Implicit Neural Representations

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.

Implicit Neural Representations (INRs) parameterized by multilayer perceptrons excel at modeling continuous signals. However, a key challenge persists as INRs fundamentally suffer from spectral bias and information cross-talk. When a single network attempts to capture multi-scale phenomena, high-frequency weight updates destructively interfere with the underlying low-frequency structural approximation. We introduce Scale and Learn INR (ScaLe-INR), a novel multi-branch architecture that resolves these limitations by explicitly matching the signal's frequency spectrum with the optimal operating region of the INR. Drawing upon the Fourier inverse scaling theorem we demonstrate that applying directional coordinate scaling expands a network's representational bandwidth along specific spatial axes. To mathematically enforce functional disentanglement and minimize task-specific information leakage between branches, we propose a Directional Edge Guidance Loss, a spatially-conditioned sparsity prior derived from ground-truth gradients. By constraining the high-frequency branches to act as strict, localized edge-filters, ScaLe-INR eliminates spectral cross-talk, accelerates convergence, and achieves high-fidelity signal reconstruction on complex multi-scale topologies. We evaluate ScaLe-INR across diverse reconstruction and inverse tasks, demonstrating substantial performance gains over existing state-of-the-art (SOTA) methods. The proposed architecture improves upon the nearest baselines by +5.16 dB in image reconstruction and +0.65 dB in image denoising. Furthermore, it achieve an impressive figure of 50.02 dB on audio reconstruction and 0.999 IOU(Intersection Over Union) on 3D reconstruction which beats the all SOTA models.

Implicit neural representation (INR) has emerged as a powerful prior for multi-dimensional data (e.g., multispectral images and videos). However, most INR methods employing periodic activation functions (e.g., Sine) predominantly rely on function composition. This mechanism introduces optimization instability as network depth increases, thereby limiting their performance. Meanwhile, these methods fail to incorporate proper physical priors to effectively alleviate spectrum bias. To address these issues, inspired by the commonalities between deep periodic networks and generalized Fourier series, we propose a novel Calibrated Harmonic Overlaid Implicit Neural Representation (CHOIR). Specifically, we utilize Coordinated Harmonic Superposition (CHS) to replace the conventional function composition used in most INRs, thereby ensuring optimization stability when scaling network depth. Furthermore, we introduce a Perceptual Spectrum Calibration (PSC) to mitigate spectrum bias. This calibration embeds the ubiquitous power-law spectrum prior of natural images and adjusts the globally fixed spectrum towards a physically plausible log-uniform distribution. Extensive experiments on various multidimensional data recovery problems demonstrate that our method achieves superior performance over state-of-the-art approaches. Code is available at https://github.com/chorl0229/CHOIR.

Implicit Neural Representation (INR) provides an effective approach for continuous signal modeling, but classical per-pixel inference results in quadratic growth in inference count, leading to dramatically increased computational costs in high-resolution application scenarios. To address this issue, we propose a patch-based approach that treats non-overlapping patches as fundamental processing units and predicts entire pixel patches in a single forward pass, significantly reducing the number of inference queries required. To validate the effectiveness of our approach, we propose a hardware acceleration architecture on the Field Programmable Gate Array (FPGA) platform for the INR model, which features a configurable pipeline and supports dual-precision computation. Our patch-based INR achieves comparable reconstruction quality to pixel-level INR (34.97 dB PSNR with 2 x 2 patches) while reducing inference latency by 75% with only 0.6% parameter overhead.

What is the geometry of a visual percept? The most widely used protocols for decomposing neural network representations into interpretable parts treat concepts as isolated directions, yet recent work shows that concepts are often realized as geometric structures in low dimensional regions of activation space. We turn to the literature of Structured sparsity to close this gap, and show that block sparsity, which groups directions into blocks, is the prior matched to a generative model in which a representation is a sparse sum of low-dimensional manifolds: the modern, learned form of a classical idea in visual neuroscience, where a visual feature is carried by a coordinated group of neurons rather than a single tuned one. We implement three variants of block-sparse featurizers (BSFs) and, through a minimum-description-length analysis, show that all three describe activations more compactly than direction-based featurizers, with the recovered concepts typically two- to four-dimensional. We then use BSFs to (i) recontextualize prior work, showing that curve detectors in InceptionV1 actually read from a single continuous curve manifold, (ii) discover novel manifolds including shadows and lighting in DINOv3, and (iii) support interpretable control of image generation in diffusion models (SDXL) via manifold steering.

Geographic implicit neural representations (INRs) learn to map any coordinate on Earth to a location embedding, implicitly encoding geospatial data into the weights of a neural network. Location embeddings are widely used off the shelf as general-purpose geospatial representations, yet users lack principled tools to audit what geographic or semantic information these embeddings capture. In this work, we analyze the information content of geographic INRs through their location embeddings. We decompose these embeddings into human-interpretable features$\unicode{x2014}$namely, (i) sparse latent concepts, (ii) natural language concepts, and (iii) visual features. The latent concept embeddings are learned using sparse autoencoders. To recover natural language concepts, we apply sparse linear concept embeddings (SpLiCE) over a predefined geospatial dictionary. Finally, visual features are extracted using saliency maps derived from CLIP Surgery. We show that location embeddings can be decomposed into human-interpretable representations while retaining high reconstruction capability, revealing interpretable geographic structures such as forests, deserts, and urban features. Across methods, sparse decompositions expose systematic differences in encoded information, ranging from urban structures to broader biome and climate signals, and pretraining-space saliency maps further highlight complementary features such as roads and landmarks. We hope this work provides a first step toward interpretable geospatial representations.

Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias. Existing attempts to resolve this trade-off introduce computational overhead or tuning frailty. We propose to model each neuron's activation as the steady-state response of a sinusoidally-forced damped harmonic oscillator, whose amplitude naturally governs the network's spectral selectivity during training. By jointly optimising the oscillator parameters alongside the network weights, our method adapts to the target signal's spectral content without explicit regularisation. Initialised in the stopband, the network exhibits a coarse-to-fine learning curriculum that progressively expands its spectral gate, capturing low-frequency structures first and high-frequency details only when justified by the reconstruction objective. Comprehensive experiments show that our approach consistently achieves state-of-the-art or competitive results against established INRs, while requiring no task-specific tuning of any hyperparameters.

Implicit Neural Representations (INRs) have recently emerged as a promising paradigm for image compression, offering a fundamentally different approach from traditional and learned codecs. Nevertheless, INR-based methods for image compression suffer from long encoding times and a consistent performance gap in classic quality metrics such as PSNR. In this work, we explore the potential of purely INR-based compression methods and we propose PaaF (Picture as a Function), a novel INR-based image codec that introduces improved architectural design, adaptive quantization, and an efficient entropy coding scheme. These components are designed to enhance rate-distortion performance while preserving the simplicity and parallelizability of INR-based decoding. Experimental results demonstrate consistent improvements over existing INR-based methods in both quantitative metrics and perceptual quality. These findings highlight the potential of INR-based approaches and contribute to narrowing the gap between functional representations and more established compression paradigms.

