arXiv subjects

Feng-Lei Fan

Publications and source records attributed to Feng-Lei Fan.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics as Code: On Model Compression via Dynamic System

The escalating size of pretrained neural networks has rendered model compression a prerequisite for deployment under stringent memory and compute constraints. With the irrational winding as an example, earlier work introduced a dynamic system (DS) paradigm that reconceptualizes compression as compact weight representation: high-dimensional parameters are encoded by the index of a trajectory produced by a dynamic system, from which the vector is recovered during decompression. This mechanism is fundamentally distinct from pruning, quantization, knowledge distillation, and low-rank decomposition. Along this direction, we prove that under a Diophantine condition, a finite trajectory of $M = O(ε^{-(d+ν)})$ states in the irrational winding constitutes an $ε$-net over the $d$-dimensional weight space, thereby linking state resolution, decompression error, and compression ratio in a predictable manner. Furthermore, we propose a generalized DS-based model compression framework by unifying four DS families---space-filling curves (Hilbert, Peano, Morton/Z-order, Snake), chaotic systems (Lorenz), congruential and pseudo-random generators (LCG, PCG), and low-discrepancy sequences (Halton). Also, we introduce the KD-tree and coordinate-template acceleration to scale to large models as well as outlier identification to control the error. Experiments on ResNet-18 and Qwen2.5-1.5B/Qwen1.5-7B validate that DS-based compression achieves competitive compression ratios without post-hoc retraining, with controllable decompression error and flexible state-space design, establishing it as a principled and practical compression approach.

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arXiv2026

Disentangle and Drop: Robust Universal Removal of Image Watermarks via Reconstructive Grayscale Residual Decomposition

Invisible image watermarks are commonly evaluated against benign postprocessing operations such as compression, resizing, blur, and color changes. These tests leave out a different threat: a learned remover that preserves semantic image content while discarding residual evidence that carries the payload. We propose Disentangle and Drop (DnD), an attack that is agnostic to the watermark method and treats watermark removal as a representation routing problem. DnD decomposes a watermarked image into a semantic grayscale carrier and an auxiliary residual branch, and then suppresses the residual branch to reduce watermark evidence. The model is trained with latent spectral perturbations and low-strength diffusion exposure so that the drop operation remains stable under adaptive reconstruction. Experiments on seven representative watermark families show that one shared operating setting gives competitive removal with high visual fidelity. Operating scans and ablations separate usable attacks from image-damaging settings: stronger noise or diffusion can raise removal scores by damaging the image, while the practical regime comes from dropping the residual latent. These results argue for evaluating watermark robustness against learned removal at the representation level, not only against conventional image edits.

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arXiv2026

Self-Improving is Often Sudden: Enlightenment-style Finetuning for Large-Scale Models

The pursuit of autonomously self-improving models has attracted growing interest in the era of large-scale foundation models. Drawing inspiration from the concept of "enlightenment" or "aha moment" in human brain, we hypothesize that large models exhibit an analogous enlightenment phenomenon-a latent capacity for sudden capability boost. Then, we propose Enlightenment, a novel training-free post-tuning paradigm for large-scale models. Our approach modifies shortcuts for key modules/layers without weight updates, while existing training-free ones predominantly manipulate attention weights. We introduce two architecture-specific instantiations: i) For large language models, we propose attention head-mixing shortcuts that recalibrate attention weights by linking the initial attention head's output to all other target heads, modulated by an adaptive scaling factor initialization strategy. ii) For vision-language models, we apply a lightweight scalar-modulated factor to residual connections in the decoder layers, regulating information flow. Extensive experiments show that Enlightenment efficiently unlocks the latent potential of pre-trained networks, yielding remarkable performance improvements across diverse benchmarks and models.

