fluid. These 3D maps offer a rich substrate for transferable microstructural representations, yet integrating them is challenging: standard representation learning struggles to disentangle the unique information in each map from their shared and synergistic interactions. We present BrainFIBRE, the first foundation model for brain microstructure, pretrained on NODDI-derived maps from 55,592 UK Biobank participants. We propose Self-supervised Partial Information Decomposition (SPID), which extends PID-guided multimodal learning to the self-supervised regime for the first time. A novel Counterfactual Candidate Construction (CCC) paradigm perturbs inter-modality alignment through modality dropping and swapping, providing the contrastive signal for a Mixture-of-Experts architecture to disentangle unique, synergistic, and redundant information without any downstream label. On both Caucasian and Asian cohorts, BrainFIBRE achieves state-of-the-art performance across diverse tasks predicting age, sex, cerebrovascular and neurodegenerative markers, and cognition, while yielding neurobiologically interpretable representations that reveal task- and cohort-specific interaction patterns. BrainFIBRE establishes a versatile foundation for neuroimaging analysis at the microstructural level.

Mechanistic interpretability has produced a rich inventory of component-level analyses that characterise what neural-network components encode and how they interact. Their outputs, however, are not easily reusable: selectivity tables, circuit diagrams, and feature lists remain locked in per-study notebooks - non-composable, not queryable in natural language, and not directly actionable for downstream audit or intervention. We study the representation layer that sits between these analyses and downstream use as a bottleneck that can be evaluated independently, and introduce Manifestation Units, a typed tuple protocol (E, S, R, D, G) extended with attention-head primitives (T) for transformer architectures, organising per-component statistics into structured fields populated automatically and queried through hybrid retrieval. Instantiated across generative vision (beta-VAE), discriminative vision (CNN), and language (GPT-2), the protocol supports two findings: typed structure substantially outperforms unstructured baselines on retrieval, and CNN filters retrieved by the schema satisfy causal sufficiency and necessity criteria under matched-budget controls. The schema absorbs attention-head primitives without modification, set-recovers known IOI circuit members under retrieval-budget-matched controls, and reveals an irreducible two-field core (S+R) with remaining fields either redundant or actively interfering. We present this as schema infrastructure for mechanistic interpretability rather than frontier-scale validation.

Artificial intelligence is transforming our capability to solve biological challenges. In dimensionality bottleneck regimes exacerbated by high-dimensional biological data, neural networks force distinct concepts into the lower dimensions known as superposition. Although this superposition is widely known to hinder interpretability, its impact on corrupting the geometry of latent spaces remains critically overlooked. Here, we utilized sparse autoencoders (SAEs) trained on over 100,000 multiplexed images of patient-derived Parkinson's disease and healthy neurons to resolve superposition. This approach bypasses the mathematical non-uniqueness of feature attribution by shifting to interpretable latent representation analysis. We theoretically and empirically demonstrate that superposition contaminates representational metric spaces, and thereby SAEs successfully recover geometric fidelity. By treating these geometrically purified representations as single-cell state vectors, we adapted single-cell RNA sequencing (scRNA-seq) data analysis methodologies directly to the image domain. Finally, we introduce GW-map, utilizing Gromov-Wasserstein optimal transport to align these image representations with authentic scRNA-seq data de novo. This coupling reconstructs hierarchical neuronal pathology pathways such as Calcium-AIS scaffold, without reference spatial transcriptomics, establishing a scalable foundation for spatial biology. Code is available at https://github.com/jijihihi/Bio\_superposition

Interactive video generation systems for camera-controlled world exploration roll out growing sequences of latent video frames, entangling state transition with high-frequency observation synthesis. We propose Walking in the Implicit, a scene-centric paradigm that changes the rollout variable from frame latents to a fixed-length, renderable implicit state, termed Neural Implicit Scene (NIS). This factorizes interactive generation into stochastic transition of a compact scene state and deterministic pose-conditioned rendering given the sampled state. We instantiate this paradigm as NeuWorld: a transformer VAE learns locally anchored NIS from sparse posed frames, and a diffusion transformer evolves NIS conditioned on future camera trajectories and geometry-aware retrieved history. By reusing the VAE encoder as a unified conditioner, NeuWorld maps camera, reference-image, and history cues into the same NIS modality, avoiding external heterogeneous encoders. Trained from scratch on public posed-view data without pretrained video backbones or auxiliary 3D reconstructors, NeuWorld achieves strong long-horizon consistency with favorable inference efficiency.

