Daily Papers

Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning method that places trainable low-rank adapters into frozen pre-trained models. Recent studies show that using fewer LoRA adapters may still maintain or even improve performance, but existing methods still distribute adapters broadly, leaving where to place a limited number of adapters to maximize performance largely open. To investigate this, we introduce PAGE (Projected Adapter Gradient Energy), a gradient-based sensitivity probe that estimates the initial trainable gradient energy available to each candidate LoRA adapter. Surprisingly, we find that PAGE is highly concentrated on a single shallow FFN down-projection across two model families and four downstream tasks. We term this module the dominant adaptation module and show that its layer index is architecture-dependent but task-stable. Motivated by this finding, we propose DomLoRA, a placement method that places a single adapter at the dominant adaptation module. With only 0.7\% of vanilla LoRA's trainable parameters, DomLoRA outperforms it on average across downstream tasks, including instruction following, mathematical reasoning, coding, and multi-turn conversation. This method also matches or improves other LoRA variants and reduces training time by up to 2.74times compared with broad placement, supporting the dominant adaptation module perspective as a practical placement guideline.

Fine-grained sparsity promises higher parametric capacity without proportional per-token compute, but often suffers from training instability, load balancing, and communication overhead. We introduce STEM (Scaling Transformers with Embedding Modules), a static, token-indexed approach that replaces the FFN up-projection with a layer-local embedding lookup while keeping the gate and down-projection dense. This removes runtime routing, enables CPU offload with asynchronous prefetch, and decouples capacity from both per-token FLOPs and cross-device communication. Empirically, STEM trains stably despite extreme sparsity. It improves downstream performance over dense baselines while reducing per-token FLOPs and parameter accesses (eliminating roughly one-third of FFN parameters). STEM learns embedding spaces with large angular spread which enhances its knowledge storage capacity. More interestingly, this enhanced knowledge capacity comes with better interpretability. The token-indexed nature of STEM embeddings allows simple ways to perform knowledge editing and knowledge injection in an interpretable manner without any intervention in the input text or additional computation. In addition, STEM strengthens long-context performance: as sequence length grows, more distinct parameters are activated, yielding practical test-time capacity scaling. Across 350M and 1B model scales, STEM delivers up to ~3--4% accuracy improvements overall, with notable gains on knowledge and reasoning-heavy benchmarks (ARC-Challenge, OpenBookQA, GSM8K, MMLU). Overall, STEM is an effective way of scaling parametric memory while providing better interpretability, better training stability and improved efficiency.

Federated Learning (FL) has gained popularity for fine-tuning large language models (LLMs) across multiple nodes, each with its own private data. While LoRA has been widely adopted for parameter efficient federated fine-tuning, recent theoretical and empirical studies highlight its suboptimal performance in the federated learning context. In response, we propose a novel, simple, and more effective parameter-efficient fine-tuning method that does not rely on LoRA. Our approach introduces a small multi-layer perceptron (MLP) layer between two existing MLP layers the up proj (the FFN projection layer following the self-attention module) and down proj within the feed forward network of the transformer block. This solution addresses the bottlenecks associated with LoRA in federated fine tuning and outperforms recent LoRA-based approaches, demonstrating superior performance for both language models and vision encoders.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input (physical) domain, which may be irregular, into a latent space with a uniform grid. The FNO model with the FFT is applied in the latent space. The resulting geo-FNO model has both the computation efficiency of FFT and the flexibility of handling arbitrary geometries. Our geo-FNO is also flexible in terms of its input formats, viz., point clouds, meshes, and design parameters are all valid inputs. We consider a variety of PDEs such as the Elasticity, Plasticity, Euler's, and Navier-Stokes equations, and both forward modeling and inverse design problems. Geo-FNO is 10^5 times faster than the standard numerical solvers and twice more accurate compared to direct interpolation on existing ML-based PDE solvers such as the standard FNO.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training expenses, and may not always achieve the desired accuracy required in many scientific and engineering disciplines. In this paper, we propose a new Spatiotemporal Fourier Neural Operator (SFNO) that learns maps between Bochner spaces, and a new learning framework to address these issues. This new paradigm leverages wisdom from traditional numerical PDE theory and techniques to refine the pipeline of commonly adopted end-to-end neural operator training and evaluations. Specifically, in the learning problems for the turbulent flow modeling by the Navier-Stokes Equations (NSE), the proposed architecture initiates the training with a few epochs for SFNO, concluding with the freezing of most model parameters. Then, the last linear spectral convolution layer is fine-tuned without the frequency truncation. The optimization uses a negative Sobolev norm for the first time as the loss in operator learning, defined through a reliable functional-type a posteriori error estimator whose evaluation is almost exact thanks to the Parseval identity. This design allows the neural operators to effectively tackle low-frequency errors while the relief of the de-aliasing filter addresses high-frequency errors. Numerical experiments on commonly used benchmarks for the 2D NSE demonstrate significant improvements in both computational efficiency and accuracy, compared to end-to-end evaluation and traditional numerical PDE solvers.

As large language models (LLMs) scale, the question is not only how large they become, but how much of their capacity is effectively utilized. Existing scaling laws relate model size to loss, yet overlook how components exploit their latent space. We study feed-forward networks (FFNs) and recast width selection as a spectral utilization problem. Using a lightweight diagnostic suite -- Hard Rank (participation ratio), Soft Rank (Shannon rank), Spectral Concentration, and the composite Spectral Utilization Index (SUI) -- we quantify how many latent directions are meaningfully activated across LLaMA, GPT-2, and nGPT families. Our key finding is an asymmetric spectral scaling law: soft rank follows an almost perfect power law with FFN width, while hard rank grows only sublinearly and with high variance. This asymmetry suggests that widening FFNs mostly adds low-energy tail directions, while dominant-mode subspaces saturate early. Moreover, at larger widths, variance further collapses into a narrow subspace, leaving much of the latent space under-utilized. These results recast FFN width selection as a principled trade-off between tail capacity and dominant-mode capacity, offering concrete guidance for inference-efficient LLM design.

Multi-vector dense retrieval methods like ColBERT systematically use a single-layer linear projection to reduce the dimensionality of individual vectors. In this study, we explore the implications of the MaxSim operator on the gradient flows of the training of multi-vector models and show that such a simple linear projection has inherent, if non-critical, limitations in this setting. We then discuss the theoretical improvements that could result from replacing this single-layer projection with well-studied alternative feedforward linear networks (FFN), such as deeper, non-linear FFN blocks, GLU blocks, and skip-connections, could alleviate these limitations. Through the design and systematic evaluation of alternate projection blocks, we show that better-designed final projections positively impact the downstream performance of ColBERT models. We highlight that many projection variants outperform the original linear projections, with the best-performing variants increasing average performance on a range of retrieval benchmarks across domains by over 2 NDCG@10 points. We then conduct further exploration on the individual parameters of these projections block in order to understand what drives this empirical performance, highlighting the particular importance of upscaled intermediate projections and residual connections. As part of these ablation studies, we show that numerous suboptimal projection variants still outperform the traditional single-layer projection across multiple benchmarks, confirming our hypothesis. Finally, we observe that this effect is consistent across random seeds, further confirming that replacing the linear layer of ColBERT models is a robust, drop-in upgrade.

Recent work on Neural Radiance Fields (NeRF) has demonstrated significant advances in high-quality view synthesis. A major limitation of NeRF is its low rendering efficiency due to the need for multiple network forwardings to render a single pixel. Existing methods to improve NeRF either reduce the number of required samples or optimize the implementation to accelerate the network forwarding. Despite these efforts, the problem of multiple sampling persists due to the intrinsic representation of radiance fields. In contrast, Neural Light Fields (NeLF) reduce the computation cost of NeRF by querying only one single network forwarding per pixel. To achieve a close visual quality to NeRF, existing NeLF methods require significantly larger network capacities which limits their rendering efficiency in practice. In this work, we propose a new representation called Neural Radiance Distribution Field (NeRDF) that targets efficient view synthesis in real-time. Specifically, we use a small network similar to NeRF while preserving the rendering speed with a single network forwarding per pixel as in NeLF. The key is to model the radiance distribution along each ray with frequency basis and predict frequency weights using the network. Pixel values are then computed via volume rendering on radiance distributions. Experiments show that our proposed method offers a better trade-off among speed, quality, and network size than existing methods: we achieve a ~254x speed-up over NeRF with similar network size, with only a marginal performance decline. Our project page is at yushuang-wu.github.io/NeRDF.

We present GRaF, Generalizable Radio-Frequency (RF) Radiance Fields, a framework that models RF signal propagation to synthesize spatial spectra at arbitrary transmitter or receiver locations, where each spectrum measures signal power across all surrounding directions at the receiver. Unlike state-of-the-art methods that adapt vanilla Neural Radiance Fields (NeRF) to the RF domain with scene-specific training, GRaF generalizes across scenes to synthesize spectra. To enable this, we prove an interpolation theory in the RF domain: the spatial spectrum from a transmitter can be approximated using spectra from geographically proximate transmitters. Building on this theory, GRaF comprises two components: (i) a geometry-aware Transformer encoder that captures spatial correlations from neighboring transmitters to learn a scene-independent latent RF radiance field, and (ii) a neural ray tracing algorithm that estimates spectrum reception at the receiver. Experimental results demonstrate that GRaF outperforms existing methods on single-scene benchmarks and achieves state-of-the-art performance on unseen scene layouts.

We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate na\"ive Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction.

We introduce NerVE, a unified eigenspectral framework for understanding how feed-forward networks (FFNs) in large language models (LLMs) organize and regulate information flow in high-dimensional latent space. Despite FFNs dominating the parameter budget, their high-dimensional dynamics remain poorly understood. NerVE addresses this gap through lightweight, memory-efficient tracking of eigenspectrum dynamics via four complementary metrics: Spectral Entropy (dispersion), Participation Ratio (effective dimensionality), Eigenvalue Early Enrichment (top-heaviness), and Jensen-Shannon divergence (distributional shifts). Our key insight is that FFN nonlinearities reinject variance across eigenmodes, fundamentally governing latent dimension utilization, and that optimizer geometry strongly modulates the extent of this variance reinjection. We validate NerVE across model scales, and diverse architectural and optimizer configurations, each uniquely shaping FFN dynamics: normalization schemes controlling variance flow; FFN weight geometries constraining latent space; positional encoding and activation functions regulating information flow; and optimizer choices redistributing effective capacity across depth. Across these settings, NerVE consistently recovers stable spectral signatures that correlate with model's generalization ability and respond predictably to design choices, generalizing beyond transformer to MLP-Mixer architectures, providing actionable insights for architectural and optimizer choices beyond trial-and-error.

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness compared to Convolutional Neural Networks (CNNs). This paper presents clear empirical evidence through spectral analysis to elucidate the superiority of FNO over CNNs: FNO is significantly more capable of learning low-frequencies. This empirical evidence also unveils FNO's distinct low-frequency bias, which limits FNO's effectiveness in learning high-frequency information from PDE data. To tackle this challenge, we introduce SpecBoost, an ensemble learning framework that employs multiple FNOs to better capture high-frequency information. Specifically, a secondary FNO is utilized to learn the overlooked high-frequency information from the prediction residual of the initial FNO. Experiments demonstrate that SpecBoost noticeably enhances FNO's prediction accuracy on diverse PDE applications, achieving an up to 71% improvement.

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations - separable spectral layers and improved residual connections - and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.

Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-DPS), combines an unconditional score-based diffusion prior, trained on high-fidelity simulations, with diffusion posterior sampling (DPS) conditioned on sparse observations and guided by a frozen neural operator. Naive integration reintroduces the surrogate's spectral bias; we resolve this with a closed-form, spectrally shaped guidance score that weights the surrogate by its frequency-dependent accuracy and needs no denoiser backpropagation. A distribution-free analysis bounds the approximation error across the frequency-diffusion-time plane and shows the guidance's frequency dependence is preserved regardless of distributional assumptions. On 3D elastic wavefield prediction at 5% and 2% sensor coverage, the method reaches near-zero spectral bias across all bands, where both the surrogate and sensor-only DPS show systematic high-frequency attenuation. Isotropic guidance, the natural baseline, improves pointwise accuracy but carries the bias into the posterior nearly intact, confirming that frequency-dependent calibration is essential, not merely beneficial. The framework needs only paired surrogate/reference data and exploits no problem-specific structure beyond the residual's approximate spectral diagonality, verifiable for new surrogates via the coherence diagnostic we provide.

Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS. Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines. The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill. This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Fourier PlenOctrees have shown to be an efficient representation for real-time rendering of dynamic Neural Radiance Fields (NeRF). Despite its many advantages, this method suffers from artifacts introduced by the involved compression when combining it with recent state-of-the-art techniques for training the static per-frame NeRF models. In this paper, we perform an in-depth analysis of these artifacts and leverage the resulting insights to propose an improved representation. In particular, we present a novel density encoding that adapts the Fourier-based compression to the characteristics of the transfer function used by the underlying volume rendering procedure and leads to a substantial reduction of artifacts in the dynamic model. Furthermore, we show an augmentation of the training data that relaxes the periodicity assumption of the compression. We demonstrate the effectiveness of our enhanced Fourier PlenOctrees in the scope of quantitative and qualitative evaluations on synthetic and real-world scenes.

Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals with a small number of parameters. However, existing INR models often fail to capture important frequency components specific to each task. To address this issue, in this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The proposed FKAN utilizes learnable activation functions modeled as Fourier series in the first layer to effectively control and learn the task-specific frequency components. In addition, the activation functions with learnable Fourier coefficients improve the ability of the network to capture complex patterns and details, which is beneficial for high-resolution and high-dimensional data. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) for the image representation task and intersection over union (IoU) for the 3D occupancy volume representation task, respectively.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4\%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

Transformer-based language models (LMs) are at the core of modern NLP, but their internal prediction construction process is opaque and largely not understood. In this work, we make a substantial step towards unveiling this underlying prediction process, by reverse-engineering the operation of the feed-forward network (FFN) layers, one of the building blocks of transformer models. We view the token representation as a changing distribution over the vocabulary, and the output from each FFN layer as an additive update to that distribution. Then, we analyze the FFN updates in the vocabulary space, showing that each update can be decomposed to sub-updates corresponding to single FFN parameter vectors, each promoting concepts that are often human-interpretable. We then leverage these findings for controlling LM predictions, where we reduce the toxicity of GPT2 by almost 50%, and for improving computation efficiency with a simple early exit rule, saving 20% of computation on average.

Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as subsurface models with salt bodies, exhibit strong scattering and phase sensitivity that challenge existing neural operators. We propose a hybrid architecture that decomposes the scattering operator into two separate contributions: a smooth background propagation and a high-contrast scattering correction. The smooth component is learned with a Fourier Neural Operator (FNO), which produces globally coupled feature tokens encoding background wave propagation; these tokens are then passed to a vision transformer, where attention is used to model the high-contrast scattering correction dominated by strong, spatial interactions. Evaluated on high-frequency Helmholtz problems with strong contrasts, the hybrid model achieves substantially improved phase and amplitude accuracy compared to standalone FNOs or transformers, with favorable accuracy-parameter scaling.

Precipitation nowcasting is critical for disaster mitigation and aviation safety. However, radar-only models frequently suffer from a lack of large-scale atmospheric context, leading to performance degradation at longer lead times. While integrating meteorological variables predicted by weather foundation models offers a potential remedy, existing architectures fail to reconcile the profound representational heterogeneities between radar imagery and meteorological data. To bridge this gap, we propose PW-FouCast, a novel frequency-domain fusion framework that leverages Pangu-Weather forecasts as spectral priors within a Fourier-based backbone. Our architecture introduces three key innovations: (i) Pangu-Weather-guided Frequency Modulation to align spectral magnitudes and phases with meteorological priors; (ii) Frequency Memory to correct phase discrepancies and preserve temporal evolution; and (iii) Inverted Frequency Attention to reconstruct high-frequency details typically lost in spectral filtering. Extensive experiments on the SEVIR and MeteoNet benchmarks demonstrate that PW-FouCast achieves state-of-the-art performance, effectively extending the reliable forecast horizon while maintaining structural fidelity. Our code is available at https://github.com/Onemissed/PW-FouCast.

Over the past few decades, extensive research has been devoted to the design of artificial reverberation algorithms aimed at emulating the room acoustics of physical environments. Despite significant advancements, automatic parameter tuning of delay-network models remains an open challenge. We introduce a novel method for finding the parameters of a Feedback Delay Network (FDN) such that its output renders target attributes of a measured room impulse response. The proposed approach involves the implementation of a differentiable FDN with trainable delay lines, which, for the first time, allows us to simultaneously learn each and every delay-network parameter via backpropagation. The iterative optimization process seeks to minimize a perceptually-motivated time-domain loss function incorporating differentiable terms accounting for energy decay and echo density. Through experimental validation, we show that the proposed method yields time-invariant frequency-independent FDNs capable of closely matching the desired acoustical characteristics, and outperforms existing methods based on genetic algorithms and analytical FDN design.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.

Dense Transformer language models have largely adhered to one consistent architectural shape: each layer consists of an attention module followed by a feed-forward network (FFN) with a narrow-wide-narrow MLP, allocating most parameters to the MLP at expansion ratios between 2 and 4. Motivated by recent results that residual wide-narrow-wide (hourglass) MLPs offer superior function approximation capabilities, we revisit the long-standing MLP shape convention in Transformer, challenging the necessity of the narrow-wide-narrow design. To study this, we develop a Transformer variant that replaces the conventional FFN with a deeper hourglass-shaped FFN, comprising a stack of hourglass sub-MLPs connected by residual pathways. We posit that a deeper but lighter hourglass FFN can serve as a competitive alternative to the conventional FFN, and that parameters saved by using a lighter hourglass FFN can be more effectively utilized, such as by enlarging model hidden dimensions under fixed budgets. We confirm these through empirical validations across model scales: hourglass FFNs outperform conventional FFNs up to 400M and achieve comparable performance at larger scales to 1B parameters; hourglass FFN variants with reduced FFN and increased attention parameters show consistent improvements over conventional configurations at matched budgets. Together, these findings shed new light on recent work and prompt a rethinking of the narrow-wide-narrow MLP convention and the balance between attention and FFN towards efficient and expressive modern language models.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

We introduce FFN Fusion, an architectural optimization technique that reduces sequential computation in large language models by identifying and exploiting natural opportunities for parallelization. Our key insight is that sequences of Feed-Forward Network (FFN) layers, particularly those remaining after the removal of specific attention layers, can often be parallelized with minimal accuracy impact. We develop a principled methodology for identifying and fusing such sequences, transforming them into parallel operations that significantly reduce inference latency while preserving model behavior. Applying these techniques to Llama-3.1-405B-Instruct, we create Llama-Nemotron-Ultra-253B-Base (Ultra-253B-Base), an efficient and soon-to-be publicly available model that achieves a 1.71X speedup in inference latency and 35X lower per-token cost while maintaining strong performance across benchmarks. Through extensive experiments on models from 49B to 253B parameters, we demonstrate that FFN Fusion becomes increasingly effective at larger scales and can complement existing optimization techniques like quantization and pruning. Most intriguingly, we find that even full transformer blocks containing both attention and FFN layers can sometimes be parallelized, suggesting new directions for neural architecture design.

Detecting small objects in UAV remote sensing images and identifying surface defects in industrial inspection remain difficult tasks. These applications face common obstacles: features are sparse and weak, backgrounds are cluttered, and object scales vary dramatically. Current transformer-based detectors, while powerful, struggle with three critical issues. First, features degrade severely as networks downsample progressively. Second, spatial convolutions cannot capture long-range dependencies effectively. Third, standard upsampling methods inflate feature maps unnecessarily. We introduce DFIR-DETR to tackle these problems through dynamic feature aggregation combined with frequency-domain processing. Our architecture builds on three novel components. The DCFA module uses dynamic K-sparse attention, cutting complexity from O(N2) down to O(NK), and employs spatial gated linear units for better nonlinear modeling. The DFPN module applies amplitude-normalized upsampling to prevent feature inflation and uses dual-path shuffle convolution to retain spatial details across scales. The FIRC3 module operates in the frequency domain, achieving global receptive fields without sacrificing efficiency. We tested our method extensively on NEU-DET and VisDrone datasets. Results show mAP50 scores of 92.9% and 51.6% respectively-both state-of-the-art. The model stays lightweight with just 11.7M parameters and 41.2 GFLOPs. Strong performance across two very different domains confirms that DFIR-DETR generalizes well and works effectively in resource-limited settings for cross-scene small object detection.

The quality of point clouds is often limited by noise introduced during their capture process. Consequently, a fundamental 3D vision task is the removal of noise, known as point cloud filtering or denoising. State-of-the-art learning based methods focus on training neural networks to infer filtered displacements and directly shift noisy points onto the underlying clean surfaces. In high noise conditions, they iterate the filtering process. However, this iterative filtering is only done at test time and is less effective at ensuring points converge quickly onto the clean surfaces. We propose IterativePFN (iterative point cloud filtering network), which consists of multiple IterationModules that model the true iterative filtering process internally, within a single network. We train our IterativePFN network using a novel loss function that utilizes an adaptive ground truth target at each iteration to capture the relationship between intermediate filtering results during training. This ensures that the filtered results converge faster to the clean surfaces. Our method is able to obtain better performance compared to state-of-the-art methods. The source code can be found at: https://github.com/ddsediri/IterativePFN.

Transformer, composed of self-attention and Feed-Forward Network, has revolutionized the landscape of network design across various vision tasks. FFN is a versatile operator seamlessly integrated into nearly all AI models to effectively harness rich representations. Recent works also show that FFN functions like key-value memories. Thus, akin to the query-key-value mechanism within self-attention, FFN can be viewed as a memory network, where the input serves as query and the two projection weights operate as keys and values, respectively. We hypothesize that the importance lies in query-key-value framework itself rather than in self-attention. To verify this, we propose converting self-attention into a more FFN-like efficient token mixer with only convolutions while retaining query-key-value framework, namely FFNification. Specifically, FFNification replaces query-key and attention coefficient-value interactions with large kernel convolutions and adopts GELU activation function instead of softmax. The derived token mixer, FFNified attention, serves as key-value memories for detecting locally distributed spatial patterns, and operates in the opposite dimension to the ConvNeXt block within each corresponding sub-operation of the query-key-value framework. Building upon the above two modules, we present a family of Fast-Forward Networks. Our FFNet achieves remarkable performance improvements over previous state-of-the-art methods across a wide range of tasks. The strong and general performance of our proposed method validates our hypothesis and leads us to introduce MetaMixer, a general mixer architecture that does not specify sub-operations within the query-key-value framework. We show that using only simple operations like convolution and GELU in the MetaMixer can achieve superior performance.