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arXiv2026

On Explicit Super-Expressive Approximation for Neural Networks

In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error. We resolve this issue by introducing the Chinese Remainder Theorem as a constructive encoding mechanism. For Lipschitz continuous functions on $[0,1]^D$, we construct a width-$\max\{D,4\}$, depth-$5$ network with explicit parameter-error trade-offs. For Hölder-smooth functions in $C^{r,γ}_A\left([0,1]^D\right)$, our fixed network of width $\max\{2D,\ D+5N+1\}$ and depth $r + 9$ achieves the parameter magnitude $\mathcal{P}$ bounded by $\log_2 \mathcal{P}=\mathcal{O}\bigl(\varepsilon^{-2D/(r+γ)}\log(1/\varepsilon)\bigr)$. This is the dual result compared to those in the parameter-bounded and architecture-unbounded paradigm.

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arXiv2026

No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural Networks

In the past decade, many successful networks are on novel architectures, which almost exclusively use the same type of neurons. Recently, more and more deep learning studies have been inspired by the idea of NeuroAI and the neuronal diversity observed in human brains, leading to the proposal of novel artificial neuron designs. Designing well-performing neurons represents a new dimension relative to designing well-performing neural architectures. Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, in our brain, neurons are often task-based. In this study, we address the following question: since the human brain is a task-based neuron user, can the artificial network design go from the task-based architecture design to the task-based neuron design? Since methodologically there are no one-size-fits-all neurons, given the same structure, task-based neurons can enhance the feature representation ability relative to the existing universal neurons due to the intrinsic inductive bias for the task. Specifically, we propose a two-step framework for prototyping task-based neurons. As the initial step, we evaluate the proposed framework using polynomials as base functions. Empirically, systematic experimental results on synthetic data, classic benchmarks, and real-world applications show that the proposed task-based neuron design is not only feasible but also delivers competitive performance over other state-of-the-art models.

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arXiv2026

Big2Small: A Unifying Neural Network Framework for Model Compression

With the development of foundational models, model compression has become a critical requirement. Various model compression approaches have been proposed such as low-rank decomposition, pruning, quantization, ergodic dynamic systems, and knowledge distillation, which are based on different heuristics. To elevate the field from fragmentation to a principled discipline, we construct a unifying mathematical framework for model compression grounded in measure theory. We further demonstrate that each model compression technique is mathematically equivalent to a neural network subject to a regularization. Building upon this mathematical and structural equivalence, we propose an experimentally-verified data-free model compression framework, termed \textit{Big2Small}, which translates Implicit Neural Representations (INRs) from data domain to the domain of network parameters. \textit{Big2Small} trains compact INRs to encode the weights of larger models and reconstruct the weights during inference. To enhance reconstruction fidelity, we introduce Outlier-Aware Preprocessing to handle extreme weight values and a Frequency-Aware Loss function to preserve high-frequency details. Experiments on image classification and segmentation demonstrate that \textit{Big2Small} achieves competitive accuracy and compression ratios compared to state-of-the-art baselines.

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arXiv2026

NeuronSeek: On Stability and Expressivity of Task-driven Neurons

Drawing inspiration from our human brain that designs different neurons for different tasks, recent advances in deep learning have explored modifying a network's neurons to develop so-called task-driven neurons. Prototyping task-driven neurons (referred to as NeuronSeek) employs symbolic regression (SR) to discover the optimal neuron formulation and construct a network from these optimized neurons. Along this direction, this work replaces symbolic regression with tensor decomposition (TD) to discover optimal neuronal formulations, offering enhanced stability and faster convergence. Furthermore, we establish theoretical guarantees that modifying the aggregation functions with common activation functions can empower a network with a fixed number of parameters to approximate any continuous function with an arbitrarily small error, providing a rigorous mathematical foundation for the NeuronSeek framework. Extensive empirical evaluations demonstrate that our NeuronSeek-TD framework not only achieves superior stability, but also is competitive relative to the state-of-the-art models across diverse benchmarks. The code is available at https://github.com/HanyuPei22/NeuronSeek.

