Atomic Perceptual Units in Vision & AI

• Atomic perceptual units are minimal, task-specific elements that serve as the basic substrates for grouping, categorization, and control across various modalities.
• They balance minimality and composability, enabling the emergence of higher-level structures such as Gestalts, latent actions for control, and semantic annotations.
• Research validates these units using diverse methods—from neurogeometric models and MEG decoding to vector-quantized latent spaces and knowledge graphs—to explain perceptual organization.

Searching arXiv for the cited works and closely related formulations of “atomic perceptual units.” Atomic perceptual units are minimal perceptual building blocks that a system treats as sufficient substrates for grouping, categorization, representation, or control. In the literature, the phrase does not denote a single ontology. It can refer to identical oriented Gabor patches whose arrangement generates distinct visual Gestalts, to coherent 3D segments stabilized by neurogeometric connectivity, to categorical eigenstates such as color percepts, to latent image-goal deltas used as control primitives, to reified perceptual semantic annotations in a knowledge graph, to length-1 concept explanations of network units, to transient and steady-state speech segments, or to repeated multi-widget items in a graphical interface (Wardle et al., 2015, Bolelli et al., 2024, Arguëlles, 2024, Chen et al., 2024, Pandiani et al., 2024, Makinwa et al., 2021, S et al., 2020, Xie et al., 2022). Taken together, these works treat atomicity as a relation between minimality and composition: the unit is small enough to be primitive for a given model, yet structured enough to combine into higher-order perceptual organization.

1. Definitions and criteria of atomicity

The cited work converges on several recurring criteria for atomicity. Minimality is explicit in the 3D neurogeometric account, where an atomic unit is a coherent subset of features in $$\xi = (r_1,r_2,r_3,\theta,\phi) \in \mathbb{R}^3 \times S^2$$ that cannot be split into smaller subgroups whose internal connectivity exceeds their connectivity to the complement. Stability is also explicit there: atomic units arise as robust stationary states of mean-field dynamics and as leading invariant subspaces of the normalized affinity operator (Bolelli et al., 2024). In symbolic settings, minimality means that each unit captures a single perceptual facet, such as an object, action, color, or emotion, rather than an end-to-end scene label (Pandiani et al., 2024). In network interpretability, an atomic concept is a single human-interpretable concept label, and an atomic perceptual unit is a network unit best explained by a length-1 logical form rather than a longer compositional one (Makinwa et al., 2021). In embodied AI, atomicity denotes a minimally sufficient perceptual delta between an initial image and a goal image, compressed into a latent action that can serve as a sub-task embedding for control (Chen et al., 2024).

Domain	Unit	Atomicity criterion
Visual neuroscience	Oriented Gabor patch	Identical local element reused across stimuli
3D neurogeometry	Cluster in $\mathbb{R}^3 \times S^2$	Minimal, coherent, stable grouping
Quantum cognition	Category eigenstate	Discrete perceptual outcome of measurement
Embodied AI	Image-goal latent action	Minimal perceptual delta for control
Knowledge graphs	Perceptual semantic unit	Single contextualized semantic facet
Interpretability	Length-1 concept explanation	Best unit explanation without composition
Speech	Perceptual acoustic unit	Transient or steady-state sound primitive
GUI analysis	Repeated item subgroup	Smallest recurring multi-widget grouping

A common feature across these definitions is that atomicity is task-relative. The same system may admit different atoms at different analytical levels. In the MEG study, the atoms are identical Gabors, while the behaviorally relevant representation is the Gestalt formed by arranging them (Wardle et al., 2015). In GUI grouping, single widgets are lower-level elements, but the atomic perceptual unit may instead be one repeated card or one list row composed of several widgets (Xie et al., 2022). This suggests that atomicity is not synonymous with indivisibility in an absolute sense; it is the minimal level at which a particular explanatory, geometric, or control framework becomes stable and reusable.