Deep neural networks (DNNs) exhibit attractive performance in various fields but often suffer from low interpretability. The neural additive model (NAM) and its variant called the neural basis model (NBM) use neural networks (NNs) as nonlinear shape functions in generalized additive models (GAMs). Both models are highly interpretable and exhibit good performance and flexibility for NN training. NAM and NBM can provide and visualize the contribution of each feature to the prediction owing to GAM-based architectures. However, when using two-input NNs to consider feature interactions or when applying them to high-dimensional datasets, training NAM and NBM becomes intractable due to the increase in the computational resources required. This paper proposes incorporating the feature selection mechanism into NAM and NBM to resolve computational bottlenecks. We introduce the feature selection layer in both models and update the selection weights during training. Our method is simple and can reduce computational costs and model sizes compared to vanilla NAM and NBM. In addition, it enables us to use two-input NNs even in high-dimensional datasets and capture feature interactions. We demonstrate that the proposed models are computationally efficient compared to vanilla NAM and NBM, and they exhibit better or comparable performance with state-of-the-art GAMs.

Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules. NeSyCat, extending ULLER, subsumes them under a single inductive definition of truth, parametric in a strong monad and an aggregation structure on truth-values. NeSyCat has so far lacked an account of predicates and functions learned by neural networks. We provide NeSyCat Torch as the missing link and interpret computational symbols via neural networks, implementing the framework in probabilistic programming and tensor-based backends. We use the distribution monad for reference semantics and metric evaluation, and complement it by a monad for numerically stable, differentiable training: the lazy log-tensor monad over the log-semiring. For efficient training in batches, we furthermore employ a batch monad. The axioms are the source code: written once in monad-based do-notation, monadic bind performs marginalisation, lazily pruning unneeded branches. On MNIST addition, our HaskTorch, JAX, and PyTorch implementations outperform LTN and DeepProbLog in speed and accuracy, while achieving nearly the accuracy of DeepStochLog. However, unlike DeepStochLog, we stay in a uniform framework that applies to many first-order NeSy approaches. Namely, the construction is parametric in the monad; instantiating it with, e.g., the Giry monad extends the approach to continuous probability (working out a neural representation here is left for future work).

One of the major difficulties in the mechanistic interpretability of neural networks is the occurrence of polysemanticity, which suggests that each neuron is typically responsible for multiple different tasks, impeding a clean interpretation of their function. The seminal paper of Elhage et al. (2022) argues that this occurs due to superposition, a phenomenon where the neural network represents distinct features as non-orthogonal directions in a lower-dimensional space, a strategy that allows much greater compression of the data without sacrificing fidelity due to the feature sparsity of input vectors. Elhage et al. (2022) empirically validates these hypotheses in a rather natural and simple autoencoder with sparse inputs. The contribution of the present work is to analyze the mathematical basis for the occurrence and optimality of superposition, while rigorously corroborating some of their findings. In particular, we provide upper and lower bounds for the L2 reconstruction loss, tight in the very sparse regime, for power activation functions. A short list of interesting open problems are also included at the end.

Oppenheim and Lim (1981) showed that natural images stay recognizable when reconstructed from their Fourier phase alone, while the magnitude carries little of their identity. We ask whether trained image classifiers reproduce this asymmetry inside their hidden layers, and we test it causally: given two images, we transplant the phase of one onto the magnitude of the other at a chosen layer and record which image the prediction follows. In PRISM2D, GFNet, and ViT-B/16 the prediction follows the phase or sign donor, and deleting all image-specific magnitude barely moves accuracy, so identity rides on phase while image-specific magnitude is largely dispensable to the readout. ResNet-50 at first seems to break the pattern, because transplanting sign after its ReLUs does nothing; a fair intervention before the ReLU reveals a strong latent sign code in the late blocks, and a DC-only control shows the readout consumes a channel-wise spatial average. Controls rule out the trivial case in which magnitude simply stops depending on the image. The architectures therefore share a phase/sign identity code but expose it in different bases, set by rectification and readout geometry, which gives a mechanistic account of the texture--shape gap between CNNs and attention models.

We study policy representation learning from unlabeled multi-policy behavioral data. Each episode is generated by a fixed policy, but policy labels are unavailable. This setting appears in robotics play, demonstrations, games, racing, and other datasets where heterogeneous behaviors are mixed without annotations. We introduce \emph{Behavioral INR}, a self-supervised generative model that adapts implicit neural representations (INRs) from vision to behavior. Instead of mapping coordinates to RGB values, Behavioral INR represents a policy as a state-action function mapping states to subsequent actions. An episode-level latent modulates this function through FiLM layers, yielding a generative prior over policies and allowing policy identity to be inferred without supervision. Because INRs treat each datapoint as samples from an underlying function, the same model naturally accommodates variable episode lengths and different sampling granularities, as in vision INRs with different image resolutions. We also define policy-level out-of-distribution (OOD) shifts along state-distribution and action-distribution axes, which arise when policies overlap in states or actions but are not captured by standard behavioral OOD settings based only on new agents or environments. We evaluate on synthetic Gaussian random field data, MuJoCo demonstrations with controlled OOD splits, and real-world chess, Formula 1 racing, robotics, and Seek-Avoid datasets. Behavioral INR most consistently improves policy identifiability in the hardest continuous state-action settings, especially when longer episodes, more policies, and OOD splits reduce the usefulness of marginal shortcuts; amortized history encoders remain competitive when policy identity can be recovered from symbolic repetition or low-dimensional action statistics. We release code and checkpoints.

Transformer models are increasingly used as computational models of cognition and neural representation, so the mechanism implemented by self-attention is of interest beyond engineering performance. A complementary tradition in cognitive science models coordination, binding, and memory through dynamical interactions such as oscillator synchrony; we bring this mechanism into self-attention by introducing the Kuramoto Attention layer, whose value update is a synchronization step. Each token carries a bank of phase oscillators, so its hidden state lives on a high-dimensional torus. The attention weights form an adaptive coupling graph, and using the raw phase states as values makes the value update exactly the Kuramoto coupling direction for fixed attention weights. The softmax selects which oscillators couple, while the value path moves each token toward the attention-weighted circular mean of the tokens it selects. We train Kuramoto Attention on enwiki8 and CodeParrot against parameter-matched RoPE and SwiGLU transformers. At 5M parameters on CodeParrot, it improves on the transformer by both median and mean, with mean gaps of 0.012 validation and 0.010 test bits per byte. At 5M on enwiki8, all six runs have lower validation/test medians than the transformer and all-seed means within 0.01 BPC; five of six also form a tight lower-mean cluster. At 1M, it trails by about 0.02 BPC on enwiki8 and by 0.013-0.015 bits per byte on CodeParrot. Ablations and phase diagnostics show how the layer's synchronization and geometry-motivated components shape model performance. The result is a self-attention mechanism whose learned computation can be read directly as adaptive synchronization on phase states.

Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations. However, owing to the reliance on frequency truncation to maintain learning efficiency of FNOs, empirical studies suggest that FNOs exhibit spectral bias toward low-frequency information, which may hinder the learning capability especially for certain PDEs with strong high-frequency oscillations. To address this limitation, we propose SirenFNO, a novel framework that leverages sinusoidal representation networks (SIRENs) to learn implicit neural representations and performs mode-wise kernel parameterization. Our SIREN parameterization learns a full-grid spectrum with a constant and discretization-independent parameter count, thereby eliminating the need for frequency truncation. We further extend SirenFNO with functional tensor decompositions to enhance parameter and learning efficiency. Empirical results show that our SirenFNO consistently outperforms FNO with approximately $4$ to $15$ times parameter reductions with preserved discretization invariance, and our functional decomposition variants obtain performance improvements with a maximum of $73$ times fewer parameters across multiple PDE benchmarks.

