Gabor Convolutional Layers in Deep Learning

• Gabor convolutional layers are a family of CNN operators where kernels are parameterized using Gabor functions to enforce orientation, frequency, phase, and scale selectivity.
• They reduce the number of trainable parameters and enhance model interpretability by replacing unconstrained filters with a small set of physically meaningful scalars.
• They are applied across diverse domains—from image recognition and signal processing to seismic interpretation—improving robustness, efficiency, and convergence speed.

Gabor convolutional layers are convolutional operators in which spatial or temporal kernels are parameterized, initialized, constrained, modulated, or replaced by Gabor functions or Gabor-derived filter banks. In contemporary deep learning, they appear in several distinct forms: fully learnable analytic kernels, fixed or partially trainable Gabor banks, landmark-modulated orientation layers, deformable Gabor convolutions, complex Gabor front ends for raw signals, and mixture-of-Gabor synthesis dictionaries. Across image recognition, denoising, adversarial robustness, seismic facies classification, hyperspectral image classification, 3D medical segmentation, raw-speech modeling, and underwater acoustic classification, the common objective is to impose explicit orientation-, frequency-, phase-, and scale-selective structure on convolutional representations while improving interpretability, reducing free parameters, or increasing robustness (Alekseev et al., 2019, Pérez et al., 2019, Qin et al., 2021).

1. Foundations and scope

Gabor-based convolutional design rests on the long-standing observation that orientation-selective image representations are naturally described by Gabor filters. One line of work emphasizes this observation directly: natural-image denoising networks were explicitly constrained so that their filters are learned 2D real Gabor filters, motivated by the fact that Gabor-like filters have been observed in the early layers of CNN classifiers and even throughout low-level image processing networks (Janjušević et al., 2022). A second line places Gabor filters inside formal feature-extraction theory. The generalized semi-discrete-frame framework permits distinct frame families in different layers, including Gabor frames, and proves translation-invariance together with deformation-stability for a broader class of deformations than the wavelet-only setting (Wiatowski et al., 2015). A third line studies fixed Gabor-scattering architectures for audio, where layer-wise invariances arise from cascaded Gabor transforms, modulus nonlinearities, and low-pass pooling (Bammer et al., 2017).

Within trainable CNNs, the most recurrent motivation is that standard DCNNs are limited in modeling orientation transformation by the internal mechanism, or that unconstrained kernels are statistically inefficient when data are scarce or noisy. This motivation is explicit in Orientation Convolution Networks for image recognition, in seismic interpretation under low signal-to-noise ratios, in hyperspectral classification with small training sets, and in biomedical imaging with complex geometric structure (Qin et al., 2021, Wang et al., 2023, Liu et al., 2019, Gong et al., 2020).

Accordingly, “Gabor convolutional layer” does not denote a single architecture. It denotes a family of constructions in which convolutional kernels inherit the analytic form, frame structure, or modulation behavior of Gabor functions. Some variants learn all Gabor parameters through backpropagation; some freeze a handcrafted or preprocessed bank; some combine fixed Gabor kernels with ordinary trainable kernels; some treat Gabor functions as masks that modulate a learned kernel; and some use Gabor parameterizations only in selected layers while leaving the remainder of the network conventional (Sarwar et al., 2017, Wong et al., 2022, Qin et al., 2021).

2. Mathematical forms of Gabor kernels

The most common 2D real-valued formulation used in CNNs is

$$g(x,y;\lambda,\theta,\psi,\sigma,\gamma) = \exp\!\Bigl(-\frac{x'^2+\gamma^2y'^2}{2\sigma^2}\Bigr) \cos\!\Bigl(2\pi\frac{x'}{\lambda}+\psi\Bigr),$$

with rotated coordinates

$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$

Here $\lambda$ is the wavelength, $\theta$ the orientation, $\psi$ the phase offset, $\sigma$ the Gaussian-envelope standard deviation, and $\gamma$ the spatial aspect ratio. This formulation appears, with minor notational variation, in work on robustness, seismic interpretation, 3D segmentation, deformable Gabor convolution, and energy-efficient CNN training (Pérez et al., 2019, Wang et al., 2023, Wong et al., 2022, Gong et al., 2020, Sarwar et al., 2017).