2. Early visual atoms and the emergence of Gestalt

A paradigmatic experimental treatment appears in the MEG study of perceptual similarity and dynamic neural activation patterns (Wardle et al., 2015). There, the atomic perceptual units are oriented Gabor patches, defined as a sinusoid multiplied by a 2D Gaussian and motivated by the classical receptive field of simple cells in early visual cortex. Every visual pattern was built from identical Gabor elements arranged on a log-polar grid spanning an inner radius of $1^\circ$ to an outer radius of $8^\circ$ visual angle, with four concentric rings and twelve radial spokes. Element size was log-scaled with eccentricity to approximately account for cortical magnification. Position, local orientation, and presence or absence were manipulated, while the Gabors themselves were otherwise identical (Wardle et al., 2015).

The design cleanly dissociated unit-level coding from emergent global organization. The stimulus set contained 26 patterns arranged as 13 complementary pairs. Nine orientation-complement pairs had 48 elements each, and four retinal-complement pairs had 24 elements each. Coherent global orientations at $0^\circ$, $45^\circ$, $90^\circ$, and $135^\circ$ were contrasted with matched incoherent versions that preserved equivalent local orientation disparity but lacked a global orientation field. Additional patterns included alternating orientation lattices, stars, spirals, rings, spokes, and complements differing only in element positions (Wardle et al., 2015).

The MEG analysis used naïve Bayes Linear Discriminant Analysis on PCA-reduced sensor patterns, with pseudo-trial averaging of four trials into one, 10 pseudo-trials per stimulus, and 100 randomizations. Decoding emerged at approximately 40 ms post-stimulus and peaked at approximately 90 ms, with a smaller second peak near stimulus offset at approximately 400 ms. The representational dissimilarity matrix at time $t$ was defined by pairwise decodability, and model RDMs were compared to MEG RDMs over time using Kendall’s $\tau_a$ rank correlation, with significance assessed by Wilcoxon signed-rank tests under FDR $\mathbb{R}^3 \times S^2$0 and a three-consecutive-time-point cluster threshold (Wardle et al., 2015).

The critical result is temporal. A retinotopic envelope model, which encoded only element presence or absence at retinotopic locations and was agnostic to orientation, showed a significant correlation from approximately 50 ms and peaked at approximately 80 ms. It then declined rapidly and fell well below the noise ceiling after approximately 100 ms. By contrast, the perceptual similarity model, derived from pairwise similarity ratings by 50 independent observers, became significant at approximately 50 ms, reached the lower bound of the noise ceiling by approximately 150 ms, peaked near 145 ms in the group visualization, and remained near-optimal beyond stimulus offset. V1-like HMAX S1 features first became significant at approximately 80 ms and peaked at approximately 140 ms, but never approached the noise ceiling. Orientation disparity and radial preference models did not significantly explain the MEG RDMs at any time point (Wardle et al., 2015).

The study therefore separates two stages. In an early window of roughly 40–100 ms, unit-level coding is dominated by position and local contrast of the atomic Gabor units. Within the next tens of milliseconds, the brain’s representational geometry becomes more strongly aligned with perceptual Gestalt than with retinotopy or local orientation coding. Additional decoding analyses reinforce this interpretation: coherent global orientation stimuli were decodable, matched incoherent stimuli were not consistently decodable, radially balanced pairs of the same global form were not decodable, and between-shape pairs such as star versus spiral were decodable despite radial balance (Wardle et al., 2015). The result is a temporally explicit account of how identical local atoms are integrated into a perceptual whole.

3. Geometric and categorical formalisms

One line of work formalizes atomic perceptual units as coherent structures induced by neurogeometry. In the binocular 3D vision model, the relevant space is $\mathbb{R}^3 \times S^2$1, with coordinates $\mathbb{R}^3 \times S^2$2 and orientation $\mathbb{R}^3 \times S^2$3. Horizontality constrains position changes to lie along the local tangent direction, implemented by the horizontal frame

$\mathbb{R}^3 \times S^2$4

The control system $\mathbb{R}^3 \times S^2$5 induces a sub-Riemannian metric with $\mathbb{R}^3 \times S^2$6, and the corresponding Carnot–Carathéodory distance defines an anisotropic geometry aligned to good continuation rather than Euclidean proximity (Bolelli et al., 2024).

