Neural Gabor Primitives

• Neural Gabor Primitives are architectural enhancements that integrate classical Gabor bases with periodic MLPs to optimize frequency coverage in implicit neural representations.
• They employ neuron-specific, Nyquist-informed frequency modulation to minimize overlapping feature redundancy and maximize performance across audio, image, and 3D tasks.
• Empirical results show improvements in PSNR, MSE, and IoU metrics, achieving faster convergence and enhanced expressivity without additional computational cost.

Neural Gabor Primitives are architectural enhancements for implicit neural representations (INRs) that seek to unify the expressivity, frequency diversity, and efficiency associated with classical Gabor bases and periodic activation-based multilayer perceptrons (MLPs), such as SIREN. These primitives adopt explicit neuron-specific frequency modulations, often inspired by orthogonal transforms such as the Discrete Sine Transform (DST), to systematically control and diversify the frequency content encoded within neural networks. This class of architectures is particularly motivated by the limitations observed in conventional periodic-activation INRs, wherein fixed frequency multipliers give rise to hidden unit redundancy and suboptimal bandwidth utilization. Recent representative instantiations include FM-SIREN and FM-FINER, which utilize Nyquist-informed frequency assignments to reduce feature overlap and enhance the representational capacity across domains ranging from audio and image fitting to 3D geometry and neural radiance fields (Alsakabi et al., 27 Sep 2025).

1. Architectural Principles of Periodic Activation INRs

Traditional INRs employing periodic activation functions, such as SIREN, represent continuous signals (images, audio, 3D shapes) via coordinate-based MLPs with layers of the form: $\sigma(x) = \sin(\omega_0 x)$ where $\omega_0$ is a scalar “frequency multiplier.” The SIREN baseline features fixed $\omega_0$ across all neurons in each layer, initialized using a uniform distribution and demonstrates superior performance in representing fine-scale details compared to ReLU or traditional MLPs (Miotto et al., 29 Jan 2025, Lanzendörfer et al., 2023). However, empirical studies reveal that this design leads to substantial redundancy in the hidden features of each layer, as numerous neurons converge to encode overlapping frequency bands, reducing expressive efficiency (Alsakabi et al., 27 Sep 2025).

2. Motivation for Gabor-like Frequency Diversity

The rationale for Neural Gabor Primitives stems from classical signal processing. The DST and Gabor transforms partition the frequency domain using orthogonal or localized basis functions that span the Nyquist interval without redundancy: $f_{\textrm{Nyquist}} = \frac{f_s}{2}$ DST bases $\varphi_k(n) = \sin(\pi k n / N),\; k=0 \ldots N-1$ uniformly tile $[0, f_{\textrm{Nyquist}}]$. This stands in contrast to fixed-$\omega_0$ SIRENs, justifying the design of architectures that assign each neuron a unique, Nyquist-informed frequency. A neuron’s expressivity and coverage of the spectrum are thereby maximized, akin to a Gabor dictionary. This theoretical alignment motivates architectures like FM-SIREN and FM-FINER (Alsakabi et al., 27 Sep 2025).

3. FM-SIREN and FM-FINER: Nyquist-Informed Frequency Modulation

FM-SIREN modifies the periodic activation MLP paradigm by assigning neuron-specific frequency multipliers: $$\omega_i = (i/K) \cdot f_{\mathrm{Nyquist}}, \quad i=0,\ldots,K-1$$ for a hidden layer with $K$ neurons. Each neuron computes: $$a_i = \sin(\omega_i z_i), \,\, z_i = w_i \cdot x + b_i$$ where the collection $\omega_0$0 forms a frequency-diverse layer. This approach is parameter-free—no additional weights—requiring only an index-based frequency assignment, trivially implemented in neural frameworks.

This frequency allocation reduces hidden-feature covariance (as measured by the Frobenius norm of the feature covariance matrix) by approximately 50% compared to standard SIREN (from 54.23 to 27.21 in typical 2-layer image models), directly addressing the feature redundancy issue (Alsakabi et al., 27 Sep 2025).

