Aliasing-aware Patch Embedding (AaPE)

• Aliasing-aware Patch Embedding (AaPE) is a method that integrates adaptive anti-aliasing filters into the patch extraction process to suppress spectral folding and preserve information integrity.
• It employs fixed, learnable, or adaptive filter banks in vision, adaptive PCA-style projections in image super-resolution, and band-limited kernels in audio for optimized performance.
• Empirical results show notable improvements, such as a 0.8% top-1 accuracy gain on ImageNet and enhanced audio classification metrics, underscoring its robustness across domains.

Aliasing-aware Patch Embedding (AaPE) refers to a class of methods and design patterns for patch-based representation learning (e.g., in vision, image restoration, and audio) that actively mitigate aliasing artifacts in the initial patchification stage. Unlike standard patch embedding, which is prone to spectral folding when downsampling without appropriate pre-filtering, AaPE incorporates explicit or adaptive anti-aliasing mechanisms—frequently combining them with adaptive subband analysis or manifold constraints—so as to preserve information integrity across downstream tasks.

1. Origins and Motivation Across Modalities

Standard patch embedding, used in Vision Transformers (ViT) and similar architectures, extracts non-overlapping image patches and projects each via a linear layer or strided convolution. This operates as uniform subsampling with stride $P$, introducing aliasing wherever signal bandlimit conditions are violated—namely, where content frequencies exceed $\pi/P$ (Qian et al., 2021). Aliasing manifests as jaggedness, spurious oscillations, or phase-dependent artifacts in learned representations. Similar concerns arise in audio: convolutional patchification of spectrograms with high temporal stride reduces the post-patch Nyquist frequency, folding relevant high-frequency structure into lower bands or into artificial “beat” patterns (Yamamoto et al., 3 Dec 2025).

In classical and modern single-image super-resolution and interpolation, patch-based manifold methods also suffer from unreliable neighborhood matching and unstable estimators in the presence of aliasing, leading to degraded reconstruction and poor visual quality (Yu et al., 2021). The ubiquity of aliasing vulnerabilities across vision, audio, and patch-manifold estimation underscores the need for domain-adaptive AaPE strategies.

2. Methodologies: Anti-Aliasing Strategies in Patch Embedding

2.1. Vision Transformers: Filtering Before Patchification

In ViTs, AaPE is realized by inserting a lightweight, channel-wise low-pass filter directly before the stride-$P$ patch-projection operation. Approaches include (Qian et al., 2021):

• Fixed Gaussian Blur: A $k \times k$ Gaussian convolutional kernel, with $\Sigma = \sigma^2 I$, is applied to attenuate frequencies above the patch Nyquist.
• Learnable Depth-wise Filtering: Parametric, channel-wise kernels $K$ are optimized via backpropagation.
• Filter Banks with Adaptive Mixing: A set $\{D_j\}_{j=1}^n$ of kernels (e.g., Gaussian, DoG) are linearly combined via channel-specific, learnable mixing coefficients $\Phi^{(i)}$, enabling adaptive spectral shaping per feature map.

Mathematically, for input $I \in \mathbb{R}^{H \times W \times C}$ and patch size $P$, the anti-aliased token $z_i$ is:

$$z_i = W_e x_i + b_e, \quad x_i = \text{vec}(\text{filtered } P \times P \text{ patch})$$

where the filtering step precedes patch extraction.

2.2. Single-Image Interpolation: Adaptive Local Spectral Suppression

For classical image super-resolution, impairment from aliasing is addressed by preconstructing an “aliasing-removed guide image” via:

• Pre-filtering with a spatially invariant Gaussian,
• Locally adaptive PCA-style projections: for each patch, the dominant subspace (from local SVD) is retained, suppressing directions associated with aliasing,
• Multi-pass iterations to enforce consistency, resulting in robust patch neighborhoods which are then embedded using affinity metrics reflecting true content similarity rather than aliased similarity (Yu et al., 2021).

Patch embedding and regression then proceed using these denoised features, with phase-aware linear models and progressive manifold-consistent refinements.

2.3. Audio: Band-Limited Complex Sinusoidal Kernels

In audio representation learning, AaPE employs the Structured Bilateral Laplace Unit (SBLU), a depthwise convolution with dynamically estimated, band-limited complex exponential kernels:

• The kernel $h[k; \alpha, \beta] = e^{-\Delta \lambda |k - c|}$, with $\lambda = \alpha + j\beta$, is learned (or predicted from input),
• Multiple subbands target frequencies between the pre- and post-patch Nyquist limits,
• A Lambda Encoder adaptively regresses both decay $\alpha$ and frequency $\beta$ from the input, ensuring spectral focus on alias-prone bands,
• Outputs are fused with the standard patch tokens and supplied to the Transformer encoder (Yamamoto et al., 3 Dec 2025).

This adaptive parallel subband approach enables aliasing suppression without indiscriminate loss of task-important high-frequency content.