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arXiv2026

A Survey on Medical Image Compression: From Traditional to Learning-Based Approaches

The exponential growth of medical imaging has created significant challenges in data storage, transmission, and management for healthcare systems. In this vein, efficient compression becomes increasingly important. Unlike natural image compression, medical image compression prioritizes preserving diagnostic details and structural integrity, imposing stricter quality requirements and demanding fast, memory-efficient algorithms that balance computational complexity with clinically acceptable reconstruction quality. Meanwhile, the medical imaging family includes a plethora of modalities, each possessing different requirements. For example, 2D medical image (e.g., X-rays, histopathological images) compression focuses on exploiting intra-slice spatial redundancy, while volumetric medical image faces require handling intra-slice and inter-slice spatial correlations, and 4D dynamic imaging (e.g., time-series CT/MRI, 4D ultrasound) additionally demands processing temporal correlations between consecutive time frames. Traditional compression methods, grounded in mathematical transforms and information theory principles, provide solid theoretical foundations, predictable performance, and high standardization levels, with extensive validation in clinical environments. In contrast, deep learning-based approaches demonstrate remarkable adaptive learning capabilities and can capture complex statistical characteristics and semantic information within medical images. This comprehensive survey establishes a two-facet taxonomy based on data structure (2D vs 3D/4D) and technical approaches (traditional vs learning-based), thereby systematically presenting the complete technological evolution, analyzing the unique technical challenges, and prospecting future directions in medical image compression.

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arXiv2025

COLI: A Hierarchical Efficient Compressor for Large Images

The escalating adoption of high-resolution, large-field-of-view imagery amplifies the need for efficient compression methodologies. Conventional techniques frequently fail to preserve critical image details, while data-driven approaches exhibit limited generalizability. Implicit Neural Representations (INRs) present a promising alternative by learning continuous mappings from spatial coordinates to pixel intensities for individual images, thereby storing network weights rather than raw pixels and avoiding the generalization problem. However, INR-based compression of large images faces challenges including slow compression speed and suboptimal compression ratios. To address these limitations, we introduce COLI (Compressor for Large Images), a novel framework leveraging Neural Representations for Videos (NeRV). First, recognizing that INR-based compression constitutes a training process, we accelerate its convergence through a pretraining-finetuning paradigm, mixed-precision training, and reformulation of the sequential loss into a parallelizable objective. Second, capitalizing on INRs' transformation of image storage constraints into weight storage, we implement Hyper-Compression, a novel post-training technique to substantially enhance compression ratios while maintaining minimal output distortion. Evaluations across two medical imaging datasets demonstrate that COLI consistently achieves competitive or superior PSNR and SSIM metrics at significantly reduced bits per pixel (bpp), while accelerating NeRV training by up to 4 times.

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arXiv2025

Depth-induced NTK: Bridging Over-parameterized Neural Networks and Deep Neural Kernels

While deep learning has achieved remarkable success across a wide range of applications, its theoretical understanding of representation learning remains limited. Deep neural kernels provide a principled framework to interpret over-parameterized neural networks by mapping hierarchical feature transformations into kernel spaces, thereby combining the expressive power of deep architectures with the analytical tractability of kernel methods. Recent advances, particularly neural tangent kernels (NTKs) derived by gradient inner products, have established connections between infinitely wide neural networks and nonparametric Bayesian inference. However, the existing NTK paradigm has been predominantly confined to the infinite-width regime, while overlooking the representational role of network depth. To address this gap, we propose a depth-induced NTK kernel based on a shortcut-related architecture, which converges to a Gaussian process as the network depth approaches infinity. We theoretically analyze the training invariance and spectrum properties of the proposed kernel, which stabilizes the kernel dynamics and mitigates degeneration. Experimental results further underscore the effectiveness of our proposed method. Our findings significantly extend the existing landscape of the neural kernel theory and provide an in-depth understanding of deep learning and the scaling law.

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arXiv2025

Compress Any Segment Anything Model (SAM)

Due to the excellent performance in yielding high-quality, zero-shot segmentation, Segment Anything Model (SAM) and its variants have been widely applied in diverse scenarios such as healthcare and intelligent manufacturing. Therefore, effectively compressing SAMs has become an increasingly pressing practical need. In this study, we propose Birkhoff, a novel data-free compression algorithm for SAM and its variants. Unlike quantization, pruning, distillation, and other compression methods, Birkhoff embodies versatility across model types, agility in deployment, faithfulness to the original model, and compactness in model size. Specifically, Birkhoff introduces a novel compression algorithm: Hyper-Compression, whose core principle is to find a dense trajectory to turn a high-dimensional parameter vector into a low-dimensional scalar. Furthermore, Birkhoff designs a dedicated linear layer operator, HyperLinear, to fuse decompression and matrix multiplication to significantly accelerate inference of the compressed SAMs. Extensive experiments on 18 SAMs in the COCO, LVIS, and SA-1B datasets show that Birkhoff performs consistently and competitively in compression time, compression ratio, post-compression performance, and inference speed. For example, Birkhoff can achieve a compression ratio of 5.17x on SAM2-B, with less than 1% performance drop without using any fine-tuning data. Moreover, the compression is finished within 60 seconds for all models.