Accelerated acquisition of fMRI enables enhanced detection of neurovascular (BOLD) activity in the brain, but image reconstruction becomes challenging with high k-space undersampling: Task-evoked BOLD signals are small in magnitude, which traditional anatomical MRI reconstruction methods fail to recover, as they favor spatial accuracy over temporal fidelity. We present DD-INR, a Dynamics-Driven Implicit Neural Representation framework tailored for accelerated fMRI that benefits from incoherent time-varying sampling and a tailored spatiotemporal prior, outperforming traditional methods, demonstrated in simulation and in-vivo acquisition, both in terms of image quality and retrieval of activation patterns. DD-INR achieves this by splitting the fMRI data into a static background and a temporally varying dynamic component, representing only the dynamics with a dedicated INR, thereby focusing the model's capacity on activation-relevant changes while remaining compact. In general, DD-INR provides a promising framework for accelerated fMRI reconstruction, with the potential to improve the sensitivity and robustness of fMRI studies within practical scan time limits. The source code is available at https://github.com/JoosenLi/DD-INR.

Many stages of the robotic lifecycle, from morphology synthesis to operation, rely fundamentally on the reachable workspace. However, current methods for approximating workspaces are slow, imprecise, or tied to a single morphology. We introduce Reachability Across Morphologies (RAM): a morphology-conditioned, implicit neural representation that acts as a fast, differentiable surrogate for pose reachability, generalising to unseen morphologies while inherently accounting for self-collisions. To train RAM, we publish a large-scale dataset of $3\cdot10^{10}$ samples generated solely from forward kinematics. Experiments show that our model achieves an $F_1$-score of $86\%$ at nanosecond inference, outperforming the baseline by $14\%$ while reducing inference time by three orders of magnitude. We further demonstrate speed-ups of one and two orders of magnitude for gradient-based morphology and trajectory optimisation, respectively. Website: https://timwalter.github.io/ram.

While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a layerwise non-uniform training mechanism: downstream classifier weights are driven by dense cross-entropy gradients into a rank-2 equiangular configuration before upstream embeddings fully reorganize, and once this classifier plane forms, backpropagated feature gradients constrain embedding motion to the same plane while weight decay suppresses orthogonal components. Second, after this subspace locking, the induced in-plane dynamics admit an entropy-regularized transport interpretation on $S^1$; combined with modular-addition labels, this reduces embedding formation to phase alignment, whose minimizers are single-frequency characters of $\mathbb{Z}/P\mathbb{Z}$ and hence equal-angle points on a circle. Third, we quantify why this solution prevails over NC: a simplex ETF gains only an $O(1)$ advantage in cross-entropy, whereas the cyclic rank-2 solution enjoys a $Θ(K)$ advantage under Schatten or weight-decay surrogates, yielding a critical threshold $λ_{\mathrm{crit}} = Θ(1/K)$. Our results explain both why classifier weights move first and why embeddings subsequently align with them, showing that grokking on modular arithmetic is governed not by maximal separation alone but by a task-structured trade-off between separation, symmetry, and complexity.

Neural networks build representations through affine maps and nonlinear activations. Injective affine maps preserve linear separability, raising the problem of how they prepare data for nonlinear improvement and how much gain can be guaranteed before complete separation. We introduce the directional linear separability measure (D-LSM), which quantifies unavoidable competing-sample intrusion over affine halfspaces retaining every target sample, characterize its supporting geometry, and prove invariance under injective affine embeddings. For gated activations including ReLU, GELU, and SiLU, pre-activation projection bounds yield sufficient conditions for preserving all previous exclusions and recovering additional samples, with a gain bound determined by the certified recovery count. Under an aggregate-tube condition, an explicit affine construction realizes recovery with sufficient width, scaling conditions, and simultaneous multiclass guarantees through a shared layer. Exact controlled experiments compare certified and realized gains, assess certificate coverage, and exhibit bound attainment before complete separation and in affine-tube constructions. In learned Vision Transformer (ViT) representations, a feasible lower-bound estimator yields earlier post-GELU saturation certificates of exact separability, while boundary transport numerically supports affine invariance.

Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solution suites for heat, viscous Burgers, and focusing cubic NLS. The analytic tests use independent-seed random controls, while the PDE benchmarks use alternate same-family source controls and auxiliary ablations. Across settings, transfer magnitude and transfer specificity separate clearly. In a 10-seed controlled 1D geometric test, Fourier Features show the largest structured transfer ($33.1\times$), followed by SIREN ($23.0\times$) and ReLU ($10.7\times$), but ReLU is far more selective: random-control transfer is $0.41\times$ for ReLU versus $14.24\times$ for SIREN. On a controlled two-parameter 1D family, the ranking changes: ReLU gives the clearest structured-versus-control separation at default settings, whereas Fourier Features improve only after bandwidth retuning. In Navier--Stokes and the broader 1D PDE suite, no single architecture dominates every equation, yet the same pattern remains: SIREN often reuses weights broadly, whereas ReLU and, in some equations, Fourier Features are more source-selective. Static diagnostics remain weak, and the heuristic scaling law $A_{\text{transfer}} \propto 1/Δt^2$ is rejected in the implemented 1D audit. These results position transfer specificity as a useful diagnostic for coordinate networks and suggest that architecture selection in scientific machine learning should be evaluated under explicit control conditions, not by transfer magnitude alone.

Existing implicit neural representation (INR) approaches suffer from stochastic initialization that does not guarantee consistent or high-quality performance across runs, with variations reaching more than 2.5 dB (~78%) in image regression. This variation is problematic for scientific computing and simulation, where result reproducibility is crucial. To address this problem, we present Jacobi-Anger Sinusoidal Representation Network (JA-SIREN), a deterministic initialization scheme for sinusoidal networks grounded in classical spectral analysis. By computing the Discrete Sine Transform (DST) of the target signal and leveraging the Jacobi-Anger expansion, we derive closed-form weights for a two-layer sinusoidal MLP that analytically match the network's initial spectral response to the target signal, requiring no random seed or additional hyperparameter tuning. On the Kodak dataset, JA-SIREN achieves a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline. This is achieved with zero run-to-run variance, confirming that spectrally-informed initialization is a more effective and reproducible alternative to stochastic initialization for sinusoidal INRs.

Cone-beam computed tomography (CBCT) frequently suffers from data truncation, which introduces severe artifacts and limits the effective field of view (FOV). Existing deep learning methods for truncated cone-beam computed tomography (CBCT) reconstruction suffer from serious limitations, including a strict reliance on supervised ground truth and a failure to account for continuous 3D spatial truncation variations. To address these challenges, we introduce a self-supervised 3D reconstruction framework based on neural scene representations. By directly mapping spatial coordinates to radiodensity under projection supervision, our approach inherently bypasses traditional filtering and backprojection operations, thereby fundamentally eliminating truncation-induced ring artifacts while enabling robust continuous 3D data extrapolation. However, coordinate networks are susceptible to an inherent spectral bias, which leads to a severe loss of clinically vital high-frequency textures. To resolve this bottleneck, we further incorporate a physics-based iterative refinement module into the neural scene representation architecture. Leveraging the artifact-free, extrapolated volume from the coordinate network as an optimal initialization, this module progressively re-extracts and injects high-frequency structural information from the original projections back into the volume. Extensive experiments on both simulated and real-world datasets demonstrate that our method successfully unifies the exceptional artifact suppression and extrapolation capabilities of neural networks with the high-fidelity detail preservation of iterative algorithms.