Atomicity is recovered spectrally from a connectivity kernel. The Kolmogorov operator

$\mathbb{R}^3 \times S^2$7

generates a fundamental solution $\mathbb{R}^3 \times S^2$8, whose time-integrated Green’s function is

$\mathbb{R}^3 \times S^2$9

A symmetrized kernel

$1^\circ$0

defines affinities $1^\circ$1 on a lifted cloud of stereo candidates, with row-normalized operator $1^\circ$2. The leading eigenvectors of $1^\circ$3 concentrate on coherent units, and significant eigenvectors are selected by $1^\circ$4, followed by thresholding cluster size by $1^\circ$5 (Bolelli et al., 2024).

This framework yields atomic units as minimal, stable, and coherent 3D figures. On a synthetic single curve with 30 points, parameters $1^\circ$6, $1^\circ$7, $1^\circ$8, $1^\circ$9, and $8^\circ$0 isolated a single salient cluster matching the curve. On a helix-plus-arc scene, $8^\circ$1, $8^\circ$2, $8^\circ$3, and $8^\circ$4 recovered two coherent clusters with only minor misassignments. On natural twigs, $8^\circ$5, $8^\circ$6, and $8^\circ$7 yielded two dominant twig clusters while consigning many false pairs to noise. Replacing the sub-Riemannian kernel with a Euclidean Gaussian produced density-driven clusters that failed to track curved continuity (Bolelli et al., 2024).

A second formalization treats atomic perceptual units as categorical eigenstates. In the quantum-cognition account of color perception, a stimulus is modeled as a pure state on the Bloch sphere, whereas the percept is the decohered density state after measurement in a category basis. For a two-category measurement with projectors $8^\circ$8 and $8^\circ$9, decoherence is

$0^\circ$0

A pure state with polar angle $0^\circ$1 becomes

$0^\circ$2

Stimulus similarity is measured by a normalized geodesic distance,

$0^\circ$3

whereas percept similarity is measured by trace distance,

$0^\circ$4

Using the mean value theorem, dilation occurs if $0^\circ$5 for some $0^\circ$6 between $0^\circ$7 and $0^\circ$8, and contraction occurs if $0^\circ$9 (Arguëlles, 2024).

The worked Light/Dark example makes the categorical effect explicit. For $45^\circ$0, $45^\circ$1, and $45^\circ$2, one obtains $45^\circ$3 and $45^\circ$4, but $45^\circ$5 and $45^\circ$6. Within-category pairs contract; across-category pairs dilate. In this framework, the category eigenstates are the atomic perceptual units because they are the discrete outcomes toward which continuous stimuli are forced by measurement (Arguëlles, 2024).

These two formalisms differ sharply in ontology. The sub-Riemannian account defines atoms as minimal connected clusters in a continuous manifold, whereas the quantum-cognitive account defines atoms as discrete perceptual outcomes. A plausible implication is that “atomic” need not mean either purely local or purely discrete; it can denote the minimal unit preserved by the geometry or measurement structure of the task.

4. Atomic units at the perception–action interface

In embodied AI, the notion of atomic perceptual units is recast as latent action representations. IGOR defines Image-GOal Representations as a unified latent action space that compresses the visual change between an initial image and its goal state into a control-oriented code (Chen et al., 2024). The inverse dynamics model infers

$45^\circ$7

and the forward dynamics model reconstructs the next frame from a single frame and the latent action,

$45^\circ$8

Training minimizes $45^\circ$9 plus the vector-quantization commitment loss. Random cropping enforces invariance across viewpoints and framing (Chen et al., 2024).