We introduce the Extender, a log-structured variant of the standard Transformer architecture. In a standard Transformer, each layer communicates with subsequent layers exclusively via the residual h, a superposition channel. The Extender adds a concatenation channel x: each layer ell emits both a residual update δ_ell which is added to h, and a much smaller extension ε_ell which is appended to x. While both the FFN and q see h, the attention kv projections take only x as input. As a result, the fully extended x contains the complete input for the kv projections of all layers, reducing the persistent attention memory footprint from 2Ld_{model} to sum|ε_ell|. We find that with |ε_ell|=32, the Extender matches Transformer accuracy on short-context (CORE) tasks at 199M-924M parameters, and exceeds Transformer accuracy on long-context (RULER) workloads, again at 924M parameters. For our 1664-wide, 924M model, the Extender's persistent attention memory footprint is 104times smaller than MHA. The memory savings grow with model width.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Vision-language foundation models (VLFMs) promise zero-shot and retrieval understanding for Earth observation. While operational satellite systems often lack full multi-spectral coverage, making RGB-only inference highly desirable for scalable deployment, the adoption of VLFMs for satellite imagery remains hindered by two factors: (1) multi-spectral inputs are informative but difficult to exploit consistently due to band redundancy and misalignment; and (2) CLIP-style text encoders limit semantic expressiveness and weaken fine-grained alignment. We present SATtxt, a spectrum-aware VLFM that operates with RGB inputs only at inference while retaining spectral cues learned during training. Our framework comprises two stages. First, Spectral Representation Distillation transfers spectral priors from a frozen multi-spectral teacher to an RGB student via a lightweight projector. Second, Spectrally Grounded Alignment with Instruction-Augmented LLMs bridges the distilled visual space and an expressive LLM embedding space. Across EuroSAT, BigEarthNet, and ForestNet, SATtxt improves zero-shot classification on average by 4.2%, retrieval by 5.9%, and linear probing by 2.7% over baselines, showing an efficient path toward spectrum-aware vision-language learning for Earth observation. Project page: https://ikhado.github.io/sattxt/

Fast feedforward networks (FFFs) are a class of neural networks that exploit the observation that different regions of the input space activate distinct subsets of neurons in wide networks. FFFs partition the input space into separate sections using a differentiable binary tree of neurons and during inference descend the binary tree in order to improve computational efficiency. Inspired by Mixture of Experts (MoE) research, we propose the incorporation of load balancing and Master Leaf techniques into the FFF architecture to improve performance and simplify the training process. We reproduce experiments found in literature and present results on FFF models enhanced using these techniques. The proposed architecture and training recipe achieves up to 16.3% and 3% absolute classification accuracy increase in training and test accuracy, respectively, compared to the original FFF architecture. Additionally, we observe a smaller variance in the results compared to those reported in prior research. These findings demonstrate the potential of integrating MoE-inspired techniques into FFFs for developing more accurate and efficient models.

Deep networks have achieved great success in image rescaling (IR) task that seeks to learn the optimal downscaled representations, i.e., low-resolution (LR) images, to reconstruct the original high-resolution (HR) images. Compared with super-resolution methods that consider a fixed downscaling scheme, e.g., bicubic, IR often achieves significantly better reconstruction performance thanks to the learned downscaled representations. This highlights the importance of a good downscaled representation in image reconstruction tasks. Existing IR methods mainly learn the downscaled representation by jointly optimizing the downscaling and upscaling models. Unlike them, we seek to improve the downscaled representation through a different and more direct way: optimizing the downscaled image itself instead of the down-/upscaling models. Specifically, we propose a collaborative downscaling scheme that directly generates the collaborative LR examples by descending the gradient w.r.t. the reconstruction loss on them to benefit the IR process. Furthermore, since LR images are downscaled from the corresponding HR images, one can also improve the downscaled representation if we have a better representation in the HR domain. Inspired by this, we propose a Hierarchical Collaborative Downscaling (HCD) method that performs gradient descent in both HR and LR domains to improve the downscaled representations. Extensive experiments show that our HCD significantly improves the reconstruction performance both quantitatively and qualitatively. Moreover, we also highlight the flexibility of our HCD since it can generalize well across diverse IR models.

Many dynamical processes unfold on the sphere but the default scientific machine learning architectures are Euclidean. Applying these architectures on a regular lat-lon grid causes problems: Cartesian convolutions become distorted at high latitude; 2D FFTs in Fourier neural operators incorrectly assume double periodicity; Cartesian positional encodings in ViTs distort spherical geodesic distances. Recent work moves towards natively spherical primitives, including spherical convolutions (e.g., DeepSphere or DISCO), Spherical Fourier Neural Operators (SFNOs), and geodesic attention. Here we propose Dandelion, a spherical version of Flower, a warp-based neural PDE solver. Layers of Dandelion predict a tangent-plane displacement and transport features along great circles. We obtain a U-Net-like structure by implementing hierarchical pooling entirely in the spherical-harmonic domain. There are thus no convolutions: spatial mixing is achieved only through spherical coordinate changes, or warps. To compare Dandelion with existing spherical architectures, we release an evolving benchmark suite of challenging, natively-spherical PDE datasets including a modified Galewsky jet, anomalous chained turbulence, Cahn-Hilliard decomposition, spherical Riemann shocks, Held-Suarez dry atmospheric transport and global ocean dynamics. This new benchmark fills the gap in existing spherical datasets which are either too small and stylized, or much too large (ERA5) for model iteration. Dandelion is best or second-best on every dataset, and the gap to non-warp baselines widens with resolution: at 256times 512, Dandelion and Flower2D occupy the top two slots in both single-step prediction and rollout.

Learned image compression (LIC) has gained traction as an effective solution for image storage and transmission in recent years. However, existing LIC methods are redundant in latent representation due to limitations in capturing anisotropic frequency components and preserving directional details. To overcome these challenges, we propose a novel frequency-aware transformer (FAT) block that for the first time achieves multiscale directional ananlysis for LIC. The FAT block comprises frequency-decomposition window attention (FDWA) modules to capture multiscale and directional frequency components of natural images. Additionally, we introduce frequency-modulation feed-forward network (FMFFN) to adaptively modulate different frequency components, improving rate-distortion performance. Furthermore, we present a transformer-based channel-wise autoregressive (T-CA) model that effectively exploits channel dependencies. Experiments show that our method achieves state-of-the-art rate-distortion performance compared to existing LIC methods, and evidently outperforms latest standardized codec VTM-12.1 by 14.5%, 15.1%, 13.0% in BD-rate on the Kodak, Tecnick, and CLIC datasets.

Radio Frequency Neural Networks (RFNNs) have demonstrated advantages in realizing intelligent applications across various domains. However, as the model size of deep neural networks rapidly increases, implementing large-scale RFNN in practice requires an extensive number of RF interferometers and consumes a substantial amount of energy. To address this challenge, we propose to utilize low-rank decomposition to transform a large-scale RFNN into a compact RFNN while almost preserving its accuracy. Specifically, we develop a Tensor-Train RFNN (TT-RFNN) where each layer comprises a sequence of low-rank third-order tensors, leading to a notable reduction in parameter count, thereby optimizing RF interferometer utilization in comparison to the original large-scale RFNN. Additionally, considering the inherent physical errors when mapping TT-RFNN to RF device parameters in real-world deployment, from a general perspective, we construct the Robust TT-RFNN (RTT-RFNN) by incorporating a robustness solver on TT-RFNN to enhance its robustness. To adapt the RTT-RFNN to varying requirements of reshaping operations, we further provide a reconfigurable reshaping solution employing RF switch matrices. Empirical evaluations conducted on MNIST and CIFAR-10 datasets show the effectiveness of our proposed method.

Great successes have been achieved using deep learning techniques for image super-resolution (SR) with fixed scales. To increase its real world applicability, numerous models have also been proposed to restore SR images with arbitrary scale factors, including asymmetric ones where images are resized to different scales along horizontal and vertical directions. Though most models are only optimized for the unidirectional upscaling task while assuming a predefined downscaling kernel for low-resolution (LR) inputs, recent models based on Invertible Neural Networks (INN) are able to increase upscaling accuracy significantly by optimizing the downscaling and upscaling cycle jointly. However, limited by the INN architecture, it is constrained to fixed integer scale factors and requires one model for each scale. Without increasing model complexity, a simple and effective invertible arbitrary rescaling network (IARN) is proposed to achieve arbitrary image rescaling by training only one model in this work. Using innovative components like position-aware scale encoding and preemptive channel splitting, the network is optimized to convert the non-invertible rescaling cycle to an effectively invertible process. It is shown to achieve a state-of-the-art (SOTA) performance in bidirectional arbitrary rescaling without compromising perceptual quality in LR outputs. It is also demonstrated to perform well on tests with asymmetric scales using the same network architecture.

Recent NVFP4 pretraining work has primarily optimized Transformer linear projections, leaving persistent optimizer states, optimizer computation, and low-precision attention forward--backward paths less explored. We present Full-Stack FP4, a modular NVFP4 framework with separate recipes for projections, AdamW states, Root/Muon computation, and attention. LoRA-SVD protects a compact projection subspace in BF16 while retaining full-shape NVFP4 computation, reducing the linear-only loss gap from 1.40\% to 0.61\%. An ordered square-root, tile-mean, and Hadamard pipeline enables stable NVFP4 AdamW momentum storage; shape-dependent coefficients and clipping stabilize direct NVFP4 Root iterations; and mixed-precision attention retains softmax-sensitive operations in BF16. On 3B pretraining with 64B tokens, BF16 and Full-Stack FP4 reach losses of 2.267 and 2.286, a 0.838\% gap. Their average zero-shot perplexities are 26.675 and 26.665, respectively, with Full-Stack FP4 averaging 0.10 percentage points lower in accuracy. Native four-block measurements on one RTX 5090 show 2.50--2.83times Root speedups over optimized BF16 and 37.9--42.5\% lower AdamW peak memory.

We present Fast-Downsampling MobileNet (FD-MobileNet), an efficient and accurate network for very limited computational budgets (e.g., 10-140 MFLOPs). Our key idea is applying an aggressive downsampling strategy to MobileNet framework. In FD-MobileNet, we perform 32times downsampling within 12 layers, only half the layers in the original MobileNet. This design brings three advantages: (i) It remarkably reduces the computational cost. (ii) It increases the information capacity and achieves significant performance improvements. (iii) It is engineering-friendly and provides fast actual inference speed. Experiments on ILSVRC 2012 and PASCAL VOC 2007 datasets demonstrate that FD-MobileNet consistently outperforms MobileNet and achieves comparable results with ShuffleNet under different computational budgets, for instance, surpassing MobileNet by 5.5% on the ILSVRC 2012 top-1 accuracy and 3.6% on the VOC 2007 mAP under a complexity of 12 MFLOPs. On an ARM-based device, FD-MobileNet achieves 1.11times inference speedup over MobileNet and 1.82times over ShuffleNet under the same complexity.

While Dynamic Convolution (DY-Conv) has shown promising performance by enabling adaptive weight selection through multiple parallel weights combined with an attention mechanism, the frequency response of these weights tends to exhibit high similarity, resulting in high parameter costs but limited adaptability. In this work, we introduce Frequency Dynamic Convolution (FDConv), a novel approach that mitigates these limitations by learning a fixed parameter budget in the Fourier domain. FDConv divides this budget into frequency-based groups with disjoint Fourier indices, enabling the construction of frequency-diverse weights without increasing the parameter cost. To further enhance adaptability, we propose Kernel Spatial Modulation (KSM) and Frequency Band Modulation (FBM). KSM dynamically adjusts the frequency response of each filter at the spatial level, while FBM decomposes weights into distinct frequency bands in the frequency domain and modulates them dynamically based on local content. Extensive experiments on object detection, segmentation, and classification validate the effectiveness of FDConv. We demonstrate that when applied to ResNet-50, FDConv achieves superior performance with a modest increase of +3.6M parameters, outperforming previous methods that require substantial increases in parameter budgets (e.g., CondConv +90M, KW +76.5M). Moreover, FDConv seamlessly integrates into a variety of architectures, including ConvNeXt, Swin-Transformer, offering a flexible and efficient solution for modern vision tasks. The code is made publicly available at https://github.com/Linwei-Chen/FDConv.

Recent work has shown that feed-forward networks (FFNs) in pre-trained Transformers are a key component, storing various linguistic and factual knowledge. However, the computational patterns of FFNs are still unclear. In this work, we study the computational patterns of FFNs and observe that most inputs only activate a tiny ratio of neurons of FFNs. This phenomenon is similar to the sparsity of the human brain, which drives research on functional partitions of the human brain. To verify whether functional partitions also emerge in FFNs, we propose to convert a model into its MoE version with the same parameters, namely MoEfication. Specifically, MoEfication consists of two phases: (1) splitting the parameters of FFNs into multiple functional partitions as experts, and (2) building expert routers to decide which experts will be used for each input. Experimental results show that MoEfication can conditionally use 10% to 30% of FFN parameters while maintaining over 95% original performance for different models on various downstream tasks. Besides, MoEfication brings two advantages: (1) it significantly reduces the FLOPS of inference, i.e., 2x speedup with 25% of FFN parameters, and (2) it provides a fine-grained perspective to study the inner mechanism of FFNs. The source code of this paper can be obtained from https://github.com/thunlp/MoEfication.