Catastrophic forgetting is commonly interpreted as the irreversible erasure of previously acquired knowledge during sequential learning. In this work, we investigate an alternative perspective: that forgetting may arise not from complete destruction of task representations but from a loss of accessibility to preserved information. We introduce a three-level framework separating knowledge storage, representation, and accessibility, and evaluate each component through a series of continual-learning experiments on sequential CIFAR-100 classification using ResNet-18. Our analysis combines checkpoint persistence, linear probing, representation geometry, classifier-reset recovery, and layer-wise recoverability experiments. We observe complete behavioral forgetting of earlier tasks, with task accuracy collapsing from 54.8% to 0%, while linear probe performance retains approximately 76% of the original representational information. Furthermore, retraining only the final classifier restores 75.7% of the original task performance without modifying the backbone network. Layer-wise analysis reveals that early and intermediate layers preserve highly recoverable task information despite severe degradation at later stages. Projection-energy and principal-angle analyses indicate that retained knowledge persists as distributed high-dimensional representations rather than through preservation of a small dominant subspace. These findings suggest that catastrophic forgetting is better characterized as an accessibility failure than complete representational erasure, and that substantial task-relevant information remains embedded within neural representations even after functional forgetting has occurred.

The ability to train spiking neural networks is essential for modeling biological neural networks as well as for neuromorphic computing. However, for the extensively used leaky integrate-and-fire (LIF) neurons, arbitrarily small parameter changes can induce spike (dis)appearances that disrupt subsequent activity, leading to unstable neural representations and permanently silent neurons during exact spike-based gradient descent. Recent work shows that a class of neuron models, which includes the quadratic integrate-and-fire (QIF) neuron, avoids these discontinuities and enables continuous and even smooth spike-based gradient descent. However, it remains unclear whether these advantages translate into practice. Here, we demonstrate that they do so via a controlled comparison between networks of LIF and QIF neurons on the popular Spiking Heidelberg Digits dataset. Specifically, in a first step, we perform a thorough hyperparameter search to optimize both models, revealing a clear performance advantage of QIF neurons. In a second step, we visualize the loss and gradient landscapes. Consistent with their inferior performance, we find that the loss landscapes of LIF neurons, which are discontinuous, appear more fragmented and the related gradients more erratic. An analysis of the landscapes of single samples indicates that these features arise from changes in the temporal order of spikes, which often cause disruptive spike (dis)appearances. Overall, our results advocate replacing LIF neurons with neuron models exhibiting continuous spiking dynamics, such as QIF neurons, for gradient descent training.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict $g_1 \star g_2$ for elements of a finite group $G$. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

Neural algorithmic reasoning has emerged as a popular research direction. It aims to train neural networks to mimic the step-by-step behavior of classical rule-based algorithms. More specifically, the execution of such algorithms can be abstracted as a sequence of states, where each state represents the intermediate outcome after an execution step. The training objective is to generate state sequences that replicate the underlying algorithmic process. A common framework for this task adopts an encoder-processor-decoder architecture, where the encoder learns representations of states, the processor simulates algorithmic steps, and the decoder reconstructs output states. While prior work has focused on improving the processor, the role of the encoder in representation learning has received little attention. Most methods rely on simple MLP encoders, raising the question of whether such representations are sufficiently informative for supporting algorithmic reasoning. This paper investigates how to improve encoder representations for neural algorithmic reasoning. We propose a reconstruction module that aims to recover the input state from its encoded representation. This auxiliary reconstruction task encourages the encoder to retain critical information about the input. We demonstrate that incorporating this task during training improves the performance of existing neural architectures on standard benchmarks. Furthermore, we observe that current encoders often underutilize the correlations among features within a state. To address this, we draw inspiration from self-supervised learning and design an enhanced variant of the auxiliary task that encourages the encoder to capture intra-state feature dependencies. Experimental results show that our method enables the encoder to learn richer representations, thereby enhancing the performance of existing processors on algorithmic reasoning tasks.

Implicit neural representations (INRs) model a signal as a continuous coordinate-to-value function. For terrain elevation data, this supports analytic derivatives, arbitrary-resolution decoding, and a smooth surface model of the underlying heightfield. However, fitting and storing a separate INR for every tile does not scale to large terrain datasets. Amortized neural representations reduce this cost with a shared network: a new tile is mapped to a compact per-tile payload, and a shared decoder reconstructs the heightfield from it. Most such methods are hypernetworks that predict the payload in a single forward pass, while others recover it through a short per-tile optimization. These methods were developed primarily for natural images, and their suitability for terrain heightfields remains unclear. We introduce a controlled benchmark on a 1 m/pixel terrain dataset and evaluate three representative methods under a unified protocol. Observing a clear cross-domain gap, we propose HUVR+SIREN, a hypernetwork that adapts the strongest benchmarked method (HUVR) by replacing its coordinate decoder with a smooth, analytically differentiable one. It attains the best height and derivative fidelity on the benchmark with no additional per-tile storage and lower decode cost, and tolerates aggressive post-training quantization with negligible quality loss, giving a compact terrain neural format. Ablations and diagnostics further identify which design choices transfer to terrain and show that the per-tile bottleneck is already near its useful limit, leaving the remaining gap in the shared hypernetwork's architectural design.

Undersampled magnetic resonance imaging (MRI) reconstruction seeks to recover temporally or contrast-varying image series from incomplete multicoil k-space data while preserving state-dependent fidelity for dynamic and quantitative MRI (qMRI). Existing scan-specific implicit neural representations (INRs) often use monolithic spatiotemporal coordinate fields, explicit subspaces, motion or deformation models, calibration variables, or sequence-specific quantitative signal models. These design choices can limit flexibility in sharing spatial information while adapting image synthesis across acquisition states. Moreover, many INR-based baselines remain computationally demanding, typically requiring per-scan optimization times on the order of hundreds to thousands of seconds. We propose MoE-dqINR, a scan-specific multicoil MRI reconstruction framework that factorizes the image-domain representation into shared spatial experts and a state-conditioned routing pathway. Spatial experts encode reusable coordinate-dependent image content, whereas routing weights, conditioned on ordered acquisition states, synthesize each dynamic frame or contrast state from a common expert bank. The representation is coupled to a multicoil MRI forward model, uses the normalized state index to drive routing in both dynamic and quantitative MRI. By separating shared spatial representation from state-dependent synthesis, the framework provides an image-first architecture for dynamic and quantitative MRI while reducing scan-specific INR optimization to approximately 30 s per scan in our experiments. The proposed formulation establishes state-conditioned mixture-of-experts INR as a scan-specific multicoil MRI reconstruction prior that unifies shared spatial representation, dynamic- and qMRI-specific synthesis, and practical per-scan efficiency.

Random, untrained neural networks consistently match or exceed trained networks in representational similarity to early visual cortex. This puzzling finding challenges the assumption that learning improves brain alignment. We investigate it by tracking representational similarity analysis (RSA) alignment to human fMRI data across training for four learning rules: backpropagation (BP), feedback alignment (FA), predictive coding (PC), and spike-timing-dependent plasticity (STDP). Using 720 object images from the THINGS database and fMRI data from three subjects across six visual ROIs, we measure Spearman correlations between model and brain representational dissimilarity matrices at eight training checkpoints (epochs 0-40). We find that (1) a single epoch of training reduces V1 alignment by 25-90%, depending on the learning rule; (2) backpropagation reduces V1 alignment most severely (delta r = -0.080), while predictive coding and STDP preserve substantially more (delta r ~ -0.04); and (3) a weaker, opposite tendency appears in object-selective cortex (LOC), where BP shows the largest increase in alignment during training, although the absolute change is small. These results suggest that untrained architectures capture low-level visual statistics through inductive biases alone, and that global error signals (BP) reshape early representations more aggressively than local learning rules (PC, STDP), which better preserve brain-like structure.