The latent action space is discrete and compact: $90^\circ$0 with $90^\circ$1 tokens, $90^\circ$2 codewords, and $90^\circ$3. These latents are treated as atomic control units because they capture minimally sufficient perceptual deltas that can be composed temporally into longer behaviors. The world model is a Rectified Flow model built on Open-Sora, modified to accept latent action tokens by cross-attention and to incorporate coarse forward-model predictions. A foundation policy predicts latent actions from language and observations using

$90^\circ$4

and a low-level policy refines the predicted latent into $90^\circ$5 robot actions on RT-1 with

$90^\circ$6

This factorization decouples sub-task selection from embodiment-specific motor execution (Chen et al., 2024).

The training scale is correspondingly large. The latent action model used a frozen DINO-v2 ViT encoder and a spatio-temporal transformer, trained with batch size 512 for 140K steps at learning rate $90^\circ$7. The world model used batch size 12 for 48K steps at learning rate $90^\circ$8. The foundation policy used a 12-layer, 12-head ST-Transformer with hidden dimension 768 and patch size 14, trained with batch size 128 for 124K steps. Pretraining used approximately 2.8M trajectories or clips, including approximately 0.8M robot and approximately 2.0M human activity videos, with actions removed and only images plus instructions retained (Chen et al., 2024).

Empirically, the latent space exhibits semantic consistency across humans and robots. On held-out RT-1, nearest neighbors in latent-action space showed matching visual changes and sub-task semantics such as “open gripper,” “move left,” and “close gripper.” Different latent actions applied to the same initial frame could selectively move different objects in a multi-object scene. Latents extracted from human videos could drive robot arm motion in robot scenes. Under low-data finetuning, using only 1% of RT-1 data for low-level training, IGOR matched or exceeded a scratch-trained low-level policy on “Pick Coke Can,” “Move Near,” and “Open/Close Drawer.” Mixed robot-plus-human pretraining reduced the latent action model’s OOD validation loss on RT-1 from 0.145 to 0.112 relative to robot-only pretraining (Chen et al., 2024).

This usage is distinct from the visual-neuroscience and geometric cases. The atomic unit is neither a raw local feature nor a category label, but a compact representation of change that is simultaneously perceptual and executable. The paper therefore places atomic perceptual units directly at the perception–action interface.

5. Symbolic, graph-based, and explanatory units

A different tradition operationalizes atomic perceptual units as contextualized semantic annotations. In the ARTstract framework, perceptual semantic units include actions, age tier, art style, dominant colors, evoked emotions, human presence, detected objects, and an automatically generated caption (Pandiani et al., 2024). These units are extracted from approximately 14,795 cultural images labeled with seven abstract concepts—comfort, danger, death, fitness, freedom, power, and safety—and integrated into the ARTstract Knowledge Graph, which contains over 1.9 million RDF triples. Each annotation is reified and linked to an AnnotationSituation that records the annotator, dataset, timestamp, and optional geographic metadata. Object and affect labels are aligned to ConceptNet, while captions are parsed through FRED into WordNet synsets and Framester frames (Pandiani et al., 2024).

This produces APUs that are minimal, compositional, and reusable. A scene such as “a woman reading a book on a sofa” may yield object annotations for woman, book, and sofa; an emotion annotation for contentment; color annotations such as warm yellow; and a caption-derived Reading frame with Reader, Text, and Location roles. The graph is then embedded with TransE using

$90^\circ$9

For downstream classification, the study compares absolute embeddings, relative representations over 700 anchors, and hybrid fusions with ViT embeddings. A two-layer MLP with ReLU and dropout 0.3 is trained for 50 epochs at learning rate 0.001 using softmax cross-entropy over the seven abstract concepts (Pandiani et al., 2024).