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises: Frequency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and Orthogonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at https://github.com/sonhm3029/FreqOrtho-SR{sonhm3029/FreqOrtho-SR}.

This paper presents a neural surrogate approach for improving the accuracy of natural convection problems simulated with a Boussinesq flow model (incompressible flow with heat transfer). Our approach, based on Fourier neural operators, uses training data consisting of matched pairs of simulations run under the computationally cheaper yet less accurate Boussinesq flow model and a more computationally expensive and more accurate compressible flow model. In both cases, we implement our parallelized simulation codes based on an implicit monolithic mixed finite element method (FEM) approach using the open-source FEniCSx framework. Our implementations are validated against a commercial software package, COMSOL, as well as standard test problems from the literature. We include a careful discussion and analysis of data set generation and present learning results in two and three spatial dimensions. Using compressible flow results as high-fidelity reference solutions, our learning approach, with a single model evaluation per simulation, substantially improves the per-channel accuracy of Boussinesq predictions, with structural similarity (SSIM) close to unity across all flow variables and test distributions and corresponding mean-squared error reductions of one to nearly three orders of magnitude. All code and data is released as open-source.

Similar to conventional video generation, current deep learning-based weather prediction frameworks often lack explicit physical constraints, leading to unphysical outputs that limit their reliability for operational forecasting. Among various physical processes requiring proper representation, radiation plays a fundamental role as it drives Earth's weather and climate systems. However, accurate simulation of radiative transfer processes remains challenging for traditional numerical weather prediction (NWP) models due to their inherent complexity and high computational costs. Here, we propose FuXi-RTM, a hybrid physics-guided deep learning framework designed to enhance weather forecast accuracy while enforcing physical consistency. FuXi-RTM integrates a primary forecasting model (FuXi) with a fixed deep learning-based radiative transfer model (DLRTM) surrogate that efficiently replaces conventional radiation parameterization schemes. This represents the first deep learning-based weather forecasting framework to explicitly incorporate physical process modeling. Evaluated over a comprehensive 5-year dataset, FuXi-RTM outperforms its unconstrained counterpart in 88.51% of 3320 variable and lead time combinations, with improvements in radiative flux predictions. By incorporating additional physical processes, FuXi-RTM paves the way for next-generation weather forecasting systems that are both accurate and physically consistent.

Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

The large number of parameters in Pretrained Language Models enhance their performance, but also make them resource-intensive, making it challenging to deploy them on commodity hardware like a single GPU. Due to the memory and power limitations of these devices, model compression techniques are often used to decrease both the model's size and its inference latency. This usually results in a trade-off between model accuracy and efficiency. Therefore, optimizing this balance is essential for effectively deploying LLMs on commodity hardware. A significant portion of the efficiency challenge is the Feed-forward network (FFN) component, which accounts for roughly 2{3} total parameters and inference latency. In this paper, we first observe that only a few neurons of FFN module have large output norm for any input tokens, a.k.a. heavy hitters, while the others are sparsely triggered by different tokens. Based on this observation, we explicitly split the FFN into two parts according to the heavy hitters. We improve the efficiency-accuracy trade-off of existing compression methods by allocating more resource to FFN parts with heavy hitters. In practice, our method can reduce model size by 43.1\% and bring 1.25sim1.56times wall clock time speedup on different hardware with negligible accuracy drop.

Image downscaling is a fundamental operation in image processing, crucial for adapting high-resolution content to various display and storage constraints. While classic methods often introduce blurring or aliasing, recent learning-based approaches offer improved adaptivity. However, achieving maximal fidelity against ground-truth low-resolution (LR) images, particularly by accounting for channel-specific characteristics, remains an open challenge. This paper introduces ADK-Net (Adaptive Downscaling Kernel Network), a novel deep convolutional neural network framework for high-fidelity supervised image downscaling. ADK-Net explicitly addresses channel interdependencies by learning to predict spatially-varying, adaptive resampling kernels independently for each pixel and uniquely for each color channel (RGB). The architecture employs a hierarchical design featuring a ResNet-based feature extractor and parallel channel-specific kernel generators, themselves composed of ResNet-based trunk and branch sub-modules, enabling fine-grained kernel prediction. Trained end-to-end using an L1 reconstruction loss against ground-truth LR data, ADK-Net effectively learns the target downscaling transformation. Extensive quantitative and qualitative experiments on standard benchmarks, including the RealSR dataset, demonstrate that ADK-Net establishes a new state-of-the-art in supervised image downscaling, yielding significant improvements in PSNR and SSIM metrics compared to existing learning-based and traditional methods.

Single image-to-3D generation is pivotal for crafting controllable 3D assets. Given its underconstrained nature, we leverage geometric priors from a 3D novel view generation diffusion model and appearance priors from a 2D image generation method to guide the optimization process. We note that a disparity exists between the training datasets of 2D and 3D diffusion models, leading to their outputs showing marked differences in appearance. Specifically, 2D models tend to deliver more detailed visuals, whereas 3D models produce consistent yet over-smooth results across different views. Hence, we optimize a set of 3D Gaussians using 3D priors in spatial domain to ensure geometric consistency, while exploiting 2D priors in the frequency domain through Fourier transform for higher visual quality. This 2D-3D hybrid Fourier Score Distillation objective function (dubbed hy-FSD), can be integrated into existing 3D generation methods, yielding significant performance improvements. With this technique, we further develop an image-to-3D generation pipeline to create high-quality 3D objects within one minute, named Fourier123. Extensive experiments demonstrate that Fourier123 excels in efficient generation with rapid convergence speed and visual-friendly generation results.

Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at significantly reduced computational cost compared to traditional numerical weather prediction (NWP) systems. However, challenges remain in ensuring the physical consistency of MLWP outputs, particularly in deterministic settings. This study presents FastNet, a graph neural network (GNN)-based global prediction model, and investigates the impact of alternative loss function designs on improving the physical realism of its forecasts. We explore three key modifications to the standard mean squared error (MSE) loss: (1) a modified spherical harmonic (MSH) loss that penalises spectral amplitude errors to reduce blurring and enhance small-scale structure retention; (2) inclusion of horizontal gradient terms in the loss to suppress non-physical artefacts; and (3) an alternative wind representation that decouples speed and direction to better capture extreme wind events. Results show that while the MSH and gradient-based losses alone may slightly degrade RMSE scores, when trained in combination the model exhibits very similar MSE performance to an MSE-trained model while at the same time significantly improving spectral fidelity and physical consistency. The alternative wind representation further improves wind speed accuracy and reduces directional bias. Collectively, these findings highlight the importance of loss function design as a mechanism for embedding domain knowledge into MLWP models and advancing their operational readiness.

Neural Radiance Field training can be accelerated through the use of grid-based representations in NeRF's learned mapping from spatial coordinates to colors and volumetric density. However, these grid-based approaches lack an explicit understanding of scale and therefore often introduce aliasing, usually in the form of jaggies or missing scene content. Anti-aliasing has previously been addressed by mip-NeRF 360, which reasons about sub-volumes along a cone rather than points along a ray, but this approach is not natively compatible with current grid-based techniques. We show how ideas from rendering and signal processing can be used to construct a technique that combines mip-NeRF 360 and grid-based models such as Instant NGP to yield error rates that are 8% - 77% lower than either prior technique, and that trains 24x faster than mip-NeRF 360.

Large language models (LLMs) deliver strong performance, but their high compute and memory costs make deployment difficult in resource-constrained scenarios. Weight-only post-training quantization (PTQ) is appealing, as it reduces memory usage and enables practical speedup without low-bit operators or specialized hardware. However, accuracy often degrades significantly in weight-only PTQ at sub-4-bit precision, and our analysis identifies two main causes: (1) down-projection matrices are a well-known quantization bottleneck, but maintaining their fidelity often requires extra bit-width; (2) weight quantization induces activation deviations, but effective correction strategies remain underexplored. To address these issues, we propose D^2Quant, a novel weight-only PTQ framework that improves quantization from both the weight and activation perspectives. On the weight side, we design a Dual-Scale Quantizer (DSQ) tailored to down-projection matrices, with an absorbable scaling factor that significantly improves accuracy without increasing the bit budget. On the activation side, we propose Deviation-Aware Correction (DAC), which incorporates a mean-shift correction within LayerNorm to mitigate quantization-induced activation distribution shifts. Extensive experiments across multiple LLM families and evaluation metrics show that D^2Quant delivers superior performance for weight-only PTQ at sub-4-bit precision. The code and models will be available at https://github.com/XIANGLONGYAN/D2Quant.

Radio-frequency coverage maps (RF maps) are extensively utilized in wireless networks for capacity planning, placement of access points and base stations, localization, and coverage estimation. Conducting site surveys to obtain RF maps is labor-intensive and sometimes not feasible. In this paper, we propose radio-frequency adversarial deep-learning inference for automated network coverage estimation (RADIANCE), a generative adversarial network (GAN) based approach for synthesizing RF maps in indoor scenarios. RADIANCE utilizes a semantic map, a high-level representation of the indoor environment to encode spatial relationships and attributes of objects within the environment and guide the RF map generation process. We introduce a new gradient-based loss function that computes the magnitude and direction of change in received signal strength (RSS) values from a point within the environment. RADIANCE incorporates this loss function along with the antenna pattern to capture signal propagation within a given indoor configuration and generate new patterns under new configuration, antenna (beam) pattern, and center frequency. Extensive simulations are conducted to compare RADIANCE with ray-tracing simulations of RF maps. Our results show that RADIANCE achieves a mean average error (MAE) of 0.09, root-mean-squared error (RMSE) of 0.29, peak signal-to-noise ratio (PSNR) of 10.78, and multi-scale structural similarity index (MS-SSIM) of 0.80.

We introduce a novel generative model, the Discrete Distribution Networks (DDN), that approximates data distribution using hierarchical discrete distributions. We posit that since the features within a network inherently capture distributional information, enabling the network to generate multiple samples simultaneously, rather than a single output, may offer an effective way to represent distributions. Therefore, DDN fits the target distribution, including continuous ones, by generating multiple discrete sample points. To capture finer details of the target data, DDN selects the output that is closest to the Ground Truth (GT) from the coarse results generated in the first layer. This selected output is then fed back into the network as a condition for the second layer, thereby generating new outputs more similar to the GT. As the number of DDN layers increases, the representational space of the outputs expands exponentially, and the generated samples become increasingly similar to the GT. This hierarchical output pattern of discrete distributions endows DDN with unique properties: more general zero-shot conditional generation and 1D latent representation. We demonstrate the efficacy of DDN and its intriguing properties through experiments on CIFAR-10 and FFHQ. The code is available at https://discrete-distribution-networks.github.io/

Deep operator networks can become statistically unstable when partial differential equation inputs are observed at thousands of strongly correlated sensors but only a small number of operator samples is available. We introduce FAST-DeepONet, a branch representation combining a fixed spectral path with a regularized projection of the orthogonal residual, in which the directional penalty acts on the effective residual map after each of its rows is normalized. On Navier--Stokes flow a plain DeepONet degrades from 0.0394 to 0.1556 mean relative L_2 error as the branch grows from 129 to 8193 coordinates, while FAST-DeepONet stays near 0.04, so the sensor grid can be refined without a statistical penalty. Across independent test sets for Navier--Stokes flow, Darcy flow, and signed terminal wavefield prediction it lowers mean relative L_2 error by 4.7% to 37.0% with three to seven times fewer trainable parameters. A spectral-only branch sharing the same basis separates the two paths: the fixed spectral path carries the improvement on Navier--Stokes and Darcy, while terminal wave prediction requires the residual path together with its directional penalty. FAST-DeepONet targets coordinate-query architectures and trains on solution values alone.