Large language models (LLMs) have emerged as powerful representation learners whose internal features increasingly align with human cognition. We study whether modern LLMs can serve as a lens for understanding neural representations in the human brain, focusing on emotional valence in EEG. We first build a one-dimensional valence direction, the V-axis, from modern LLMs using only nine emotion-evocative sentences. We validate it through zero-shot transfer to sentiment benchmarks and cross-model consistency across fourteen LLMs. We then show that this LLM-derived direction maps onto human neural activity. On a public EEG cohort of 123 subjects watching affective videos, a single linear projection on EEG features tracks the V-axis position of each stimulus. Moreover, 36 EEG emotion classifiers trained without exposure to the V-axis spontaneously rediscover the same direction in their internal representations, suggesting that the same valence structure emerges in both language models and human electrophysiology. Yet this convergence does not provide an effective training signal. We test twenty-five alignment strategies, including knowledge distillation, representational similarity, contrastive, and topographic losses; none improve decoding, and sixteen significantly reduce accuracy. We formalize this result as the saturation regularity: once task labels alone drive a brain-decoding network onto the target direction, additional supervision mainly distorts an already-saturated basin, while the load-bearing within-class residual receives little useful gradient. This regularity also indicates where improvement should come from: the residual subspace unreachable by supervision. Motivated by this insight, we ensemble across residual diversity rather than supervising the basin, improving balanced accuracy by 10.5% over the prior best on FACED, with the same effect replicated on SEED-V.

Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of reconstruction. We show that this reconstruction step is unnecessary; under mild conditions, compact-set universality on the model input space transfers to the data space whenever the embedding from data to input is continuous and injective. Guided by this result, and building on the rectilinear control path for Neural Controlled Differential Equations (NCDEs), we introduce a continuous and injective embedding for Log-NCDEs, a universal class of continuous-time models. Our approach records observations as increments and composes them over arbitrary query intervals to directly form log-signatures. This provides interval-level summaries without first interpolating the observed variables, while supporting online computation. Experiments on synthetic controlled dynamics and real-world time-series datasets show that the representation is accurate, efficient, and robust to irregular, asynchronous, and sparse observations.

Modeling the interplay between external stimuli and internal neural representations is a pivotal research area for Brain-Computer Interfaces (BCIs). A major limitation of prior work is the prevailing paradigm of specialized, single-task models, which curtails versatility and neglects inter-task synergies. To address this, we propose Mind-Omni, the first versatile framework that unifies seven distinct encoding and decoding tasks through a discrete diffusion paradigm. At its core is a novel Brain Tokenizer that transforms heterogeneous, continuous brain signals into standardized, discrete tokens. This enables direct, token-level interactions for mutual understanding and generation between any two or more modalities within a shared semantic space. To unlock advanced reasoning capabilities, we further curate a specialized Brain Question Answering (BQA) instruction-tuning dataset. Our model not only establishes a new state-of-the-art among multi-task unified frameworks but also provides strong evidence for multi-task synergy. By demonstrating performance competitive with, and at times superior to, larger specialized models, our work offers a powerful new paradigm for neural modeling and paves the way for foundation models of neural activity. The code is publicly available at https://github.com/ReedOnePeck/Mind-Omni.

Understanding how cortical activity represents natural whole-body behaviors in primates remains challenging. Limited by the diversity of movements and inaccessibility of large-scale neural representation of whole-body kinematics, previous motor decoding studies focused on constrained tasks and limited limb movements. Here, we present a neural-behavioral recording and modeling framework for freely moving monkeys, combining large-scale epidural cortical signals from distributed sensory- and motor-related areas with synchronized multi-view motion capture through a custom-made data collection platform. We reconstructed whole-body monkey kinematics and learned a compact behavior prior using an autoregressive encoder-decoder model. Conditioned on neural signals, the model decoded accurate and realistic whole-body movement without explicit physical constraints. Our results provide a novel proof-of-concept approach for decoding natural whole-body movements in primates using large-scale intracranial neural activity.

GeRaF is the first method to use neural implicit learning for near-range 3D geometry reconstruction from radio frequency (RF) signals. Unlike RGB or LiDAR-based methods, RF sensing can see through occlusion but suffers from low resolution and noise due to its lensless imaging nature. While lenses in RGB imaging constrain sampling to 1D rays, RF signals propagate through the entire space, introducing significant noise and leading to cubic complexity in volumetric rendering. Moreover, RF signals interact with surfaces via specular reflections, requiring fundamentally different modeling. To address these challenges, GeRaF (1) introduces filter-based rendering to suppress irrelevant signals, (2) implements a physics-based RF volumetric rendering pipeline, and (3) proposes a novel lensless sampling and lensless alpha blending strategy that makes full-space sampling feasible during training. By learning signed distance functions, reflectiveness, and signal power through MLPs and trainable parameters, GeRaF takes the first step towards reconstructing millimeter-level geometry from RF signals in real-world settings.

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Implicit neural representations have emerged as a promising paradigm for video compression, with recent methods achieving competitive performance on natural video. However, screen content video -- common in remote desktop, online education, and cloud gaming -- exhibits distinct statistics: sharp edges, limited color palettes, and strong temporal redundancy. Existing neural representation methods, designed for natural scenes, lack mechanisms to exploit these properties, leaving substantial room for improvement. In this paper, we propose NeR-SC, a neural representation framework tailored for screen content video. Building on the SNeRV backbone, NeR-SC introduces three screen-content-specific modules: (i) a learnable color palette that models the discrete color structure of screen content by restricting the low-frequency sub-band to a learned color set; (ii) a multi-gate dense fusion module that replaces sequential feature fusion with dense, attention-gated cross-stage interaction; and (iii) an embedding-level frame skip strategy that bypasses redundant decoder invocations for static frames, with zero training overhead. Experiments on DSCVC and VCD show that NeR-SC achieves 40.32dB and 41.73dB average PSNR, outperforming representative neural video representation methods and, at low bitrates, surpassing H.264 and H.265. The skip strategy enables real-time decoding with no loss in quality.

A panoramic X-ray compresses a 3D jaw into a 2D strip; we aim to recover the missing depth cleanly and fast. Existing implicit neural representations render realistic volumes but are slow to train, sensitive to sampling and positional encodings, and costly in practice. Pure CNN baselines are efficient yet struggle with the dental arch's long-range geometry, blur fine enamel-dentin boundaries, and offer little interpretability. We present K-U-KAN, a three-stage pipeline that (i) lifts 2D features into depth-aware observables with Kolmogorov-Arnold Networks, (ii) advances these observables by a stable, phase-aware linear evolution via a Koopman token block, and (iii) places the predicted depth bins onto focal-trough rays before a lightweight 3D attention U-KAN refines the volume. This marriage of physics (Beer-Lambert image formation), geometry (horseshoe focal trough), and learned linear dynamics yields sharp anatomy, fewer artifacts, and robust behavior on native radiographic intensities with batch size one. On held-out data, K-U-KAN matches transformer/implicit baselines on signal and structure metrics, clearly improves perceptual quality, and trains in roughly half the time-making single-view PX $\to$ CBCT reconstruction more practical for clinical pipelines.