Model	Hidden Feature Redundancy (Frobenius Norm)	Approximate Reduction
SIREN	54.23	–
FM-SIREN	27.21	49.92%

In practice, FM-SIREN can be incorporated into standard MLPs by replacing each hidden layer’s activations with: $\omega_0$6 No new trainable parameters are introduced beyond the original network.

4. Empirical Performance Across Modalities

FM-SIREN and FM-FINER demonstrate improved performance in diverse INR tasks:

• Audio fitting (4 kHz Spoken Wikipedia, MSE ↓): FM-SIREN achieves $\omega_0$1, improving over SIREN ($\omega_0$2).
• Image reconstruction (Kodak/BSDS500, PSNR ↑): FM-SIREN achieves 32.29/38.12 dB vs. SIREN 26.77/29.49 dB.
• 3D shape fitting (IoU ↑): Gains of 0.002–0.015 over SIREN; e.g., FM-SIREN 0.990 (Thai Statue) vs. SIREN 0.960.
• NeRF synthesis (Blender, PSNR ↑): FM-SIREN 33.36 dB vs. SIREN 33.14 dB and with up to 14.5% reduction in training time (Alsakabi et al., 27 Sep 2025).

The architectures outperform their respective baselines in both quantitative metrics (PSNR, MSE, IoU) and convergence speed, without requiring additional depth, width, or hyperparameter search.

5. Frequency Allocation, Depth, and Design Guidelines

Ablation studies indicate that frequency-diverse primitives yield optimal results in shallow architectures (2–3 layers), with diminishing returns in very deep networks due to the propagation of high-frequency noise. FM-SIREN/FINER consistently outperform baselines across various width settings but performance saturates for width >512. The Nyquist factor parameter ($\omega_0$3) allows tuning the proportional coverage of the spectral interval, with $\omega_0$4 optimal for FM-SIREN and $\omega_0$5 for FM-FINER. Importantly, these modifications incur negligible computational cost.

Network Width	SIREN PSNR (dB)	FM-SIREN PSNR (dB)
128	26.77	Higher
256	26.77	32.29
512–1024	≈ Saturates	≈ Saturates

6. Broader Context and Related Approaches

The drive toward Neural Gabor Primitives aligns with other advances in INR frequency manipulation. For instance, H-SIREN introduces a hyperbolic periodic activation in the input layer to extend the supported frequency set, improving fidelity in both 2D/3D coordinate regression and NeRF without expanding network size (Gao et al., 2024). These frequency-enhancing modifications share the goal of controlling frequency bias, bandwidth, and expressivity at the architectural level, enabling robust modeling of multiscale, high-frequency signals.

7. Implications and Prospective Directions

The development and deployment of Neural Gabor Primitives establish a principled link between classical signal processing frameworks and neural implicit representations. Explicit frequency allocation—by design, not tuning—bridges theoretical optimality (Nyquist allocation) and empirical performance, reducing redundancy and accelerating training with no added complexity (Alsakabi et al., 27 Sep 2025). This foundational approach suggests the viability of a rich family of frequency-diverse neural architectures for graphics, physics, and audio tasks—potentially extending to adaptive or data-driven spectral allocations, hybrid Gabor-wavelet networks, or localized frequency control for spatially varying signals.

References:

• "FM-SIREN & FM-FINER: Nyquist-Informed Frequency Multiplier for Implicit Neural Representation with Periodic Activation" (Alsakabi et al., 27 Sep 2025)
• "H-SIREN: Improving implicit neural representations with hyperbolic periodic functions" (Gao et al., 2024)
• "Pressure Field Reconstruction with SIREN: A Mesh-Free Approach for Image Velocimetry in Complex Noisy Environments" (Miotto et al., 29 Jan 2025)
• "Siamese SIREN: Audio Compression with Implicit Neural Representations" (Lanzendörfer et al., 2023)