Several papers adopt equivalent but differently parameterized forms. In underwater acoustic classification, the kernel is written as a normalized real Gabor with parameters $(\sigma,\gamma,f_0,\phi,\theta)$, where $f_0$ is the center frequency and $\phi$ is the phase offset; the layer uses a centered $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$0 grid and fixes $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$1 (Domingos et al., 9 Dec 2025). In GDLNet, the authors use a vectorized parameterization

$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$2

where $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$3 is an overall scale, $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$4 controls spatial extent and aspect ratio, $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$5 is the center-frequency vector, and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$6 is the phase offset; each convolutional filter can be a sum of several such atoms (Janjušević et al., 2022).

Other domains motivate more specialized parameter sets. In raw speech, CGCNN uses a complex 1D Gabor impulse response

$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$7

with trainable cutoff frequencies $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$8 from which $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$9 and $\lambda$0 are derived, so that each first-layer filter remains a band-limited Gabor with an interpretable bandwidth (Noé et al., 2020). In hyperspectral image classification, “phase-induced” Gabor kernels collapse the traditional complex real and imaginary parts into a single real-valued filter

$\lambda$1

where the learnable phase $\lambda$2 mixes low-frequency and high-frequency components in real arithmetic (Liu et al., 2019).

These parameterizations differ in notation, but they preserve the same structural decomposition: a localized Gaussian envelope modulates a sinusoidal carrier, and learning is transferred from unconstrained pixel-wise weights to a small set of physically interpretable scalars.

3. Learning mechanisms and optimization

The standard trainable formulation synthesizes each kernel from learnable Gabor parameters during the forward pass and uses ordinary backpropagation through the closed-form generator. GaborNet replaces the first convolutional layer by kernels constrained to the real Gabor function, learning only four scalars per filter, namely $\lambda$3, instead of the full $\lambda$4 weight map (Alekseev et al., 2019). Seismic interpretation similarly replaces the conventional first-layer tensor by learnable vectors $\lambda$5, evaluates the kernel on the spatial grid at each forward pass, and clips $\lambda$6 and $\lambda$7 after each gradient step to encode expected frequency bands and dip ranges in seismic images (Wang et al., 2023). In underwater acoustics, all learnable parameters remain trainable under standard autodiff, with positivity enforced for $\lambda$8 and a fixed $\lambda$9; the first Gabor layer decodes parameter vectors into 64 real $\theta$0 kernels at each forward pass (Domingos et al., 9 Dec 2025). The 3D segmentation formulation makes all Gabor parameters trainable and derives explicit gradients with respect to $\theta$1, while enforcing validity through sigmoid- or softplus-based parameter mappings (Wong et al., 2022).

A distinct strategy appears in Orientation Convolution Networks, where Gabor structure is not learned end-to-end from random initialization inside each convolutional layer. Instead, the method first constructs an original Gabor-filter bank $\theta$2 and learns a reduced set of Landmark Gabor Filters through a joint low-rank and sparse factorization,

$\theta$3

At convergence, $\theta$4, so the landmark bank is $\theta$5 and each original filter is approximated by a sparse linear combination of the landmarks. These learned landmarks are then frozen and used to modulate a standard CNN kernel $\theta$6 by element-wise multiplication, while only $\theta$7 is updated during backpropagation (Qin et al., 2021).

Other variants reduce training cost by limiting or avoiding parameter updates for Gabor filters. In energy-efficient CNN training, certain convolutional kernels are replaced by fixed Gabor filters, and a partial-training regime allows them to be trainable for only a small fraction $\theta$8 of total epochs before freezing them (Sarwar et al., 2017). Deformable Gabor Feature Networks keep the analytic Gabor parameters fixed a priori but learn scale masks $\theta$9 and deformable offsets; adaptive Gabor filters are formed as $\psi$0 and combined with deformable convolution responses (Gong et al., 2020). Hyperspectral Gabor-Nets learn four parameters per filter—orientation, frequency, scale, and phase—with closed-form derivatives for each parameter and random phase initialization in $\psi$1 to improve convergence behavior (Liu et al., 2019).

Across these variants, the optimization problem is shifted from unconstrained kernel estimation to structured parameter estimation. The main consequence is a drastic reduction in degrees of freedom per filter, although the precise training dynamics depend on whether the Gabor components are fixed, fully trainable, partially trainable, or used only as modulators.

4. Architectural patterns

The architectural role of a Gabor convolutional layer varies markedly across papers.