3. Signal Processing Justifications and Theoretical Basis

All AaPE approaches are unified by classical sampling theory: any subsampling or strided operation exceeding the Nyquist limit induces spectral folding (aliasing), generating low-frequency artifacts that are harmful in both statistical learning and perceptual quality. Anti-aliasing filtering, when properly matched to the patch-stride, enforces a hard bandlimit $|\omega| > \pi/P \implies H(\omega) \approx 0$, with $H(\omega)$ the filter frequency response (Qian et al., 2021). Adaptive spatial or spectral filters further tune this effect, focusing on the frequency bands and spatial neighborhoods where aliasing is most damaging (Yamamoto et al., 3 Dec 2025, Yu et al., 2021).

A plausible implication is that domain-specific adaptive filtering—e.g., through parameterized filter banks, input-conditioned subband selection, or patch-manifold projections—outperforms static, hand-tuned low-pass prefilters in preserving both robustness and fine detail for downstream tasks.

4. Integration in Learning Pipelines and Empirical Validation

4.1. Vision

In ViTs, AaPE modules are inserted just before the patch-embedding layer. Empirical results on ImageNet show:

Model Variant	Top-1 (%)	Δ vs. Baseline
Swin-T baseline (224$^2$)	81.2	–
+ Gaussian blur	81.5	+0.3
+ learnable conv	81.6	+0.4
+ filter bank (n=8)	82.0	+0.8

Consistent gains of 0.5–1.0% are observed on diverse SOTA backbones and robustness to distribution shift improves (ImageNet-C mCE: 60.7 → 59.8) (Qian et al., 2021).

4.2. Single Image Interpolation

On 27 standard test images (upsampling ×2):

Method	PSNR (dB)
Bicubic	29.00
NARM	30.23
ANSM	30.59
NLPC	30.48
MISTER (AaPE)	31.20

MISTER (“aliasing-aware patch embedding”) achieves +0.61 dB over ANSM and +0.97 dB over NARM, with visible improvement in both edge smoothness and texture fidelity (Yu et al., 2021).

4.3. Audio SSL

On AudioSet-2M, ESC-50, and other benchmarks, AaPE (with adaptive SBLU) achieves:

Model	AS-2M mAP	AS-20K mAP	ESC-50 Acc
SSLAM	50.2	40.9	96.2
ASDA	49.0	41.5	96.1
EAT	48.6	40.2	95.9
AaPE	49.8	41.9	97.5

AaPE leads on AS-20K and ESC-50, attaining state-of-the-art or highly competitive status. Adaptivity in SBLU ($\alpha,\beta$ dynamically estimated) provides further measurable gains (Yamamoto et al., 3 Dec 2025).

5. Algorithmic and Implementation Details

The core AaPE operator in ViT-style pipelines consists of a cascade: (1) a channel- or depth-wise anti-aliasing filter (Gaussian, learned, or filter bank), followed by (2) the patch-projection convolution and spatial flattening into tokens. Adaptive mixing or subband selection is realized via small neural “heads” (e.g., 1×1 convs or Transformers) predicting filter parameters per input channel or time-frame (Qian et al., 2021, Yamamoto et al., 3 Dec 2025). In audio, the SBLU’s kernel size (default $K=63$) and the parameterization of decay and frequency are crucial for robust subband analysis.

For manifold-based image restoration, the aliasing-removal step leverages local PCA projections informed by patch similarity, iteratively re-aligning the guide image’s neighborhood structure; the patch embedding distills nearest-neighbor affinities for phase-aware regression and multi-stage global refinement (Yu et al., 2021).

6. Interpretability, Placement, and Limitations

Figures from both vision and audio studies indicate that removing aliasing at the patch stem yields smoother, more semantically meaningful attention maps and more robust, interpretable spectral features (Qian et al., 2021, Yamamoto et al., 3 Dec 2025). In vision, placing AaPE just before or after the self-attention maximizes gain, while excessive smoothing in deeper layers is detrimental. Audio ablations show that adaptivity of subband parameters is beneficial but requires careful regularization to avoid discarding transient cues.

A common misconception is that any pre-filtering suffices; empirical results contradict this, showing clear benefits for adaptive, input- or channel-conditioned anti-aliasing compared to fixed or overly aggressive low-pass filtering. A plausible implication is that future architectures should treat the patchification—and associated anti-aliasing operation—as a first-class, learnable component, rather than a static, task-agnostic preprocessing step.

7. Broader Impact and Future Directions

AaPE enables more accurate and robust self-supervised and supervised learning by aligning input tokenization with fundamental signal processing constraints. It consistently improves performance, data efficiency, and robustness across domains and benchmarks (Qian et al., 2021, Yu et al., 2021, Yamamoto et al., 3 Dec 2025). Anticipated future directions include: (a) further exploration of domain-adaptive and multi-resolution anti-aliasing modules, (b) integration with graph-based or nonlocal patch selection in manifold methods, and (c) expansion into non-Euclidean or multi-modal signal domains. The paradigm established by AaPE offers a rigorous, theoretically justified foundation for patch-based deep learning, promoting uniformity of high-fidelity representation in both classical and deep architectures.