Current fMRI decoders face a performance-fidelity trade-off where efficient ID encoders outperform geometrically faithful surface-based models. We argue this is partly driven by inefficient surface tokenization and the failure to use anatomy as a predictive signal. We present NeurIPS, a framework that improves surface-based decoding by reframing anatomical variation from a nuisance to a powerful inductive prior. NeurIPS unites two innovations: a Selective ROI Spherical Tokenizer (SRST) for efficient geometric encoding, and a Structure-Guided Mixture of Experts (SG-MoE) that explicitly models individual anatomy using cortical features. On the Natural Scenes Dataset, NeurIPS establishes a new state-of-the-art for surface decoders and achieves performance comparable to strong 1D baselines. This is achieved with unprecedented efficiency, as the model converges dramatically faster (10 vs. 600 epochs). This efficiency enables rapid adaptation to new subjects using only 20% of data and ensures robust scalability as the training cohort is expanded. Ablations provide causal evidence that these gains are driven by the model's use of cortical features, not by memorizing subject IDs. By leveraging anatomical priors, NeurIPS provides a principled and scalable path toward robust, generalizable brain decoding.

Visual decoding from brain signals is a key challenge at the intersection of computer vision and neuroscience, requiring methods that bridge neural representations and computational models of vision. We introduce a tri-modal contrastive framework for EEG-based visual decoding that aligns EEG, visual, and textual representations within a unified latent space. Our approach follows a two-stage design. First, we pre-train an EEG encoder via masked reconstruction on unlabeled trials, learning spatio-temporal regularities that transfer robustly to downstream tasks. Second, we jointly align EEG, image, and LLM-generated textual descriptions through contrastive learning, where text supervision acts as a semantic regularizer that injects linguistic structure into the shared space without overwhelming the primary EEG-image signal. The encoder integrates subject-specific adaptation, graph-attention over channels, and temporal-spatial convolutional embeddings. On the Things-EEG2 200-way zero-shot benchmark, our framework achieves 54.1% Top-1 and 83.4% Top-5 accuracy, substantially exceeding the strongest prior baseline (32.4% / 64.0%), with paired Wilcoxon tests confirming significance (p < 0.01) over all in-subject baselines. We validate generalization on Things-MEG. Analysis reveals that compact embedding geometries (CN-CLIP) outperform much larger backbones, and that decoding aligns with established neurophysiology of visual processing. This work is a critical step towards robust, semantically-grounded visual decoding from non-invasive temporal neural signals. The source code is publicly available in https://github.com/anon-eeg/eeg_image_decoding.

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

The Thousand Brains Theory (TBT) and its open-source Monty framework model object recognition through sensorimotor inference -- identifying objects by actively moving a sensor across their surface and building evidence contact by contact. The current implementation encodes each contact as a dense floating-point vector. While Monty tracks inter-step displacement and accumulates evidence across contacts, it treats the feature activation pattern at each contact as an unordered set - the directional sequence in which features are encountered carries no representational weight. In TBT, the sequence of contacts carries spatial meaning: knowing that feature A was felt before feature B during a left-to-right sweep tells you something about where A and B sit on the object. Dense vectors discard this ordering. We propose replacing dense vectors with rank-order spike packets: each contact produces a brief burst of neural events where the most strongly activated neuron fires first. The time gap between successive bursts implicitly encodes sensor displacement without explicit coordinate calculations. A biologically motivated learning rule (STDP) encodes traversal direction into synaptic weights. A learnable parameter lambda adjusts reliance on earlier versus recent contacts, adapting to each object's geometry. We derive three testable predictions and specify an implementation of four components in approximately 450 lines of NumPy. Three synthetic experiments confirm the core claims: temporal coding achieves perfect discrimination accuracy on objects with identical features in different spatial arrangements, where dense accumulation performs at chance; temporal coding maintains a 30-50 percentage point advantage across all tested noise levels; the adaptive lambda converges to distinct values, reflecting object geometric complexity. End-to-end evaluation on Monty's YCB benchmark is left for future work.

What can representational similarity matrices (RSMs) tell us about a neural code? As the popularity of these summary statistics grows, so too does the need for a more complete characterization of their properties. Here, we show that symmetries in network inputs can confound RSM-based analyses. Stimulus symmetries render many representations functionally equivalent, but these different configurations can lead to different RSMs. These different RSMs reflect qualitatively different representational geometries. We show that stochastic gradient descent or energetic regularization can generate sparse, drifting codes, leading in turn to drifting RSMs. Moreover, we demonstrate that these phenomena are present in networks trained to encode image data, where the symmetry is latent. Our results illustrate the challenges inherent in comparing nonlinear neural codes, when functionally-equivalent representations are not related by a simple rotation.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

Functional MRI data exhibit high-dimensional spatiotemporal structure, making both prediction and decoding challenging. In this work, we investigate neural integral-operator-based models for encoding and decoding tasks in fMRI, with particular emphasis on the role of nonlocal spatiotemporal context. We implement a latent neural integral operator framework that performs fixed point iterations in an auxiliary space from which classification and stimuli prediction is performed via a decoder. We evaluate our model on two open-source fMRI datasets. Our experiments examine both decoding of stimuli from fMRI recordings and encoding of fMRI dynamics from stimulus representations. A main focus is the effect of spatiotemporal context: we systematically compare short and long temporal windows, as well as the use of visual cortex vs whole brain recordings, and analyze their influence on performance and latent-space geometry. Across tasks and datasets, larger temporal windows generally improve results and produce more structured learned representations. In decoding experiments, the learned latent space often provides clearer class separation than the raw data. In encoding experiments, although absolute performance remains moderate due to the difficulty of the task, longer temporal windows still yield consistent gains. These findings suggest that neural integral operators provide a promising framework for modeling fMRI dynamics and that broader spatiotemporal context can be beneficial for both prediction and representation learning. More broadly, the results indicate that exploiting distributed nonlocal structure in brain dynamics requires model architectures specifically designed to capture such dependencies.

We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss function, and can operate on different momentum meshes, enabling evaluating the representability conditions across multiple meshes, which we call interpolated representability condition. The framework can be used either to predict 2-RDMs on large momentum meshes by interpolating exact results from small meshes, or as a variational 2-RDM ansatz optimized by energy minimization on arbitrary meshes. We apply this approach to the fractional Chern insulator in the one-band projected model of twisted bilayer MoTe$_2$ at twist angle $3.89^\circ$ and hole filling $2/3$. Trained on exact-diagonalization (ED) 2-RDMs from meshes with $12$ or $18$ momentum points using six different NN architectures, the best NN is the residual multilayer perceptron, which predicts the $6\times6$ 2-RDM with $97.07\%-98.18\%$ accuracy relative to the ED 2-RDM but predicts an energy $77.353$ meV above ED ground-state energy. We then variationally optimize the NN on several meshes including $6\times6$, predicting a $6\times 6$ energy of just $0.104$ meV below ED while maintaining $98.94\%-98.96\%$ accuracy. Compared with the conventional boundary-point semidefinite programming, which gives an energy $5.560$ meV below ED with $96.40\%-98.94\%$ accuracy, the NN achieves a more accurate energy and similar accuracy while using only less than 1/20 as many parameters. Eventually, we add a symmetric mesh of $48$ momentum points to the variational optimization of the NN, and provide a prediction of the many-body ground-state energy and the many-body quantum metric on that mesh.

3D Lookup Tables (3D LUTs) are widely used for color mapping, but their grid-based representation requires discretizing the RGB space, leading to a capacity-memory trade-off that becomes prohibitive when storing large numbers of LUTs. Recent approaches adopt implicit neural representations to improve scalability, yet their black-box nature limits interpretability and hinders intuitive, localized editing. In this paper, we propose Gaussian LUT (GLUT), a continuous and explicit color representation that models color transformations using a set of learnable 3D Gaussian primitives. By avoiding fixed-resolution grids, GLUT achieves flexible representational capacity while maintaining a compact memory footprint. Its explicit, spatially localized formulation further enables both accurate modeling and interpretability. Building on this representation, we introduce a compact conditional generator (CGLUT) that predicts GLUT parameters for multiple LUT instances, encoding diverse color styles in a single framework to enable smooth and controllable LUT style blending. Moreover, GLUT supports efficient, user-friendly editing by allowing localized adjustments to specific color regions without global retraining. Experimental results demonstrate that our approach outperforms prior neural LUT representations in both accuracy and efficiency, while offering improved interpretability and interactive control.