The empirical pattern is clear. Absolute ViT achieved Macro F1 of 0.30, absolute KGE 0.22, absolute KGE concatenated with absolute ViT 0.31, relative ViT 0.28, relative KGE 0.27, relative Hadamard fusion 0.29, and relative concatenation of KGE and ViT 0.33, which was the best result within the study. The interpretability analysis further distinguished the modalities: ViT grouped images by pixel-level visual attributes and textures, whereas KGE better captured abstract semantic scene elements such as Statue of Liberty imagery for freedom or crosses for death (Pandiani et al., 2024).

In neural network interpretability, atomicity is formulated at the level of explanation length. A unit is a neuron or channel whose activation pattern is analyzed across a dataset. An atomic concept is a single concept label from a concept bank; a logical form is a propositional expression built from atomic concepts using $135^\circ$0, $135^\circ$1, and $135^\circ$2; and the explanation length $135^\circ$3 is the number of literals in the logical form (Makinwa et al., 2021). Detection Accuracy evaluates whether a candidate explanation agrees with a unit’s firing pattern:

$135^\circ$4

Because this metric symmetrically rewards both positive and negative agreement, it can compare length-1 and longer explanations without the length bias associated with F1 or IoU-derived heuristics. The paper argues that DA can also serve as the stopping criterion for compositional search and exposes specialized units whose length-1 explanations are the perceptual abstractions of longer explanations (Makinwa et al., 2021).

These two lines of work show that atomic perceptual units need not be sub-symbolic. They can be explicitly named, contextualized, and reasoned over. They can also serve as explanations for learned units rather than merely as inputs to a model. A recurring misconception is that atomicity excludes semantics. The evidence here is the opposite: atomicity can be strengthened by provenance, lexical alignment, and logical evaluation.

6. Acoustic and interface units

In zero-resource speech synthesis, atomic perceptual units are defined as perceptual acoustic units consisting of transient and steady-state regions. The method first segments continuous speech into CVC-like units using a processed short-time energy contour, then clusters these segments by a connected-components graph built from dynamic time warping distances, and finally initializes each segment as onset/attack, rhyme, and offset/decay sub-units before allowing them to reorganize under an HMM-GMM framework (S et al., 2020). The onset and offset correspond to CV and VC transients; the rhyme corresponds to a steady-state, typically vowel or other sonorant, and the authors also include fricatives that behave perceptually as steady acoustic textures (S et al., 2020).

The resulting AUs function as text-free symbolic units for synthesis. Stage 1 trains HMMs on segmented CVC units; Stage 2 decodes continuous speech and retrains on the unsegmented data. System 1 used 170 AUs for English development and 112 AUs for Indonesian test; System 2 compressed the inventory to approximately 40 AUs and retrained. On the ZeroSpeech 2019 development language, System 1 achieved MOS 2.82, CER 0.55, speaker similarity 2.76, ABX 29.66, and bit-rate 138.59, while System 2 achieved MOS 2.77, CER 0.61, speaker similarity 3.00, ABX 28.16, and bit-rate 92.75. Both outperformed the zero-resource baseline, and the paper attributes their effectiveness to the perceptual relevance of transient–steady decomposition rather than arbitrary frame clustering (S et al., 2020).

In GUI perception, the term “atomic perceptual units” is not used explicitly, but the method operationalizes the concept as the smallest repeated multi-widget items within a larger block (Xie et al., 2022). Starting from pixels only, the system detects text with Google Cloud Vision OCR and non-text regions with an enhanced UIED pipeline, recognizes rectangular wireframe containers, clusters widgets by similarity using several one-dimensional DBSCAN passes, and then pairs proximate, compositionally compatible clusters into repeated subgroups. These subgroups correspond to one card in a grid, one row in a list, or one tab in a tab bar. Containers and blocks are higher-order groups; widgets are lower-level elements; the atomic item is the minimal repeated multi-widget grouping (Xie et al., 2022).