The Transformer architecture has two main non-embedding components: Attention and the Feed Forward Network (FFN). Attention captures interdependencies between words regardless of their position, while the FFN non-linearly transforms each input token independently. In this work we explore the role of the FFN, and find that despite taking up a significant fraction of the model's parameters, it is highly redundant. Concretely, we are able to substantially reduce the number of parameters with only a modest drop in accuracy by removing the FFN on the decoder layers and sharing a single FFN across the encoder. Finally we scale this architecture back to its original size by increasing the hidden dimension of the shared FFN, achieving substantial gains in both accuracy and latency with respect to the original Transformer Big.

Text-to-image generation powered by Diffusion Transformers (DiTs) has made remarkable strides, yet remote sensing (RS) synthesis lags behind due to two barriers: the absence of a domain-specialized DiT prior and the prohibitive cost of training at the large resolutions that RS applications demand. Training-free resolution promotion via Rotary Position Embedding (RoPE) rescaling offers a practical remedy, but every existing method applies a static positional scaling rule throughout the denoising process. This uniform compression is particularly harmful for RS imagery, whose substantially denser medium- and high-frequency energy encodes the fine structures critical for aerial-scene realism, such as vehicles, building contours, and road markings. Addressing both challenges requires a domain-specialized generative prior coupled with a denoising-aware positional adaptation strategy. To this end, we fine-tune FLUX on over 100,000 curated RS images to build a strong domain prior (RS-FLUX), and propose Spectrum-aware Highly-dynamic Adaptation for Resolution Promotion (SHARP), a training-free method that introduces a rational fractional time schedule k_rs(t) into RoPE. SHARP applies strong positional promotion during the early layout-formation stage and progressively relaxes it during detail recovery, aligning extrapolation strength with the frequency-progressive nature of diffusion denoising. Its resolution-agnostic formulation further enables robust multi-scale generation from a single set of hyperparameters. Extensive experiments across six square and rectangular resolutions show that SHARP consistently outperforms all training-free baselines on CLIP Score, Aesthetic Score, and HPSv2, with widening margins at more aggressive extrapolation factors and negligible computational overhead. Code and weights are available at https://github.com/bxuanz/SHARP.

CNN-based generative modelling has evolved to produce synthetic images indistinguishable from real images in the RGB pixel space. Recent works have observed that CNN-generated images share a systematic shortcoming in replicating high frequency Fourier spectrum decay attributes. Furthermore, these works have successfully exploited this systematic shortcoming to detect CNN-generated images reporting up to 99% accuracy across multiple state-of-the-art GAN models. In this work, we investigate the validity of assertions claiming that CNN-generated images are unable to achieve high frequency spectral decay consistency. We meticulously construct a counterexample space of high frequency spectral decay consistent CNN-generated images emerging from our handcrafted experiments using DCGAN, LSGAN, WGAN-GP and StarGAN, where we empirically show that this frequency discrepancy can be avoided by a minor architecture change in the last upsampling operation. We subsequently use images from this counterexample space to successfully bypass the recently proposed forensics detector which leverages on high frequency Fourier spectrum decay attributes for CNN-generated image detection. Through this study, we show that high frequency Fourier spectrum decay discrepancies are not inherent characteristics for existing CNN-based generative models--contrary to the belief of some existing work--, and such features are not robust to perform synthetic image detection. Our results prompt re-thinking of using high frequency Fourier spectrum decay attributes for CNN-generated image detection. Code and models are available at https://keshik6.github.io/Fourier-Discrepancies-CNN-Detection/

Normalizing flow models have been used successfully for generative image super-resolution (SR) by approximating complex distribution of natural images to simple tractable distribution in latent space through Invertible Neural Networks (INN). These models can generate multiple realistic SR images from one low-resolution (LR) input using randomly sampled points in the latent space, simulating the ill-posed nature of image upscaling where multiple high-resolution (HR) images correspond to the same LR. Lately, the invertible process in INN has also been used successfully by bidirectional image rescaling models like IRN and HCFlow for joint optimization of downscaling and inverse upscaling, resulting in significant improvements in upscaled image quality. While they are optimized for image downscaling too, the ill-posed nature of image downscaling, where one HR image could be downsized to multiple LR images depending on different interpolation kernels and resampling methods, is not considered. A new downscaling latent variable, in addition to the original one representing uncertainties in image upscaling, is introduced to model variations in the image downscaling process. This dual latent variable enhancement is applicable to different image rescaling models and it is shown in extensive experiments that it can improve image upscaling accuracy consistently without sacrificing image quality in downscaled LR images. It is also shown to be effective in enhancing other INN-based models for image restoration applications like image hiding.

Swarm aerial robots are required to maintain close proximity to successfully traverse narrow areas in cluttered environments. However, this movement is affected by the downwash effect generated from other quadrotors in the swarm. This aerodynamic effect is highly nonlinear and hard to describe through mathematical modeling. Additionally, the existence of the downwash disturbance can be predicted based on the states of neighboring quadrotors. If this prediction is considered, the control loop can proactively handle the disturbance, resulting in improved performance. To address these challenges, we propose an approach that integrates a Neural network Downwash Predictor with Nonlinear Model Predictive Control (NDP-NMPC). The neural network is trained with spectral normalization to ensure robustness and safety in uncollected cases. The predicted disturbances are then incorporated into the optimization scheme in NMPC, which enforces constraints to ensure that states and inputs remain within safe limits. We also design a quadrotor system, identify its parameters, and implement the proposed method on board. Finally, we conduct a prediction experiment to validate the safety and effectiveness of the network. In addition, a real-time trajectory tracking experiment is performed with the entire system, demonstrating a 75.37% reduction in tracking error in height under the downwash effect.

Recent research has demonstrated that Feed-Forward Networks (FFNs) in Large Language Models (LLMs) play a pivotal role in storing diverse linguistic and factual knowledge. Conventional methods frequently face challenges due to knowledge confusion stemming from their monolithic and redundant architectures, which calls for more efficient solutions with minimal computational overhead, particularly for LLMs. In this paper, we explore the FFN computation paradigm in LLMs and introduce FactorLLM, a novel approach that decomposes well-trained dense FFNs into sparse sub-networks without requiring any further modifications, while maintaining the same level of performance. Furthermore, we embed a router from the Mixture-of-Experts (MoE), combined with our devised Prior-Approximate (PA) loss term that facilitates the dynamic activation of experts and knowledge adaptation, thereby accelerating computational processes and enhancing performance using minimal training data and fine-tuning steps. FactorLLM thus enables efficient knowledge factorization and activates select groups of experts specifically tailored to designated tasks, emulating the interactive functional segmentation of the human brain. Extensive experiments across various benchmarks demonstrate the effectiveness of our proposed FactorLLM which achieves comparable performance to the source model securing up to 85% model performance while obtaining over a 30% increase in inference speed. Code: https://github.com/zhenwuweihe/FactorLLM.

FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the spatially correlated probabilistic nature of the problem, resulting in stable spectra and realistic dynamics across multiple scales. FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-based methods, while producing forecasts 8 to 60 times faster than these approaches. In contrast to other ML approaches, FourCastNet 3 demonstrates excellent probabilistic calibration and retains realistic spectra, even at extended lead times of up to 60 days. All of these advances are realized using a purely convolutional neural network architecture tailored for spherical geometry. Scalable and efficient large-scale training on 1024 GPUs and more is enabled by a novel training paradigm for combined model- and data-parallelism, inspired by domain decomposition methods in classical numerical models. Additionally, FourCastNet 3 enables rapid inference on a single GPU, producing a 60-day global forecast at 0.25{\deg}, 6-hourly resolution in under 4 minutes. Its computational efficiency, medium-range probabilistic skill, spectral fidelity, and rollout stability at subseasonal timescales make it a strong candidate for improving meteorological forecasting and early warning systems through large ensemble predictions.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

Diffusion models have achieved remarkable success in image generation but their practical application is often hindered by the slow sampling speed. Prior efforts of improving efficiency primarily focus on compressing models or reducing the total number of denoising steps, largely neglecting the possibility to leverage multiple input resolutions in the generation process. In this work, we propose LowDiff, a novel and efficient diffusion framework based on a cascaded approach by generating increasingly higher resolution outputs. Besides, LowDiff employs a unified model to progressively refine images from low resolution to the desired resolution. With the proposed architecture design and generation techniques, we achieve comparable or even superior performance with much fewer high-resolution sampling steps. LowDiff is applicable to diffusion models in both pixel space and latent space. Extensive experiments on both conditional and unconditional generation tasks across CIFAR-10, FFHQ and ImageNet demonstrate the effectiveness and generality of our method. Results show over 50% throughput improvement across all datasets and settings while maintaining comparable or better quality. On unconditional CIFAR-10, LowDiff achieves an FID of 2.11 and IS of 9.87, while on conditional CIFAR-10, an FID of 1.94 and IS of 10.03. On FFHQ 64x64, LowDiff achieves an FID of 2.43, and on ImageNet 256x256, LowDiff built on LightningDiT-B/1 produces high-quality samples with a FID of 4.00 and an IS of 195.06, together with substantial efficiency gains.

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this limitation, we propose a unified differentiable formulation of the STFT that enables gradient-based optimization of its parameters. This approach addresses the limitations of traditional STFT parameter tuning methods, which often rely on computationally intensive discrete searches. It enables fine-tuning of the time-frequency representation (TFR) based on any desired criterion. Moreover, our approach integrates seamlessly with neural networks, allowing joint optimization of the STFT parameters and network weights. The efficacy of the proposed differentiable STFT in enhancing TFRs and improving performance in downstream tasks is demonstrated through experiments on both simulated and real-world data.

FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at 0.25^{circ} resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for variables with complex fine-scale structure, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

Recent works have shown that 3D-aware GANs trained on unstructured single image collections can generate multiview images of novel instances. The key underpinnings to achieve this are a 3D radiance field generator and a volume rendering process. However, existing methods either cannot generate high-resolution images (e.g., up to 256X256) due to the high computation cost of neural volume rendering, or rely on 2D CNNs for image-space upsampling which jeopardizes the 3D consistency across different views. This paper proposes a novel 3D-aware GAN that can generate high resolution images (up to 1024X1024) while keeping strict 3D consistency as in volume rendering. Our motivation is to achieve super-resolution directly in the 3D space to preserve 3D consistency. We avoid the otherwise prohibitively-expensive computation cost by applying 2D convolutions on a set of 2D radiance manifolds defined in the recent generative radiance manifold (GRAM) approach, and apply dedicated loss functions for effective GAN training at high resolution. Experiments on FFHQ and AFHQv2 datasets show that our method can produce high-quality 3D-consistent results that significantly outperform existing methods.

The diversity of time series applications and scarcity of domain-specific data highlight the need for time-series models with strong few-shot learning capabilities. In this work, we propose a novel training scheme and a transformer-based architecture, collectively referred to as TimePFN, for multivariate time-series (MTS) forecasting. TimePFN is based on the concept of Prior-data Fitted Networks (PFN), which aims to approximate Bayesian inference. Our approach consists of (1) generating synthetic MTS data through diverse Gaussian process kernels and the linear coregionalization method, and (2) a novel MTS architecture capable of utilizing both temporal and cross-channel dependencies across all input patches. We evaluate TimePFN on several benchmark datasets and demonstrate that it outperforms the existing state-of-the-art models for MTS forecasting in both zero-shot and few-shot settings. Notably, fine-tuning TimePFN with as few as 500 data points nearly matches full dataset training error, and even 50 data points yield competitive results. We also find that TimePFN exhibits strong univariate forecasting performance, attesting to its generalization ability. Overall, this work unlocks the power of synthetic data priors for MTS forecasting and facilitates strong zero- and few-shot forecasting performance.