Pattern	Core mechanism	Representative papers
First-layer parametric Gabor	Generate the initial convolutional kernels from learnable Gabor parameters	(Alekseev et al., 2019, Wang et al., 2023, Domingos et al., 9 Dec 2025)
Fixed or partially trained Gabor kernels	Replace some kernels by fixed Gabor filters, optionally training them for only part of the schedule	(Sarwar et al., 2017)
Full-network phase-induced Gabor CNN	Replace every standard 2D convolutional kernel by a real-valued phase-induced Gabor filter	(Liu et al., 2019)
Landmark-modulated orientation convolution	Multiply a learned kernel by landmark Gabor masks indexed by orientation or scale	(Qin et al., 2021)
Complex Gabor front end	Convolve the raw waveform with complex Gabor kernels and continue with complex-valued layers	(Noé et al., 2020)
Deformable/adaptive Gabor convolution	Combine analytic Gabor kernels with learned masks and deformable sampling offsets	(Gong et al., 2020)
Mixture-of-Gabor synthesis dictionary	Represent analysis and synthesis convolutional filters as sums of Gabor atoms	(Janjušević et al., 2022)

The most common design choice is to place Gabor structure in the earliest layers. GaborNet replaces only the first convolutional layer in Dogs vs Cats, AffectNet, and AlexNet on ImageNet (Alekseev et al., 2019). GSE ResNeXt replaces only the very first convolutional block by a learnable GaborConv1 with 64 filters of size $\psi$2 and stride 2, followed by ordinary ResNeXt bottlenecks with cardinality $\psi$3 and squeeze-and-excitation attention (Domingos et al., 9 Dec 2025). The seismic U-Net places an $\psi$4 Gabor layer at the front and leaves deeper layers as standard $\psi$5 convolutions (Wang et al., 2023). Robustness-oriented image classifiers replace the first one or several convolutional layers in LeNet, AlexNet, VGG16, and WideResNet with Gabor layers, using depthwise Gabor filtering followed by a $\psi$6 pointwise convolution (Pérez et al., 2019).

Other papers push Gabor parameterization more deeply into the network. Gabor-Nets for hyperspectral classification replace every standard 2D convolutional kernel with a phase-induced Gabor kernel, so that each conv layer is represented by parameter matrices for $\psi$7 rather than free weight tensors (Liu et al., 2019). GDLNet uses mixture-of-Gabor analysis and synthesis convolutions throughout an unrolled ISTA-style denoiser, with soft-thresholding as the only nonlinearity and no batch normalization or ReLU (Janjušević et al., 2022). In 3D segmentation, mixed-kernel designs combine conventional and Gabor-based kernels inside a compact V-Net-style architecture (Wong et al., 2022). In deformable biomedical classification, selected high-level $\psi$8 layers are replaced by DGConv blocks that jointly model orientation-selective structure and geometric deformation (Gong et al., 2020).

A separate branch of work uses Gabor layers primarily for compression or energy reduction. One approach constrains early VGG-16 or altered ResNet-20 layers to Gabor functions with learnable parameters and then prunes channels or kernels aggressively (Imamura et al., 2021). Another uses fixed Gabor filters in LeNet or Network-in-Network so that backpropagation and weight updates are skipped for those kernels, thereby lowering training energy, memory-access energy, and storage (Sarwar et al., 2017).

5. Analytical properties and inductive biases

Gabor-based convolutional constructions admit several analytical interpretations that are not typically available for generic learned kernels. In the semi-discrete-frame formulation, generalized deep convolutional feature extractors built from Gabor frames are translation-invariant and deformation-stable, and the proofs are detached from the specific algebraic structure of the underlying frames by continuous frame theory (Wiatowski et al., 2015). In Gabor scattering for audio, the entire feature extractor is contractive when the upper frame bounds satisfy $\psi$9, and the two-layer construction yields specific invariances: the first layer becomes invariant to slow changes in envelope, while the second layer becomes invariant to carrier pitch and sensitive to amplitude-modulation rate (Bammer et al., 2017).

For trainable Gabor CNNs, one of the strongest formal results concerns Lipschitz behavior. Because the filter is given in closed form, a valid Lipschitz constant for a sampled 2D Gabor layer under circular convolution can be bounded by

$\sigma$0

where $\sigma$1 and $\sigma$2 for $\sigma$3, with an analogous definition for $\sigma$4 and $\sigma$5. This bound motivates regularizers of the form

$\sigma$6

or

$\sigma$7

which were introduced specifically to enhance adversarial robustness (Pérez et al., 2019).