Biological visual systems learn from limited experience, unlike deep learning models that rely on millions of training images. What learning principles make this possible? We tested whether efficient coding, the idea that neural representations capture the statistical structure of natural inputs, can build a hierarchy of human-aligned visual features from limited data. We developed an unsupervised learning procedure in which each layer of a deep network compresses its inputs onto the dominant modes of variation in natural images, using only local statistics and no labels, tasks, or backpropagation. This unsupervised procedure yields features that progress from edges and colors to textures and shapes. The features of this deep efficient coding model are readily recognized by human observers and are predictive of image-evoked fMRI responses in human visual cortex. Furthermore, a hybrid learning procedure that combines efficient coding with supervised fine-tuning yields better brain alignment in low-data settings and more rapid category learning. These findings suggest that efficient coding may shape representations across the entire visual hierarchy and help explain the data efficiency of biological vision.

Leveraging the universal representations of pre-trained LLMs and MLLMs offers a promising path toward brain foundation models. However, visually-evoked EEG datasets remain scarce, leading existing methods to align neural signals mainly with abstract text, a lossy translation that may discard fine-grained perceptual information encoded in brain activity. We propose Generative Visual Grounding (GVG), a framework that visualizes the invisible by using an EEG-to-image generative model as a visual translator. Instead of forcing EEG into text alone, GVG hallucinates instance-specific proxy images for non-visual EEG, providing structured visual contexts that allow MLLMs to exploit their visual priors for clinical-state interpretation. We validate this idea on two MLLM backbones, GVG-X-Omni and GVG-Janus. Image-only alignment is already competitive: the lightweight GVG-X-Omni matches 1.7B-parameter text-aligned baselines while tuning only 170M parameters on a frozen 7B backbone. We further extend GVG-Janus with trimodal Image+Text alignment, where text supplies categorical semantic anchors and visual proxies enrich neural representations with perceptual details. Experiments show consistent gains in EEG understanding and visual generation, suggesting visual proxy grounding as an effective complement to textual alignment.

A widespread assumption in local feature research holds that classical handcrafted descriptors are accuracy-limited relics best replaced by learned alternatives. We show this is wrong. Through an 8-configuration ablation spanning four benchmarks (HPatches, ROxford5K, IMC Phototourism, MegaDepth), we demonstrate that classical SIFT with DSP multi-scale pooling outperforms neural descriptor and orientation replacements (HardNet, OriNet) on every accuracy metric--while running 2--18$\times$ faster--and that learned matchers (LightGlue) complement rather than supersede classical features. The conclusion reframes a decade of work: not "replace SIFT" but "compose with SIFT," classical extraction paired with learned matching only where geometric context demands it. This finding was invisible because no prior GPU SIFT kept the complete pipeline in VRAM or offered modularity for controlled classical-vs-learned ablations. We present PySIFT, the first fully GPU-resident SIFT, implemented in CuPy/Numba CUDA kernels with DLPack zero-copy handoff to downstream DL frameworks--submillisecond O(1) metadata swap regardless of keypoint count. On a laptop-grade NVIDIA RTX 3050 (4 GB VRAM), PySIFT achieves: (i) higher Mean Matching Accuracy (MMA) than OpenCV SIFT on HPatches, (ii) 383 ms faster per pair on high-resolution MegaDepth, (iii) higher geometric accuracy on cross-dataset benchmarks (+5.6 pp AUC@10${}^\circ$ on MegaDepth, more inliers on IMC Phototourism), and (iv) bitwise deterministic output--identical keypoints and descriptors across runs, with detection reproducing identically even across GPU architectures: a guarantee that learned extractors cannot match without significant performance sacrifice, and cannot achieve at all across GPU architectures due to cuDNN's architecture-dependent algorithm selection. PySIFT is open-source, requiring no C++ compilation.

Learning meaningful latent representations from nonlinear fMRI data remains a fundamental challenge in neuroimaging analysis. Traditional independent component analysis, widely used due to its ability to estimate interpretable functional brain networks, relies on a linear mixing assumption for latent sources, limiting its ability to capture the inherently nonlinear and complex organization of brain dynamics. More recently, deep representation learning methods have emerged as promising alternatives for modeling nonlinear latent structure. However, many of these approaches have been evaluated primarily on simulated datasets or natural image benchmarks, with comparatively limited validation on real-world neuroimaging data such as fMRI. In this work, we are motivated by the $β$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the $β$-VAE framework for learning latent representations without introducing additional hyperparameters during training. We adapt and modify this model to fMRI data for nonlinear source disentanglement, aiming to separate mixed spatial and temporal brain signals into interpretable components. We show that the $β$-TCVAE framework can recover meaningful nonlinear spatial components with biological relevance, including well-established intrinsic connectivity networks such as the default mode network. Furthermore, we evaluate the learned representations using functional network connectivity, showing that the latent structure captures coherent and interpretable brain organization patterns. This study provides a pilot investigation that bridges nonlinear representation learning and fMRI analysis.

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations, incorporating tools from multi-view learning into this field for the first time. Our key technical observation is that a broad class of similarity measures based on representational similarity matrices (RSMs) admits a closed-form equivalent formulation in terms of row-stochastic Markov matrices, opening the door to manipulations from diffusion geometry. As a first application, we develop multi-scale variants of Centered Kernel Alignment and Distance Correlation, which utilise the $t^{th}$ power of the underlying transition matrix to probe the data geometry at adjustable diffusion scales. Going further, we introduce variants of these measures which fuse the Markov matrices of several layers via alternating diffusion into a single operator that captures the network's joint sample geometry, allowing similarity to be computed across multiple layers and shifting the comparison from layer-to-layer to network-to-network. We perform extensive numerical experiments, evaluating our measures on the Representational Similarity (ReSi) benchmark comprising 14 architectures trained on 7 datasets across three different domains. Our methods achieve SoTA results in accuracy and output correlation for both language and vision tasks across different models. We furthermore show SoTA performance on an additional benchmark evaluating on out-of-distribution data.

A central goal in understanding human vision is to uncover the visual features that drive neuronal activity. A growing body of work has used artificial neural networks as encoding models to predict cortical responses to natural images, revealing the visual content that activates category-selective regions. However, existing approaches are largely correlational and treat the encoder as a black box, leaving open which image features drive each voxel's response. We introduce Mechanistically Interpretable Neural Encoding (MINE), a framework that opens this black box by applying mechanistic-interpretability tools to localize the features within natural images that drive millimeter-scale (voxel-level) activity. MINE predicts each voxel's response using language-aligned image representations, and produces semantically interpretable descriptions of the features critical for the voxel's activation. We further generalize these per-image features into per-voxel functional profiles. To validate the per-image descriptions, we show they are sufficient to generate images that elicit voxel responses matching the responses to the original images, more accurately than images generated from random or low-attribution controls. Moreover, counterfactually inserting or removing the predicted features from images shifts activation in the expected direction, providing causal evidence. Counterfactual editing guided by the per-voxel activation profiles produces even stronger activation shifts, indicating that the profiles faithfully capture each voxel's selectivity. Finally, we apply MINE to well-studied category-selective brain regions, showing it recovers their known categorical preferences while revealing fine-grained unique voxel structure within each region. Overall, our results establish mechanistic interpretability as a path to discover and causally validate fine-grained hypotheses about neural function.