Trial-to-trial variability limits how reliably neural population geometry can be estimated, while comparisons across populations depend on neuron and trial counts, response quality, and clustered sampling. We quantified within-session geometric reliability using Shesha, the Spearman correlation between representational dissimilarity matrices estimated from independent trial subsets, in all 39 Steinmetz Neuropixels sessions and in olfactory bulb and piriform cortex recordings from Bolding and Franks. Steinmetz analyses matched neurons and repetitions, compared observed reliability with a stationary residual-bootstrap expectation, and used mouse-level or mouse-clustered inference. Mean matched reliability was 0.0402 across 312 area-by-session recordings. Regional differences and reliability above the stationary benchmark did not survive correction. Temporal effects received the strongest support: interleaving early and late trials increased reliability relative to blocked allocation ($Δ=0.02666$, $q=0.001953$), and RDM similarity declined with within-session lag (mean mouse-level slope $=-0.01912$, $q=0.001953$; $n=10$ mice). Outer-cross-fitted reliability was not associated with choice-direction coupling or stimulus or response-direction decoding after correction. Olfactory comparisons remained descriptive because few paired sessions and no animal identities were available. In held-out simulations, associative recurrence outperformed feedforward subspace denoising but not divisive normalization. Representational geometry became less reproducible with temporal separation within a session, and comparisons across neural populations require sampling calibration and independent inference.

Periodic Implicit Neural Representations (INRs) such as SIREN and FINER assign every neuron, the same global frequency, spending the representational budget inefficiently when local signal content varies. We introduce FiRe (Frequency Reparameterization), that accelerates optimization by reparameterizing per-neuron frequency of periodic INRs without changing their underlying activation function. FiRe gives each neuron a bounded, input-dependent frequency via a separate low-rank gating path and is applicable to any periodic activation function. The gate acts as an implicit preconditioner that improves optimization conditioning at initialization via the Neural Tangent Kernel (NTK). This better-conditioned initialization makes optimization converge faster, and the high-frequency content of the reconstruction tracks the target more closely at a fixed computational budget. On 2D image fitting, FiRe increases PSNR over a parameter-matched baseline (up to +1 dB at short training budgets), with gains that vary with resolution and diminish at full convergence. We characterize how performance depends on resolution, rank, and training budget, and give an NTK account that predicts these trends.

Implicit neural representations (INRs) have recently emerged as a promising approach to video compression, delivering competitive rate-distortion performance alongside rapid decoding. However, existing neural video codecs struggle to balance complexity and scalability. Lightweight models often suffer from degraded compression performance when scaled to different bitrate/quality levels, whereas high-performance models exhibit limited scalability, as their model complexity typically increases with quality. This lack of a unified architecture capable of maintaining consistent complexity across a wide range of bitrates severely limits their diverse real-world deployment. To address these challenges, we introduce NVRC++, a novel INR-based video codec that utilizes a lightweight INR with multiple high-resolution feature grids, providing high scalability at any given complexity level. This is paired with an optimization framework that enables efficient overfitting on high-resolution grids for long video sequences, thereby exploiting spatio-temporal redundancies without prohibitive computational or memory overhead. Additionally, an advanced entropy model is designed for efficiently compressing the high-dimensional grid parameters. As a result, NVRC++ provides four complexity levels (from 7kMACs/pixel to 360kMACs/pixel), each spanning wide bitrate and quality ranges while supporting real-time decoding. The experimental results show that NVRC++ offers a much faster decoding speed (up to 7.6x) compared to the SOTA INR-based video codec, NVRC, while delivering comparable performance.