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible for high-resolution inputs. To cope with this challenge, we propose Adaptive Fourier Neural Operator (AFNO) as an efficient token mixer that learns to mix in the Fourier domain. AFNO is based on a principled foundation of operator learning which allows us to frame token mixing as a continuous global convolution without any dependence on the input resolution. This principle was previously used to design FNO, which solves global convolution efficiently in the Fourier domain and has shown promise in learning challenging PDEs. To handle challenges in visual representation learning such as discontinuities in images and high resolution inputs, we propose principled architectural modifications to FNO which results in memory and computational efficiency. This includes imposing a block-diagonal structure on the channel mixing weights, adaptively sharing weights across tokens, and sparsifying the frequency modes via soft-thresholding and shrinkage. The resulting model is highly parallel with a quasi-linear complexity and has linear memory in the sequence size. AFNO outperforms self-attention mechanisms for few-shot segmentation in terms of both efficiency and accuracy. For Cityscapes segmentation with the Segformer-B3 backbone, AFNO can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms.

Vision-language verifiers and routers must distinguish errors repairable by more reasoning from those caused by visual evidence never reaching the language model. This distinction lacks ground truth because annotators see full-resolution images while models receive preprocessed tensors. We introduce AliasForge to create cases where the relevant fact is provably absent from the interface. Fixed-point resampling makes the pre-rounding resize an exact integer linear map that can send nonzero integer perturbations to zero. Hiding a label-flipping perturbation there produces images with opposite step-correctness labels but bit-identical interface states. Every verifier therefore has the same output law on both members, giving pair-balanced accuracy exactly one half and zero gain from language-side repair. We prove that every fixed-point downscaler has such null vectors and bound their smallest size at the most common ratios, which rules out an 8-bit fit whenever the bound exceeds 255. From the resize configuration alone, a lattice criterion supplies realizable collisions and certifies their absence within the specified construction family. It resolves all 20 screened configurations, 17 as constructible and 3 as non-constructible. We construct certified pairs across three architectures and certify four additional processors, with zero decision-logit gap on all 18 scored pairs and none of the 18 controls. The pairs also screen routers that waste computation on re-attention or further reasoning. On natural items, per-item routing headroom exists, but no tested interface-only router improves over stopping. Our fiber ceiling bounds the headroom recoverable from the interface. Code: https://github.com/KurbanIntelligenceLab/aliasforge.

Conventional self-attention mechanisms incur quadratic complexity, limiting their scalability on long sequences. We introduce FFTNet, an adaptive spectral filtering framework that leverages the Fast Fourier Transform (FFT) to achieve global token mixing in O(nlog n) time. By transforming inputs into the frequency domain, FFTNet exploits the orthogonality and energy preservation guaranteed by Parseval's theorem to capture long-range dependencies efficiently. A learnable spectral filter and modReLU activation dynamically emphasize salient frequency components, providing a rigorous and adaptive alternative to traditional self-attention. Experiments on the Long Range Arena and ImageNet benchmarks validate our theoretical insights and demonstrate superior performance over fixed Fourier and standard attention models.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP fails to learn high frequencies both in theory and in practice. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

We propose a neural network for both forward and inverse continuous nonlinear Fourier transforms, NFT and INFT respectively. We demonstrate the network's capability to perform NFT and INFT for a random mix of NFDM-QAM signals. The network transformations (NFT and INFT) exhibit true characteristics of these transformations; they are significantly different for low and high-power input pulses. The network shows adequate accuracy with an RMSE of 5e-3 for forward and 3e-2 for inverse transforms. We further show that the trained network can be used to perform general nonlinear Fourier transforms on arbitrary pulses beyond the training pulse types.

The vast majority of time-series forecasting approaches require a substantial training dataset. However, many real-life forecasting applications have very little initial observations, sometimes just 40 or fewer. Thus, the applicability of most forecasting methods is restricted in data-sparse commercial applications. While there is recent work in the setting of very limited initial data (so-called `zero-shot' forecasting), its performance is inconsistent depending on the data used for pretraining. In this work, we take a different approach and devise ForecastPFN, the first zero-shot forecasting model trained purely on a novel synthetic data distribution. ForecastPFN is a prior-data fitted network, trained to approximate Bayesian inference, which can make predictions on a new time series dataset in a single forward pass. Through extensive experiments, we show that zero-shot predictions made by ForecastPFN are more accurate and faster compared to state-of-the-art forecasting methods, even when the other methods are allowed to train on hundreds of additional in-distribution data points.

Efficient neural networks are essential for scaling machine learning models to real-time applications and resource-constrained environments. Fully-connected feedforward layers (FFLs) introduce computation and parameter count bottlenecks within neural network architectures. To address this challenge, in this work, we propose a new class of dense layers that generalize standard fully-connected feedforward layers, Efficient, Unified and General dense layers (EUGens). EUGens leverage random features to approximate standard FFLs and go beyond them by incorporating a direct dependence on the input norms in their computations. The proposed layers unify existing efficient FFL extensions and improve efficiency by reducing inference complexity from quadratic to linear time. They also lead to the first unbiased algorithms approximating FFLs with arbitrary polynomial activation functions. Furthermore, EuGens reduce the parameter count and computational overhead while preserving the expressive power and adaptability of FFLs. We also present a layer-wise knowledge transfer technique that bypasses backpropagation, enabling efficient adaptation of EUGens to pre-trained models. Empirically, we observe that integrating EUGens into Transformers and MLPs yields substantial improvements in inference speed (up to 27\%) and memory efficiency (up to 30\%) across a range of tasks, including image classification, language model pre-training, and 3D scene reconstruction. Overall, our results highlight the potential of EUGens for the scalable deployment of large-scale neural networks in real-world scenarios.

Unmanned aerial vehicle object detection (UAV-OD) has been widely used in various scenarios. However, most existing UAV-OD algorithms rely on manually designed components, which require extensive tuning. End-to-end models that do not depend on such manually designed components are mainly designed for natural images, which are less effective for UAV imagery. To address such challenges, this paper proposes an efficient detection transformer (DETR) framework tailored for UAV imagery, i.e., UAV-DETR. The framework includes a multi-scale feature fusion with frequency enhancement module, which captures both spatial and frequency information at different scales. In addition, a frequency-focused down-sampling module is presented to retain critical spatial details during down-sampling. A semantic alignment and calibration module is developed to align and fuse features from different fusion paths. Experimental results demonstrate the effectiveness and generalization of our approach across various UAV imagery datasets. On the VisDrone dataset, our method improves AP by 3.1\% and AP_{50} by 4.2\% over the baseline. Similar enhancements are observed on the UAVVaste dataset. The project page: https://github.com/ValiantDiligent/UAV-DETR

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a global and stationary spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose Neural Spectral Transport Representation (NSTR), the first INR framework that explicitly models a spatially varying local frequency field. NSTR introduces a learnable frequency transport equation, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field S(x) and a frequency transport network F_θ enforcing nabla S(x) approx F_θ(x, S(x)), NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum.

State-of-the-art LLMs often rely on scale with high computational costs, which has sparked a research agenda to reduce parameter counts and costs without significantly impacting performance. Our study focuses on Transformer-based LLMs, specifically applying low-rank parametrization to the computationally intensive feedforward networks (FFNs), which are less studied than attention blocks. In contrast to previous works, (i) we explore low-rank parametrization at scale, up to 1.3B parameters; (ii) within Transformer language models rather than convolutional architectures; and (iii) starting from training from scratch. Experiments on the large RefinedWeb dataset show that low-rank parametrization is both efficient (e.g., 2.6times FFN speed-up with 32\% parameters) and effective during training. Interestingly, these structured FFNs exhibit steeper scaling curves than the original models. Motivated by this finding, we develop the wide and structured networks surpassing the current medium-sized and large-sized Transformer in perplexity and throughput performance. Our code is available at https://github.com/CLAIRE-Labo/StructuredFFN/tree/main.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

Blur was naturally analyzed in the frequency domain, by estimating the latent sharp image and the blur kernel given a blurry image. Recent progress on image deblurring always designs end-to-end architectures and aims at learning the difference between blurry and sharp image pairs from pixel-level, which inevitably overlooks the importance of blur kernels. This paper reveals an intriguing phenomenon that simply applying ReLU operation on the frequency domain of a blur image followed by inverse Fourier transform, i.e., frequency selection, provides faithful information about the blur pattern (e.g., the blur direction and blur level, implicitly shows the kernel pattern). Based on this observation, we attempt to leverage kernel-level information for image deblurring networks by inserting Fourier transform, ReLU operation, and inverse Fourier transform to the standard ResBlock. 1x1 convolution is further added to let the network modulate flexible thresholds for frequency selection. We term our newly built block as Res FFT-ReLU Block, which takes advantages of both kernel-level and pixel-level features via learning frequency-spatial dual-domain representations. Extensive experiments are conducted to acquire a thorough analysis on the insights of the method. Moreover, after plugging the proposed block into NAFNet, we can achieve 33.85 dB in PSNR on GoPro dataset. Our method noticeably improves backbone architectures without introducing many parameters, while maintaining low computational complexity. Code is available at https://github.com/DeepMed-Lab/DeepRFT-AAAI2023.

Feed-forward 3D Gaussian Splatting methods enable single-pass reconstruction and real-time rendering. However, they typically adopt rigid pixel-to-Gaussian or voxel-to-Gaussian pipelines that uniformly allocate Gaussians, leading to redundant Gaussians across views. Moreover, they lack an effective mechanism to control the total number of Gaussians while maintaining reconstruction fidelity. To address these limitations, we present F4Splat, which performs Feed-Forward predictive densification for Feed-Forward 3D Gaussian Splatting, introducing a densification-score-guided allocation strategy that adaptively distributes Gaussians according to spatial complexity and multi-view overlap. Our model predicts per-region densification scores to estimate the required Gaussian density and allows explicit control over the final Gaussian budget without retraining. This spatially adaptive allocation reduces redundancy in simple regions and minimizes duplicate Gaussians across overlapping views, producing compact yet high-quality 3D representations. Extensive experiments demonstrate that our model achieves superior novel-view synthesis performance compared to prior uncalibrated feed-forward methods, while using significantly fewer Gaussians.

Underwater images often suffer from various issues such as low brightness, color shift, blurred details, and noise due to light absorption and scattering caused by water and suspended particles. Previous underwater image enhancement (UIE) methods have primarily focused on spatial domain enhancement, neglecting the frequency domain information inherent in the images. However, the degradation factors of underwater images are closely intertwined in the spatial domain. Although certain methods focus on enhancing images in the frequency domain, they overlook the inherent relationship between the image degradation factors and the information present in the frequency domain. As a result, these methods frequently enhance certain attributes of the improved image while inadequately addressing or even exacerbating other attributes. Moreover, many existing methods heavily rely on prior knowledge to address color shift problems in underwater images, limiting their flexibility and robustness. In order to overcome these limitations, we propose the Embedding Frequency and Dual Color Encoder Network (FDCE-Net) in our paper. The FDCE-Net consists of two main structures: (1) Frequency Spatial Network (FS-Net) aims to achieve initial enhancement by utilizing our designed Frequency Spatial Residual Block (FSRB) to decouple image degradation factors in the frequency domain and enhance different attributes separately. (2) To tackle the color shift issue, we introduce the Dual-Color Encoder (DCE). The DCE establishes correlations between color and semantic representations through cross-attention and leverages multi-scale image features to guide the optimization of adaptive color query. The final enhanced images are generated by combining the outputs of FS-Net and DCE through a fusion network. These images exhibit rich details, clear textures, low noise and natural colors.

Can we build continuous generative models which generalize across scales, can be evaluated at any coordinate, admit calculation of exact derivatives, and are conceptually simple? Existing MLP-based architectures generate worse samples than the grid-based generators with favorable convolutional inductive biases. Models that focus on generating images at different scales do better, but employ complex architectures not designed for continuous evaluation of images and derivatives. We take a signal-processing perspective and treat continuous image generation as interpolation from samples. Indeed, correctly sampled discrete images contain all information about the low spatial frequencies. The question is then how to extrapolate the spectrum in a data-driven way while meeting the above design criteria. Our answer is FunkNN -- a new convolutional network which learns how to reconstruct continuous images at arbitrary coordinates and can be applied to any image dataset. Combined with a discrete generative model it becomes a functional generator which can act as a prior in continuous ill-posed inverse problems. We show that FunkNN generates high-quality continuous images and exhibits strong out-of-distribution performance thanks to its patch-based design. We further showcase its performance in several stylized inverse problems with exact spatial derivatives.