Several papers tie the usefulness of Gabor layers to domain-specific inductive biases. In raw speech, the Gaussian envelope is said to give the optimal time-frequency trade-off and the theoretical minimum of the time-frequency uncertainty principle, while the complex representation preserves phase information and supports analytic-signal extraction for instantaneous-frequency cues (Noé et al., 2020). In underwater acoustics, each Gabor kernel is described as a 2D band-pass filter localized in frequency and orientation, and the first Gabor layer decomposes spectrograms of ship-radiated noise into a bank of sub-bands before channel attention reweights them (Domingos et al., 9 Dec 2025). In GDLNet, the learned dictionaries consist of clean, centered oriented edge detectors, and untied learned scale parameters across layers are interpreted as evidence that the network acts as an accelerated sparse-coding solver (Janjušević et al., 2022). In seismic interpretation, the claim is that seismic images are dominated by diverse wavelet textures corresponding to seismic facies and are suitably represented by Gabor functions (Wang et al., 2023).

These results do not imply that Gabor layers are universally optimal. They do show, however, that the parameterization introduces explicit control over orientation, bandwidth, phase, and spatial extent, and that this control can be connected to invariance, stability, or interpretability arguments more directly than in unconstrained convolution.

6. Empirical landscape, applications, and trade-offs

In image recognition under orientation variability, Orientation Convolution Networks report substantial gains. On MNIST-rot, OCN with 4 orientations and $\sigma$8 kernels achieves $\sigma$9 error, compared with $\gamma$0 for GCN and $\gamma$1 for ORN, while parameter counts remain approximately $\gamma$2M versus more than $\gamma$3M for the baselines. On CIFAR-10 and CIFAR-100, OCN-ResNet-40 with $\gamma$4M parameters yields $\gamma$5 error, improving on plain ResNet-40 at $\gamma$6 and matching Wide ResNet-40 with $\gamma$7M parameters at significantly fewer FLOPs; the timing overhead is only about $\gamma$8–$\gamma$9 per forward or backward epoch, with $(\sigma,\gamma,f_0,\phi,\theta)$0–$(\sigma,\gamma,f_0,\phi,\theta)$1 fewer overall parameters (Qin et al., 2021). In adversarially robust vision models, clean-accuracy changes are modest—often under $(\sigma,\gamma,f_0,\phi,\theta)$2 and at most about $(\sigma,\gamma,f_0,\phi,\theta)$3—while adversarial accuracy can improve substantially; for example, on CIFAR-10 with VGG16 under PGD-$(\sigma,\gamma,f_0,\phi,\theta)$4 at $(\sigma,\gamma,f_0,\phi,\theta)$5, accuracy moves from $(\sigma,\gamma,f_0,\phi,\theta)$6 to $(\sigma,\gamma,f_0,\phi,\theta)$7, and to $(\sigma,\gamma,f_0,\phi,\theta)$8 with the Lipschitz-based regularizer, while clean test accuracy changes from $(\sigma,\gamma,f_0,\phi,\theta)$9 to $f_0$0 (Pérez et al., 2019). In deformable biomedical classification, DGConv improves INbreast-Deform AUC from $f_0$1 to $f_0$2, raises ChestX-ray14 average AUC from $f_0$3 to $f_0$4 off-the-shelf and from $f_0$5 to $f_0$6 when fine-tuned, and improves noisy CIFAR-10 from $f_0$7 to $f_0$8 (Gong et al., 2020).

In small-sample remote sensing and seismic interpretation, the gains are tied to parameter reduction and noise robustness. On Pavia University with 50 samples per class, Gabor-Net reaches $f_0$9, compared with $\phi$0 for a regular CNN, $\phi$1 for a 3-D CNN, and $\phi$2 for a CNN using Gabor features as additional input; on Houston, Gabor-Net obtains $\phi$3 versus $\phi$4 for the regular CNN (Liu et al., 2019). On the Netherland F3 seismic dataset, an $\phi$5 Gabor first layer converges roughly twice as fast, about 45 epochs versus about 90 for standard first-layer convolutions, and maintains superior performance under lower SNR. Under $\phi$6 salt-and-pepper noise, the Gabor model reaches PA/MCA/FWIU of $\phi$7, whereas $\phi$8 and $\phi$9 standard convolutions reach $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$00 and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$01 respectively; under speckle noise with variance $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$02, the corresponding values are $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$03 for Gabor, $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$04 for $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$05 standard convolution, and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$06 for $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$07 standard convolution (Wang et al., 2023).

