From Edges to Depth: Probing the Spatial Hierarchy in Vision Transformers

Vision Transformers (ViTs) commonly rely on injected positional mechanisms to address self-attention's permutation invariance. Motivated by the spatial regularities of natural images, we ask whether spatial organization can be induced from data rather than explicitly injected. Under controlled, matched from-scratch training, we propose Active Spatial Guidance (Guidance), a training-only objective that disables positional injection and applies an auxiliary 2D coordinate-regression loss to the final-layer patch tokens. The guidance head is used only during training and removed for inference; the deployed model consists of a positional-injection-free ViT encoder and the task-specific prediction module. Using DINOv3 ViT backbones, Guidance consistently improves performance on ImageNet-100 classification, ADE20K semantic segmentation, and Hypersim monocular depth estimation, outperforming strong injected baselines such as learned absolute positional embeddings and rotary positional embeddings under identical training protocols. On ImageNet-100, broader comparisons against representative injected positional designs further support Guidance's effectiveness. Guidance also improves robustness under resolution transfer, and multi-resolution training further strengthens accuracy across input sizes. Overall, our results suggest that spatial inductive bias in ViTs need not be architecturally injected, but can be shaped through training-time supervision. The code used for training and evaluation is publicly available in https://github.com/cloudlc/asg.

Vision transformers (ViTs) have become the de facto standard for image encoding across many perception tasks. Despite their empirical success, it remains mechanistically unclear how they encode low-level features, given their lack of inductive biases: ViTs process information globally rather than relying on local structure. Biological visual systems, in contrast, build low-level features, such as orientation selectivity in the primary visual cortex, by combining information from small, localized regions of the visual field. These features are general-purpose representations, shared and required across multiple specialized neural pathways, unlike higher-level, task-specific semantic features. This raises the question if such biologically-grounded features arise in ViTs. In this work, we systematically study how orientation selectivity emerges in ViTs by introducing a suite of neuroscience-inspired metrics: representational similarity score (RSS), orientation recruitment score (ORS), and orientation tuning bandwidth to quantify how orientation is encoded in representational geometry and as a function of model depth. Through extensive analysis, we find that: (1) the training paradigm is the strongest determinant of orientation selectivity, with models sharing an objective, peaking at comparable relative depths regardless of scale (2) many units are orientation-selective early in training, with early-to-middle layers recruiting more such units over time, while deeper layers lose selectivity and broaden their tuning toward semantic encoding and (3) our metrics offer a mechanistic heuristic for how many layers to unfreeze for best downstream generalization. Our framework presents a way to track biologically-grounded features during ViT training, probes how desired properties are encoded in transformer representations, and builds a systematic understanding of how ViTs generalize across tasks.

Positional embeddings (PEs) in Vision Transformers (ViTs) are known to impact performance and robustness, but their role in shaping internal spatial representations is not well understood. In this work, we study how different forms of PEs influence the representational geometry of ViTs and how these changes relate to robustness under content-disrupting distribution shifts. We introduce a metric, the Spatial Similarity Distance Correlation (SSDC), to quantify spatial structure in token representations. Using this metric, we show that ViTs trained without PEs still develop non-trivial spatial structure, but this structure is driven by visual content and collapses under token permutation. In contrast, we find that all PEs considered (learned absolute, sinusoidal, and rotary) are associated with a consistent shift toward an index-anchored spatial organization. Representations in these models remain stable under perturbations that disrupt content, and exhibit substantially improved robustness to such distributional shifts. We further show that while different PEs produce distinct depth-wise trajectories of spatial structure, their robustness properties are largely similar (with secondary variation across encoding schemes), suggesting that robustness appears to depend on the presence of a stable positional reference frame more than it depends on the specific encoding mechanism. These results offer a geometric account of how positional encodings shape internal representations, with implications for the principled design of future encoding schemes.