Differentiable volumetric rendering-based methods made significant progress in novel view synthesis. On one hand, innovative methods have replaced the Neural Radiance Fields (NeRF) network with locally parameterized structures, enabling high-quality renderings in a reasonable time. On the other hand, approaches have used differentiable splatting instead of NeRF's ray casting to optimize radiance fields rapidly using Gaussian kernels, allowing for fine adaptation to the scene. However, differentiable ray casting of irregularly spaced kernels has been scarcely explored, while splatting, despite enabling fast rendering times, is susceptible to clearly visible artifacts. Our work closes this gap by providing a physically consistent formulation of the emitted radiance c and density {\sigma}, decomposed with Gaussian functions associated with Spherical Gaussians/Harmonics for all-frequency colorimetric representation. We also introduce a method enabling differentiable ray casting of irregularly distributed Gaussians using an algorithm that integrates radiance fields slab by slab and leverages a BVH structure. This allows our approach to finely adapt to the scene while avoiding splatting artifacts. As a result, we achieve superior rendering quality compared to the state-of-the-art while maintaining reasonable training times and achieving inference speeds of 25 FPS on the Blender dataset. Project page with videos and code: https://raygauss.github.io/

Lower numerical precision reduces storage and memory traffic but raises the perturbation floor. We study rank compensation: reinvesting saved memory in a larger approximation rank. For matrices, the singular-value error identity yields a directly testable sufficient condition requiring the additional singular component to offset the perturbation from storing the rank-augmented approximation in lower precision. On ten SuiteSparse matrices, all 100 truncation-dominated configurations (50 FP32 and 50 FP16) are certified non-increases and strict accuracy wins, with mean error ratio 0.963 and storage ratios 58.8% and 29.4% relative to the FP64 baseline. FP16 failures occur only in tail-rank stress tests near the perturbation floor. At the largest resident matrix-application batch, compensated FP32 and FP16 achieve geometric-mean A100 speedups of 1.28times and 2.12times; neither accelerates the smallest batch. For Tensor-Train (TT) approximation, we give a conditional a posteriori extension based on the measured truncation gain and rounded-core perturbation. Across three-way and six-way synthetic tests, FP32 and FP16 achieve combined accuracy-memory wins in 10 of 20 and 14 of 20 trials. On public hyperspectral tensors and FROSTT top-active subtensors, the corresponding counts are 44 of 60 and 54 of 60; four FP16 Salinas-A tail-stress cases fail. No certified TT case exceeds the FP64 error beyond numerical tolerance. Reconstruction of six public tensors yields geometric-mean compensated speedups of 1.38times (FP32) and 1.94times (FP16). Timings cover resident downstream kernels, not factorization, transfers, or end-to-end acceleration.

Large language models (LLMs) show excellent performance in difficult tasks, but they often require massive memories and computational resources. How to reduce the parameter scale of LLMs has become research hotspots. In this study, we make an important observation that the multi-head self-attention (MHA) sub-layer of Transformer exhibits noticeable low-rank structure, while the feed-forward network (FFN) sub-layer does not. With this regard, we design a mixed compression model, which organically combines Low-Rank matrix approximation And structured Pruning (LoRAP). For the MHA sub-layer, we propose an input activation weighted singular value decomposition method to strengthen the low-rank characteristic. Furthermore, we discover that the weight matrices in MHA sub-layer have different low-rank degrees. Thus, a novel parameter allocation scheme according to the discrepancy of low-rank degrees is devised. For the FFN sub-layer, we propose a gradient-free structured channel pruning method. During the pruning, we get an interesting finding that the least important 1% of parameter actually play a vital role in model performance. Extensive evaluations on zero-shot perplexity and zero-shot task classification indicate that our proposal is superior to previous structured compression rivals under multiple compression ratios.

We propose Frequency-Guided Attention (FGA), a lightweight upsampling module for single image super-resolution. Conventional upsamplers, such as Sub-Pixel Convolution, are efficient but frequently fail to reconstruct high-frequency details and introduce aliasing artifacts. FGA addresses these issues by integrating (1) a Fourier feature-based Multi-Layer Perceptron (MLP) for positional frequency encoding, (2) a cross-resolution Correlation Attention Layer for adaptive spatial alignment, and (3) a frequency-domain L1 loss for spectral fidelity supervision. Adding merely 0.3M parameters, FGA consistently enhances performance across five diverse super-resolution backbones in both lightweight and full-capacity scenarios. Experimental results demonstrate average PSNR gains of 0.12~0.14 dB and improved frequency-domain consistency by up to 29%, particularly evident on texture-rich datasets. Visual and spectral evaluations confirm FGA's effectiveness in reducing aliasing and preserving fine details, establishing it as a practical, scalable alternative to traditional upsampling methods.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

Alternating projections (AP) near a clean intersection of smooth manifolds can converge slowly when the Friedrichs angle is small. We develop the Fixed-Point Manifold Acceleration (FPMA) framework for {local convergence and polynomial acceleration of} smooth maps that fix a manifold pointwise. {Under suitable regularity and uniform normal spectral stability, FPMA establishes local R-linear convergence and a smooth limiting map inducing a local retraction. At fixed points, consistent polynomial acceleration with p(1)=1 preserves the selected limit's first-order response to normal initial perturbations whenever the transformed normal blocks are uniformly spectrally stable. Under sufficient smoothness, we give a curvature criterion for second-order induced retractions and show that stable consistent polynomial acceleration preserves both the quadratic retraction expansion and this criterion. {As a special case, we establish new local R-linear convergence guarantees for fixed-degree Chebyshev-accelerated exact AP and second-order induced retractions. For uniform Friedrichs angle θ_Fin(0,π/2), acceleration strictly improves the local convergence rate per AP evaluation. The large-degree limiting spectral factor at fixed θ_F predicts O(θ_F^{-1}) evaluations for fixed relative error reduction as θ_Fdownarrow0, versus O(θ_F^{-2}) for ordinary AP.}} {The framework also covers} inexact, relaxed, and generalized AP {under their respective regularity and stability conditions.}

Diffusion transformers deliver strong image generation, but their training cost grows superlinearly with resolution. Recent work justifies training or sampling at reduced resolution on a spectral premise: at high noise, a downscaled latent preserves almost the full surviving signal. Whether a downscaled step also preserves the native training gradient signal, however, has remained unresolved. We reduce how that signal changes under downscaling to two terms: a noise-dependent term governed by the downscale ratio, which decays at high noise as the spectral premise predicts, and a σ-independent floor governed by the target grid's absolute token count, carried by the compute graph itself and removed by no noise level. The measured (route, σ) map corroborates the account and uncovers structure the spectral picture cannot express: on the 1024->768 route, a window (0.65 < σ< 0.95), predicted by no spectral criterion at any tolerance, where the downscaled gradient stays within a small margin of the native one. Training LoRA adapters with downscaled steps restricted to the routes and noise windows the map validates reduces training time by 14.6% at a fixed step budget while remaining near-native in weight space. Code is available at https://github.com/sorryhyun/anima_lora.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.

The upper 6 GHz (U6G) band with XL-MIMO is a key enabler for sixth-generation wireless systems, yet intelligent radiomap prediction for such systems remains challenging. Existing datasets support only small-scale arrays (up to 8x8) with predominantly isotropic antennas, far from the 1024-element directional arrays envisioned for 6G. Moreover, current methods encode array configurations as scalar parameters, forcing neural networks to extrapolate array-specific radiation patterns, which fails when predicting radiomaps for configurations absent from training data. To jointly address data scarcity and generalization limitations, this paper advances XL-MIMO radiomap prediction from three aspects. To overcome data limitations, we construct the first XL-MIMO radiomap dataset containing 78400 radiomaps across 800 urban scenes, five frequency bands (1.8-6.7 GHz), and nine array configurations up to 32x32 uniform planar arrays with directional elements. To enable systematic evaluation, we establish a comprehensive benchmark framework covering practical scenarios from coverage estimation without field measurements to generalization across unseen configurations and environments. To enable generalization to arbitrary beam configurations without retraining, we propose the beam map, a physics-informed spatial feature that analytically computes array-specific coverage patterns. By decoupling deterministic array radiation from data learned multipath propagation, beam maps shift generalization from neural network extrapolation to physics-based computation. Integrating beam maps into existing architectures reduces mean absolute error by up to 60.0% when generalizing to unseen configurations and up to 50.5% when transferring to unseen environments. The complete dataset and code are publicly available at https://lxj321.github.io/MulticonfigRadiomapDataset/.

We introduce GeoFWI3D, a large-scale open-source benchmark dataset of geologically plausible 3D subsurface models designed to accelerate deep learning (DL) assisted seismic imaging and full waveform inversion (FWI). FWI is a physics-driven, wave-equation-based optimization technique used in seismic imaging to estimate the subsurface properties. However, traditional FWI is highly non-linear, non-unique, and ill-posed. The iterative process often converges to local minima when the starting model is insufficiently accurate. Most importantly, 3D FWI is prohibitively expensive. With the advent of DL, a direct mapping between the shot gathers and subsurface properties can be established by training a network on realistic models. The primary bottleneck for such approaches is the lack of large-scale, realistic training datasets. GeoFWI3D addresses this gap with 10,000 geologically diverse velocity models at 96x96x96 resolution, spanning four structural complexity classes: pure stratigraphy, faulted networks, salt diapirism, and complex coupled fault-salt systems. Each model is accompanied by co-registered multi-modal labels including compressional velocity (Vp), zero-offset seismic reflectivity, relative geologic time (RGT), and semantic fault/salt masks. To facilitate systematic evaluation, we introduce benchmark tasks covering fault detection, joint salt body segmentation and chronostratigraphy prediction, FWI, wavefield and traveltime surrogates using neural operators, and generative modeling with a 3D diffusion model. We present baseline results for each task to establish reference performance metrics for future users. The dataset is publicly available under Creative Commons Attribution 4.0 International.

Neural Radiance Fields (NeRF) face significant challenges in few-shot scenarios, primarily due to overfitting and long training times for high-fidelity rendering. Existing methods, such as FreeNeRF and SparseNeRF, use frequency regularization or pre-trained priors but struggle with complex scheduling and bias. We introduce FrugalNeRF, a novel few-shot NeRF framework that leverages weight-sharing voxels across multiple scales to efficiently represent scene details. Our key contribution is a cross-scale geometric adaptation scheme that selects pseudo ground truth depth based on reprojection errors across scales. This guides training without relying on externally learned priors, enabling full utilization of the training data. It can also integrate pre-trained priors, enhancing quality without slowing convergence. Experiments on LLFF, DTU, and RealEstate-10K show that FrugalNeRF outperforms other few-shot NeRF methods while significantly reducing training time, making it a practical solution for efficient and accurate 3D scene reconstruction.