In signal processing applications, learnable or complex Gabor front ends often improve both convergence and interpretability. On TIMIT phoneme recognition, CGCNN obtains an average Phone Error Rate of $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$08 and best $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$09, compared with about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$10 for SincNet and about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$11 for Gabor-CNN-CTC, while preserving an interpretable band-limited first layer through trainable cutoffs $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$12 (Noé et al., 2020). In underwater acoustic classification, GSE ResNeXt reaches $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$13 MCC on the “beginning vs end” vessel-generalization task, compared with $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$14 for Xception, $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$15 for ResNet-18, and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$16 for MobileNetV2. The Gabor-fronted model reaches a stable validation MCC by epoch 33 rather than epoch 46, a $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$17 faster convergence rate, and its validation curves are smoother (Domingos et al., 9 Dec 2025).

In low-level restoration and segmentation, Gabor parameterizations can approach larger unconstrained networks with far fewer parameters. On BSD68 denoising, GDLNet-S with MoG order 3 and 188k parameters reports PSNRs of approximately $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$18 at noise levels $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$19, compared with DnCNN at 556k parameters and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$20, and CDLNet-S at 507k parameters and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$21; blind denoising with noise-adaptive thresholds retains “near-perfect” generalization across $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$22 (Janjušević et al., 2022). In 3D brain MRI segmentation on 43 volumes with 19 anatomical structures, a mixed conventional-plus-Gabor design reaches an average Dice coefficient of about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$23 with only 1.60M parameters, matching a conventional-only variant at $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$24M parameters and outperforming a pure-Gabor design at about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$25 with 1.53M parameters; the paper also states that the resulting network is 44 times smaller than the original V-Net with 71M parameters (Wong et al., 2022).

Compression- and efficiency-oriented studies treat Gabor layers as structured replacements for early convolutions. In one CIFAR-10 study, the first layer of VGG-16 has 192 kernels or features, but learning Gabor filters requires an average of 29.4 kernels; on an altered ResNet-20, an average of $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$26 and $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$27 of kernels in the first and second layer can be removed, and the first layer of VGG experiences about a $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$28 drop in MACs with zero accuracy loss (Imamura et al., 2021). Fixed-Gabor CNN training yields $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$29–$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$30 improvement in training energy, up to $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$31 in training time, up to $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$32 in storage requirements, and up to $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$33 in memory-access energy, with accuracy degradation within $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$34–$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$35 of the baseline; partial training of Gabor kernels for $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$36–$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$37 of epochs recovers about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$38–$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$39 accuracy (Sarwar et al., 2017).

The limitations are equally consistent. Excessive fixation of Gabor kernels in deeper layers can cause substantial accuracy degradation; for example, using fixed Gabor kernels in both early LeNet layers incurs a $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$40 accuracy loss on MNIST, whereas a balanced half-Gabor design limits the loss to $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$41 (Sarwar et al., 2017). In first-layer Gabor AlexNet on ImageNet, standard AlexNet is slightly faster in the first 10 epochs and the final converged accuracy is the same after the learning-rate drops, even though the Gabor model leads by about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$42 during epochs 10–30 (Alekseev et al., 2019). Per-epoch training can also be slower because kernels must be synthesized and differentiated, with a reported overhead of about $$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$43–$$x' = x\cos\theta + y\sin\theta,\qquad y' = -x\sin\theta + y\cos\theta.$$44 per epoch in GaborNet (Alekseev et al., 2019). In hyperspectral image classification, the learned maps can oversmooth small objects or fine edges, and the strong band-pass or orientational prior may be suboptimal when the domain is not well described by local harmonic patterns (Liu et al., 2019).

Taken together, these results establish Gabor convolutional layers as a heterogeneous but technically coherent class of structured convolutions. Their central promise lies not in a single universal accuracy advantage, but in a repeatable combination of analytic inductive bias, lower-dimensional parameterization, and domain-aligned feature geometry.