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arXiv2025

On Expressivity of Height in Neural Networks

In this work, beyond width and depth, we augment a neural network with a new dimension called height by intra-linking neurons in the same layer to create an intra-layer hierarchy, which gives rise to the notion of height. We call a neural network characterized by width, depth, and height a 3D network. To put a 3D network in perspective, we theoretically and empirically investigate the expressivity of height. We show via bound estimation and explicit construction that given the same number of neurons and parameters, a 3D ReLU network of width $W$, depth $K$, and height $H$ has greater expressive power than a 2D network of width $H\times W$ and depth $K$, \textit{i.e.}, $\mathcal{O}((2^H-1)W)^K)$ vs $\mathcal{O}((HW)^K)$, in terms of generating more pieces in a piecewise linear function. Next, through approximation rate analysis, we show that by introducing intra-layer links into networks, a ReLU network of width $\mathcal{O}(W)$ and depth $\mathcal{O}(K)$ can approximate polynomials in $[0,1]^d$ with error $\mathcal{O}\left(2^{-2WK}\right)$, which improves $\mathcal{O}\left(W^{-K}\right)$ and $\mathcal{O}\left(2^{-K}\right)$ for fixed width networks. Lastly, numerical experiments on 5 synthetic datasets, 15 tabular datasets, and 3 image benchmarks verify that 3D networks can deliver competitive regression and classification performance.

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arXiv2024

Deep ReLU Networks Have Surprisingly Simple Polytopes

A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural networks. So far, either theoretical or empirical studies on polytopes only stay at the level of counting their number, which is far from a complete characterization. Here, we propose to study the shapes of polytopes via the number of faces of the polytope. Then, by computing and analyzing the histogram of faces across polytopes, we find that a ReLU network has relatively simple polytopes under both initialization and gradient descent, although these polytopes can be rather diverse and complicated by a specific design. This finding can be appreciated as a kind of generalized implicit bias, subjected to the intrinsic geometric constraint in space partition of a ReLU network. Next, we perform a combinatorial analysis to explain why adding depth does not generate a more complicated polytope by bounding the average number of faces of polytopes with the dimensionality. Our results concretely reveal what kind of simple functions a network learns and what will happen when a network goes deep. Also, by characterizing the shape of polytopes, the number of faces can be a novel leverage for other problems, \textit{e.g.}, serving as a generic tool to explain the power of popular shortcut networks such as ResNet and analyzing the impact of different regularization strategies on a network's space partition.

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arXiv2024

Retinal Vessel Segmentation via Neuron Programming

The accurate segmentation of retinal blood vessels plays a crucial role in the early diagnosis and treatment of various ophthalmic diseases. Designing a network model for this task requires meticulous tuning and extensive experimentation to handle the tiny and intertwined morphology of retinal blood vessels. To tackle this challenge, Neural Architecture Search (NAS) methods are developed to fully explore the space of potential network architectures and go after the most powerful one. Inspired by neuronal diversity which is the biological foundation of all kinds of intelligent behaviors in our brain, this paper introduces a novel and foundational approach to neural network design, termed ``neuron programming'', to automatically search neuronal types into a network to enhance a network's representation ability at the neuronal level, which is complementary to architecture-level enhancement done by NAS. Additionally, to mitigate the time and computational intensity of neuron programming, we develop a hypernetwork that leverages the search-derived architectural information to predict optimal neuronal configurations. Comprehensive experiments validate that neuron programming can achieve competitive performance in retinal blood segmentation, demonstrating the strong potential of neuronal diversity in medical image analysis.