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

Large Language Models (LLMs) typically represent numbers using multiple tokens, which requires the model to aggregate these tokens to interpret numerical values. This fragmentation makes both training and inference less efficient and adversely affects the model's performance on number-related tasks. Inspired by the observation that pre-trained LLMs internally learn Fourier-like features for number tokens, we propose Fourier Number Embedding (FoNE), a novel method that directly maps numbers into the embedding space with their Fourier features. FoNE encodes each number as a single token with only two embedding dimensions per digit, effectively capturing numerical values without fragmentation. This compact representation accelerates both training and inference. Compared to traditional subword and digit-wise embeddings, FoNE not only reduces computational overhead but also achieves higher accuracy across various numerical tasks including addition, subtraction and multiplication. On 6-digit decimal addition, FoNE requires 64times less data to achieve 99% accuracy than subword and digit-wise embeddings while using 3times and 6times fewer tokens per number, respectively. Furthermore, FoNE is the only method that yields 100% accuracy on over 100,000 test examples for addition, subtraction, and multiplication. The codes and visualization are available at https://fouriernumber.github.io/.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

SiFo, a wireless foundation model-based framework, is proposed for low-overhead site-specific channel state information (CSI) feedback. In 3GPP NR, Type-II feedback provides an expressive codebook-based CSI representation, but it requires substantial reference-signal overhead, UE-side search, and feedback. Learning-based site-specific feedback can reduce these online costs while retaining high-quality subspace representation by exploiting deployment-dependent propagation structure. However, existing site-specific designs typically train a dedicated neural network for each new site, which limits scalability when the number of deployments is large. SiFo addresses this scalability issue by pretraining a CSI feedback model across source sites and adapting it to a target site through lightweight calibration. A small set of target-site users reports low-dimensional reference signal received power (RSRP) fingerprints, and their full-CSI-based subspace labels are stored as calibration memory. During online operation, a served user is matched to calibrated users through the same SSB probing and RSRP reporting procedure, so nearby calibration samples provide site-specific subspace guidance without updating model parameters. SiFo therefore transfers common propagation knowledge while retaining local adaptation. Numerical results across ten city scenarios demonstrate that SiFo (i) achieves higher CSI-capture efficiency than separately trained site-specific learning baselines under the same target-site labeled budget, (ii) approaches the high-overhead 3GPP NR Type-II feedback reference using only RSRP measurements collected during online SSB probing, and (iii) converts the high CSI-capture efficiency and low overhead into effective spectral efficiency improvement under limited target-site data.

We present a novel Parameter-Efficient Fine-Tuning (PEFT) method, dubbed as Adaptive Freezing of Low Rank Adaptation (AFLoRA). Specifically, for each pre-trained frozen weight tensor, we add a parallel path of trainable low-rank matrices, namely a down-projection and an up-projection matrix, each of which is followed by a feature transformation vector. Based on a novel freezing score, we the incrementally freeze these projection matrices during fine-tuning to reduce the computation and alleviate over-fitting. Our experimental results demonstrate that we can achieve state-of-the-art performance with an average improvement of up to 0.85% as evaluated on GLUE benchmark while yeilding up to 9.5times fewer average trainable parameters. While compared in terms of runtime, AFLoRA can yield up to 1.86times improvement as opposed to similar PEFT alternatives. Besides the practical utility of our approach, we provide insights on the trainability requirements of LoRA paths at different modules and the freezing schedule for the different projection matrices. Code will be released.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

This research addresses the challenge of developing a universal deepfake detector that can effectively identify unseen deepfake images despite limited training data. Existing frequency-based paradigms have relied on frequency-level artifacts introduced during the up-sampling in GAN pipelines to detect forgeries. However, the rapid advancements in synthesis technology have led to specific artifacts for each generation model. Consequently, these detectors have exhibited a lack of proficiency in learning the frequency domain and tend to overfit to the artifacts present in the training data, leading to suboptimal performance on unseen sources. To address this issue, we introduce a novel frequency-aware approach called FreqNet, centered around frequency domain learning, specifically designed to enhance the generalizability of deepfake detectors. Our method forces the detector to continuously focus on high-frequency information, exploiting high-frequency representation of features across spatial and channel dimensions. Additionally, we incorporate a straightforward frequency domain learning module to learn source-agnostic features. It involves convolutional layers applied to both the phase spectrum and amplitude spectrum between the Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (iFFT). Extensive experimentation involving 17 GANs demonstrates the effectiveness of our proposed method, showcasing state-of-the-art performance (+9.8\%) while requiring fewer parameters. The code is available at {\cred https://github.com/chuangchuangtan/FreqNet-DeepfakeDetection}.

Feed-forward 3D Gaussian Splatting (3DGS) has emerged as a highly effective solution for novel view synthesis. Existing methods predominantly rely on a pixel-aligned Gaussian prediction paradigm, where each 2D pixel is mapped to a 3D Gaussian. We rethink this widely adopted formulation and identify several inherent limitations: it renders the reconstructed 3D models heavily dependent on the number of input views, leads to view-biased density distributions, and introduces alignment errors, particularly when source views contain occlusions or low texture. To address these challenges, we introduce VolSplat, a new multi-view feed-forward paradigm that replaces pixel alignment with voxel-aligned Gaussians. By directly predicting Gaussians from a predicted 3D voxel grid, it overcomes pixel alignment's reliance on error-prone 2D feature matching, ensuring robust multi-view consistency. Furthermore, it enables adaptive control over Gaussian density based on 3D scene complexity, yielding more faithful Gaussian point clouds, improved geometric consistency, and enhanced novel-view rendering quality. Experiments on widely used benchmarks including RealEstate10K and ScanNet demonstrate that VolSplat achieves state-of-the-art performance while producing more plausible and view-consistent Gaussian reconstructions. In addition to superior results, our approach establishes a more scalable framework for feed-forward 3D reconstruction with denser and more robust representations, paving the way for further research in wider communities. The video results, code and trained models are available on our project page: https://lhmd.top/volsplat.

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

With advancements in satellite imaging technology, acquiring high-resolution multi-view satellite imagery has become increasingly accessible, enabling rapid and location-independent ground model reconstruction. However, traditional stereo matching methods struggle to capture fine details, and while neural radiance fields (NeRFs) achieve high-quality reconstructions, their training time is prohibitively long. Moreover, challenges such as low visibility of building facades, illumination and style differences between pixels, and weakly textured regions in satellite imagery further make it hard to reconstruct reasonable terrain geometry and detailed building facades. To address these issues, we propose Sat-DN, a novel framework leveraging a progressively trained multi-resolution hash grid reconstruction architecture with explicit depth guidance and surface normal consistency constraints to enhance reconstruction quality. The multi-resolution hash grid accelerates training, while the progressive strategy incrementally increases the learning frequency, using coarse low-frequency geometry to guide the reconstruction of fine high-frequency details. The depth and normal constraints ensure a clear building outline and correct planar distribution. Extensive experiments on the DFC2019 dataset demonstrate that Sat-DN outperforms existing methods, achieving state-of-the-art results in both qualitative and quantitative evaluations. The code is available at https://github.com/costune/SatDN.

Existing video recognition algorithms always conduct different training pipelines for inputs with different frame numbers, which requires repetitive training operations and multiplying storage costs. If we evaluate the model using other frames which are not used in training, we observe the performance will drop significantly (see Fig.1), which is summarized as Temporal Frequency Deviation phenomenon. To fix this issue, we propose a general framework, named Frame Flexible Network (FFN), which not only enables the model to be evaluated at different frames to adjust its computation, but also reduces the memory costs of storing multiple models significantly. Concretely, FFN integrates several sets of training sequences, involves Multi-Frequency Alignment (MFAL) to learn temporal frequency invariant representations, and leverages Multi-Frequency Adaptation (MFAD) to further strengthen the representation abilities. Comprehensive empirical validations using various architectures and popular benchmarks solidly demonstrate the effectiveness and generalization of FFN (e.g., 7.08/5.15/2.17% performance gain at Frame 4/8/16 on Something-Something V1 dataset over Uniformer). Code is available at https://github.com/BeSpontaneous/FFN.

Dynamic radiance fields have emerged as a promising approach for generating novel views from a monocular video. However, previous methods enforce the geometric consistency to dynamic radiance fields only between adjacent input frames, making it difficult to represent the global scene geometry and degenerates at the viewpoint that is spatio-temporally distant from the input camera trajectory. To solve this problem, we introduce point-based dynamic radiance fields (Point-DynRF), a novel framework where the global geometric information and the volume rendering process are trained by neural point clouds and dynamic radiance fields, respectively. Specifically, we reconstruct neural point clouds directly from geometric proxies and optimize both radiance fields and the geometric proxies using our proposed losses, allowing them to complement each other. We validate the effectiveness of our method with experiments on the NVIDIA Dynamic Scenes Dataset and several causally captured monocular video clips.

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

In this work, we show that a single Transformer block, applied recurrently, can match the accuracy of a full-depth vision encoder at comparable inference FLOPs without intermediate feature distillation. reViT restores depth-specific transformations by representing the FFN at each recurrent depth as a convex combination of a small shared expert bank. A continuous normalized-depth coordinate programs this mixture, defining a resampleable trajectory through FFN parameter space. We evaluate this design in two regimes: supervised ImageNet-1k training and distillation from a DINOv2 teacher. Across both regimes, controlled adaptations identify weight-space merging as the strongest tested MoE family at a matching one-FFN budget, ahead of the token-dispatch and output-mixture alternatives. Trained from scratch, reViT-B/16 attains DeiT III accuracy with about 70\% fewer stored parameters. An 8-experts model distilled using only the teacher's output features retains nearly all of its DINOv2 teacher's linear-probe accuracy and transfers across classification, segmentation, and depth prediction. Elastic-depth training allows one checkpoint (trained model) to operate at multiple tested depths by resampling the same normalized coordinate interval. For fixed-depth deployment, the recurrent block can be materialized as a conventional dense graph, removing online routing and merging without changing the one-FFN-per-depth compute but expanding deployment storage.

The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based models exhibit great potential in generating high-quality images for super-resolution tasks. However, existing models encounter difficulties in directly predicting high-frequency information of wide bandwidth by solely utilizing the high-resolution ground truth as the target for all sampling timesteps. To tackle this problem and achieve higher-quality super-resolution, we propose a novel Frequency Domain-guided multiscale Diffusion model (FDDiff), which decomposes the high-frequency information complementing process into finer-grained steps. In particular, a wavelet packet-based frequency complement chain is developed to provide multiscale intermediate targets with increasing bandwidth for reverse diffusion process. Then FDDiff guides reverse diffusion process to progressively complement the missing high-frequency details over timesteps. Moreover, we design a multiscale frequency refinement network to predict the required high-frequency components at multiple scales within one unified network. Comprehensive evaluations on popular benchmarks are conducted, and demonstrate that FDDiff outperforms prior generative methods with higher-fidelity super-resolution results.

Modern metrics for generative learning like Fréchet Inception Distance (FID) and DINOv2-Fréchet Distance (FD-DINOv2) demonstrate impressive performance. However, they suffer from various shortcomings, like a bias towards specific generators and datasets. To address this problem, we propose the Fréchet Wavelet Distance (FWD) as a domain-agnostic metric based on the Wavelet Packet Transform (W_p). FWD provides a sight across a broad spectrum of frequencies in images with a high resolution, preserving both spatial and textural aspects. Specifically, we use W_p to project generated and real images to the packet coefficient space. We then compute the Fréchet distance with the resultant coefficients to evaluate the quality of a generator. This metric is general-purpose and dataset-domain agnostic, as it does not rely on any pre-trained network, while being more interpretable due to its ability to compute Fréchet distance per packet, enhancing transparency. We conclude with an extensive evaluation of a wide variety of generators across various datasets that the proposed FWD can generalize and improve robustness to domain shifts and various corruptions compared to other metrics.

Consistent 3D geometry estimation from streaming RGB input is crucial for real-world applications such as autonomous driving, embodied AI, and large-scale reconstruction. While modern monocular geometry foundation models achieve strong single-image accuracy, they exhibit severe temporal inconsistency on continuous input, notably dominated by scale--shift drifting. Through targeted empirical analysis, we trace this instability to its root cause: fluctuations in latent feature statistics, whose mean and variance directly determine the predicted depth's scale and shift. Building on this insight, we introduce Dynamic Feature Normalization (DyFN), a lightweight, causal recurrent module that dynamically and robustly modulates feature statistics to maintain stable geometry over time. We adapt powerful pretrained monocular geometry models for streaming by finetuning only DyFN, a mere 2\% additional parameters, while keeping the backbone frozen, thereby achieving temporal consistency without compromising single-image accuracy. Extensive experiments across four benchmarks show that DyFN effectively eliminates temporal artifacts such as disjointed layering and positional jitter, and achieves state-of-the-art temporal stability, improving over prior streaming methods by up to 14\% and even outperforming heavier non-causal video baselines. Project Page: https://shawlyu.github.io/DyFN