Data augmentation is widely recognized for improving generalization in deep networks, yet its impact on the geometry of learned representations remains poorly understood. In this work, we characterize how different data augmentation strategies reshape internal representations in neural networks. Using tools from shape analysis, we embed network hidden representations into a metric space where distance is invariant to scaling, translation, rotation and reflection. We show that increasing augmentation strength leads to well-behaved trajectories in this space, and that different augmentation types steer representations in distinct directions. Moreover, we investigate how neural representation shapes are distorted along data augmentation trajectories, and show that insights from neural geometry can predict which representations provide the most improvement when ensembling models. Our results reveal shared geometric patterns across architectures and seeds, and suggest that analyzing shape-space trajectories offers a principled tool for understanding and comparing data augmentation methods.

Recent advances in generative models have yielded impressive progress on motion in-betweening, allowing for more complex, varied, and realistic motion transitions. However, recent methods still exhibit noticeable limitations in preserving keyframe information and ensuring motion continuity. In this paper, we propose a novel pipeline and sampling optimization strategy for latent diffusion models (LDM) based on motion implicit neural representations (INR). By establishing a mapping between INR and sparse spatial or temporal information within latent diffusion, our model can sample the INR parameters from extremely sparse and ambiguous keyframe data and reconstruct plausible and smooth motions from the manifold. Our experiments demonstrate the superior performance of our model, which significantly improves motion generation quality in scenarios with few keyframes while ensuring both keyframe accuracy and diversity of in-between motions.

Implicit Neural Representations (INRs) model continuous signals using multilayer perceptrons (MLPs), enabling compact, differentiable, and high-fidelity representations of data across diverse domains. However, due to the low-frequency bias of MLPs that prevents effective learning of small details, the model's frequency must be carefully tuned through the embedding layer. Prior work established that this tuning can be performed before training based on the target signal, but it did not account for the significant effect of model depth, indicating that our understanding of the relationship between frequency and INR performance remains limited. To gain insights into this relationship, we utilize the Spectral Energy Centroid (SEC) metric that quantifies the frequency of target images and the spectral bias of INR models. We show that SEC is a versatile tool for INR analysis, demonstrating its utility across three tasks: (1) a data-driven strategy (SEC-Conf) for hyperparameter selection that outperforms existing heuristics and is robust to model depth, (2) a reliable proxy for signal complexity, and (3) effective alignment of spectral biases across diverse INR architectures.

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a representation should therefore be stable under the relevant representation symmetries rather than be tied to a particular basis. We study this group action in the tractable exact setting of the final readout layer, where equivalent realizations induce affine changes of hidden coordinates. The resulting symmetry principle singles out a unique hierarchy of shallow coordinate-stable probes, with linear probes as its degree-1 member. We also show that a natural object for cross-model probe transfer is a shared probe-visible quotient--the representation modulo directions invisible to the probe family--rather than the full hidden state. Experiments on synthetic and real-world tasks support both predictions, showing where degree-2 probes help beyond linear ones and how quotient-based transfer enables coverage-aware monitor portability across model families. These results point toward a broader geometric representation theory of neural probing, with coverage-aware monitor transfer as a concrete operational consequence.

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the Kantorovich dual and reformulate the associated c-transform as a proximal fixed-point problem. This yields a stable single-network framework in which dual feasibility is enforced exactly through proximal optimality conditions rather than adversarial training. Despite the inner fixed-point computation, gradients can be computed without differentiating through the fixed-point iterations, enabling efficient training without requiring implicit differentiation. We further establish convergence of stochastic gradient descent. The resulting framework is efficient, scalable, and broadly applicable: it simultaneously recovers forward and backward transport maps and naturally extends to class-conditional settings. Experiments on high-dimensional Gaussian benchmarks, physical datasets, and image translation tasks demonstrate strong transport accuracy together with improved training stability and favorable computational and memory efficiency.

Spatio-temporal fetal brain atlases are important for characterizing normative neurodevelopment and identifying congenital anomalies. However, existing atlas construction pipelines necessitate days for slice-to-volume reconstruction (SVR) to generate high-resolution 3D brain volumes and several additional days for iterative volume registration, thereby rendering atlas construction from large-scale cohorts prohibitively impractical. We address these limitations with INFANiTE, an Implicit Neural Representation (INR) framework for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI scans, bypassing both the costly SVR and the iterative non-rigid registration steps entirely, thereby substantially accelerating atlas construction. Extensive experiments demonstrate that INFANiTE outperforms existing baselines in subject consistency, reference fidelity, intrinsic quality and biological plausibility, even under challenging sparse-data settings. Additionally, INFANiTE reduces the end-to-end processing time (i.e., from raw scans to the final atlas) from days to hours compared to the traditional 3D volume-based pipeline (e.g., SyGN), facilitating large-scale population-level fetal brain analysis. Code: https://github.com/hu2274898/INFANiTE

Many downstream decisions in complex terrain require fast wind estimates at a small number of user-specified locations and heights for a given forecast valid time, rather than another dense forecast field on a fixed grid. We present WindINR, a latent-state implicit neural representation framework for continuous high-resolution local wind query and sparse-observation correction. WindINR maps static terrain descriptors, a low-resolution background field, and continuous query coordinates to a high-resolution wind state through a latent-conditioned decoder. To enable rapid inference-time correction, WindINR separates reusable representation learning from sample-specific latent-state correction. During training, a privileged encoder infers a reference latent state from high-resolution supervision, a deployable latent predictor estimates an initial latent state from inference-time inputs alone, and their discrepancies are summarized into a dataset-adaptive Gaussian prior over latent corrections. At inference time, within the WindINR module, network weights remain fixed and only the latent state is updated by minimizing a regularized correction objective using sparse observations and their uncertainty. In controlled OSSEs over the Senja region, including a UAV-aided approach scenario and random-observation robustness tests, WindINR improves local high-resolution wind estimates by updating only a compact latent state rather than the full network. The corrected representation remains continuously queryable at arbitrary coordinates and, in our CPU benchmark, yields about a $2.6\times$ online-correction speedup over full-network fine-tuning, suggesting a practical interface between kilometer-scale background products, sparse local observations, and wind queries in complex terrain.

Understanding the intricate mappings between visual stimuli and neural responses is a fundamental challenge in cognitive neuroscience. While current approaches predominantly align images and functional magnetic resonance imaging (fMRI) responses in Euclidean space, this geometry often struggles to preserve fine-grained semantic relationships and latent hierarchical structures across visual and neural modalities. To overcome this, we propose HyNeuralMap, a framework that employ hyperbolic Lorentz model to map visual semantics into a shared, cross-subject neural hierarchy. By leveraging the negative curvature of hyperbolic space as an inductive bias, the proposed framework better captures hierarchical semantic organization and cross-subject neural similarities. Specifically, visual and neural embeddings are jointly optimized through hyperbolic geometric alignment, where geodesic distances preserve semantic proximity and hierarchical relationships more effectively than Euclidean embeddings. Experiments demonstrate that HyNeuralMap consistently outperforms state-of-the-art Euclidean baselines in both multi-label semantic prediction and cross-modal retrieval tasks. This confirms hyperbolic geometry's superiority for cross-modal semantic alignment and hierarchical modeling, providing a new avenue for vision-neural representation learning.