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arXiv2024

Spatial-Frequency Discriminability for Revealing Adversarial Perturbations

The vulnerability of deep neural networks to adversarial perturbations has been widely perceived in the computer vision community. From a security perspective, it poses a critical risk for modern vision systems, e.g., the popular Deep Learning as a Service (DLaaS) frameworks. For protecting deep models while not modifying them, current algorithms typically detect adversarial patterns through discriminative decomposition for natural and adversarial data. However, these decompositions are either biased towards frequency resolution or spatial resolution, thus failing to capture adversarial patterns comprehensively. Also, when the detector relies on few fixed features, it is practical for an adversary to fool the model while evading the detector (i.e., defense-aware attack). Motivated by such facts, we propose a discriminative detector relying on a spatial-frequency Krawtchouk decomposition. It expands the above works from two aspects: 1) the introduced Krawtchouk basis provides better spatial-frequency discriminability, capturing the differences between natural and adversarial data comprehensively in both spatial and frequency distributions, w.r.t. the common trigonometric or wavelet basis; 2) the extensive features formed by the Krawtchouk decomposition allows for adaptive feature selection and secrecy mechanism, significantly increasing the difficulty of the defense-aware attack, w.r.t. the detector with few fixed features. Theoretical and numerical analyses demonstrate the uniqueness and usefulness of our detector, exhibiting competitive scores on several deep models and image sets against a variety of adversarial attacks.

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arXiv2024

Don't Fear Peculiar Activation Functions: EUAF and Beyond

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR10, Tiny-ImageNet, and ImageNet. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.

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arXiv2024

Quadratic Neuron-empowered Heterogeneous Autoencoder for Unsupervised Anomaly Detection

Inspired by the complexity and diversity of biological neurons, a quadratic neuron is proposed to replace the inner product in the current neuron with a simplified quadratic function. Employing such a novel type of neurons offers a new perspective on developing deep learning. When analyzing quadratic neurons, we find that there exists a function such that a heterogeneous network can approximate it well with a polynomial number of neurons but a purely conventional or quadratic network needs an exponential number of neurons to achieve the same level of error. Encouraged by this inspiring theoretical result on heterogeneous networks, we directly integrate conventional and quadratic neurons in an autoencoder to make a new type of heterogeneous autoencoders. To our best knowledge, it is the first heterogeneous autoencoder that is made of different types of neurons. Next, we apply the proposed heterogeneous autoencoder to unsupervised anomaly detection for tabular data and bearing fault signals. The anomaly detection faces difficulties such as data unknownness, anomaly feature heterogeneity, and feature unnoticeability, which is suitable for the proposed heterogeneous autoencoder. Its high feature representation ability can characterize a variety of anomaly data (heterogeneity), discriminate the anomaly from the normal (unnoticeability), and accurately learn the distribution of normal samples (unknownness). Experiments show that heterogeneous autoencoders perform competitively compared to other state-of-the-art models.

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arXiv2023

VDIP-TGV: Blind Image Deconvolution via Variational Deep Image Prior Empowered by Total Generalized Variation

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves encouraging results in the nonblind deblurring problem. However, since the relationship between images and the network architectures is unclear, it is hard to find a suitable architecture to provide sufficient constraints on the estimated blur kernels and clean images. Also, DIP uses the sparse maximum a posteriori (MAP), which is insufficient to enforce the selection of the recovery image. Recently, variational deep image prior (VDIP) was proposed to impose constraints on both blur kernels and recovery images and take the standard deviation of the image into account during the optimization process by the variational principle. However, we empirically find that VDIP struggles with processing image details and tends to generate suboptimal results when the blur kernel is large. Therefore, we combine total generalized variational (TGV) regularization with VDIP in this paper to overcome these shortcomings of VDIP. TGV is a flexible regularization that utilizes the characteristics of partial derivatives of varying orders to regularize images at different scales, reducing oil painting artifacts while maintaining sharp edges. The proposed VDIP-TGV effectively recovers image edges and details by supplementing extra gradient information through TGV. Additionally, this model is solved by the alternating direction method of multipliers (ADMM), which effectively combines traditional algorithms and deep learning methods. Experiments show that our proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and qualitatively.

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