The evaluation used 1,091 GUI screenshots from 772 mobile apps and 20 UI design mockups. Enhanced widget detection improved overall F1 from 0.524 to 0.626 relative to original UIED. For grouping on Android GUIs at edit-distance threshold $135^\circ$5, metadata-based evaluation yielded precision 0.607, recall 0.754, and F1 0.672; detection-based evaluation yielded precision 0.546, recall 0.650, and F1 0.593. Runtime was approximately 1.7 seconds per image on CPU, split into approximately 1.1 seconds for detection and 0.6 seconds for grouping (Xie et al., 2022).

Both speech and GUI studies make atomicity explicitly temporal or structural. In speech, the atoms are brief acoustic events aligned with perceptually salient transitions and nuclei. In GUIs, the atoms are repeated visual items whose internal composition remains consistent across a block. In both cases, the unit is not the smallest measurable fragment but the smallest perceptually stable component useful for higher-level organization.

7. Cross-domain properties, misconceptions, and open problems

Several cross-domain properties recur. First, atomicity does not preclude hierarchy. Identical Gabor atoms combine into distinct global Gestalts; sub-Riemannian atomic units merge into larger structures at larger diffusion scales; sequences of latent actions compose long-horizon behaviors; perceptual semantic units assemble into scene constellations and abstract-concept predictions; and repeated GUI items form higher-order blocks (Wardle et al., 2015, Bolelli et al., 2024, Chen et al., 2024, Pandiani et al., 2024, Xie et al., 2022). A common misconception is therefore that an atomic perceptual unit must be the terminal representational level. In the cited work, it is instead the minimal level that remains coherent under a given grouping, decoding, or control mechanism.

Second, atomicity is not tied to a single representational format. Some frameworks use identical local features or continuous manifolds, as in Gabor-based vision and sub-Riemannian stereo (Wardle et al., 2015, Bolelli et al., 2024). Others use discrete tokens or categorical states, as in vector-quantized latent actions and eigenstate-based color categories (Chen et al., 2024, Arguëlles, 2024). Symbolic and explanatory frameworks use graph nodes or length-1 logical forms (Pandiani et al., 2024, Makinwa et al., 2021). This suggests that the relevant distinction is not discrete versus continuous, but whether the unit is minimal and reusable for the target computation.

Third, most formulations are explicit about their limits. The Gabor-MEG study used abstract patterns composed of identical units and notes that naturalistic objects introduce semantics, texture, and shape complexity; whole-brain MEG decoding also lacks cortical specificity (Wardle et al., 2015). IGOR identifies attribution ambiguity between agent-caused changes and camera motion, possible embodiment gaps in the world model, and granularity limits from $135^\circ$6 and $135^\circ$7 discrete tokens (Chen et al., 2024). The ARTstract pipeline depends on off-the-shelf detectors applied to art images, is culturally biased toward Euro/Western imagery, and does not report statistical significance for the Macro F1 comparisons (Pandiani et al., 2024). The 3D neurogeometric method can be confounded by repetitive patterns and low-signal disparity, while the GUI method is sensitive to OCR and detection errors, ambiguous groupings, and occlusions (Bolelli et al., 2024, Xie et al., 2022). The speech pipeline inherits the limitations of energy-based segmentation, all-pairs DTW scalability, and cross-speaker steady-state variability (S et al., 2020). The quantum-cognitive model depends on the chosen measurement basis, making category structure explicitly context-sensitive (Arguëlles, 2024).

A final misconception is that atomic perceptual units are always pre-given. Several of these works instead infer them. In stereo vision they emerge from affinity spectra; in GUI analysis they emerge from pairing and continuity constraints; in speech they are discovered without transcripts; in embodied AI they are distilled from mixed human and robot videos; and in network interpretability they are recovered by explanation search under Detection Accuracy (Bolelli et al., 2024, Xie et al., 2022, S et al., 2020, Chen et al., 2024, Makinwa et al., 2021). Atomicity, in this sense, is not merely a property of the world or of the stimulus. It is a property of the model’s successful decomposition of perceptual organization into minimal, stable, and composable units.