Emergent Temporal Abstractions

• Emergent temporal abstractions are naturally developed high-level behaviors that encapsulate extended timeframes in decision processes.
• They enhance reinforcement learning efficiency by decomposing long-horizon tasks into manageable, temporally-extended actions with demonstrated improvements in various simulations.
• Their discovery leverages scalable architectures and dynamic evaluation protocols, offering actionable insights for designing robust, hierarchical systems.

SpatialTree-Bench refers to a class of benchmarking frameworks designed to rigorously evaluate spatial structure learning, reasoning, and mapping under broad methodological and application-defined scenarios. Three distinct instantiations of SpatialTree-Bench have gained prominence: (1) a benchmark within large-agent biological tissue simulations that probes the impact of spatial hierarchy data structures on computational cost (Dmitrenok et al., 2016); (2) a hierarchical, cognitive-science–aligned evaluation suite for spatial abilities in multimodal LLMs (MLLMs) (Xiao et al., 23 Dec 2025); and (3) a standardized protocol for benchmarking individual tree detection and mapping in sub-meter remote sensing imagery (Gominski et al., 2023). Each embodies distinctive goals but converges on foundational principles of task decomposition, error analysis, and robust comparison across algorithmic paradigms.

1. Biological Simulation: SpatialTree-Bench for Tissue Simulators

SpatialTree-Bench in biological modeling is a benchmarking suite integrated in the BioDynaMo simulator, targeting spatial organization challenges in center-based tissue models (Dmitrenok et al., 2016). Its objectives include:

• Quantifying how spatial-hierarchy data structures—octrees, k-d trees, and R-trees—affect the computational costs of broad-phase neighborhood detection and agent reinsertion.
• Systematic parameter sweep (tree depth $D$, leaf capacity $C$, splitting heuristic) to locate optimal configurations for up to $10^6$ spatial agents.
• Guiding both shared-memory (single-node) optimizations and future distributed-memory octree partitions.

The testing protocol generates $N$ uniformly-distributed agents, incrementally inserts all into the spatial index, and issues a fixed-radius neighbor query per agent ($r=10^{-3}, 10^{-5}$). Timing is reported as $T_\text{insert}$, $T_\text{query}$, and $T_\text{total}$.

Spatial trees compared:

• Octree: Subdivides root cube as capacity or depth thresholds are reached. Average-case operations are $O(\log N)$ for both insertion and search.
• k-d Tree: Four splitting heuristics: MMAS (cycle axes at median), MSAS (longest axis, median), CS (cyclic axes, box center), SAHS (surface-area heuristic). MSAS offers fastest search for small $r$, MMAS is robust to $r$, SAHS is not beneficial for point data.
• R-Tree: B-tree analogue based on bounding-rectangle volume, with performance hampered by high MBR overlap and rebalancing.

Key results (for $N=10^6$):

Tree Type (params)	$r=10^{-3}$ (ms)	$r=10^{-5}$ (ms)
Octree (1000, 10)	9,419	9,426
k-d MMAS (1000, 10)	5,605	5,402
k-d MSAS (1000, 10)	48,838†	3,149‡
R-tree (M=25)	>180,000	>180,000

† For MSAS and large $r$, poor pruning inflates cost; ‡ for tight $r$, MSAS dominates.

Significance: k-d MSAS is optimal for highly localized interactions, MMAS preferable for broader-radius queries. Octrees trade off 1.5–2$\times$ worse total runtime for easier implementation and suitability for distributed partitioning. R-trees are unsuitable for high-throughput point-neighborhood search.

Best practices: For $N\sim10^6$, tight interaction radius, use k-d MSAS with $C=10$, $D=1000$. Recursive axis-aligned box–ball queries yield $O(\log N + k)$ average query time. In dynamic settings, sacrificing some insertion speed for faster search is preferable (Dmitrenok et al., 2016).

2. Multimodal LLMs: SpatialTree-Bench as a Hierarchical Spatial Capability Benchmark

SpatialTree-Bench, as introduced in the context of multimodal LLMs, organizes spatial ability into a cognitively-motivated four-level hierarchy (Xiao et al., 23 Dec 2025):

• L1 Perception (11 sub-abilities): Geometry (distance, size, shape estimation), Motion (egocentric, allocentric), Orientation, Relations (topology, correspondence), Localization.
• L2 Mental Mapping (7): Captioning, semantic relations, motion understanding, perspective taking, affordance, cognitive mapping, memory.
• L3 Simulation (5): Causal reasoning (geometry puzzles, dynamics), sequential planning.
• L4 Agentic (4): Goal-driven navigation, robot/human manipulation, open-ended exploration.

SpatialTree-Bench aggregates over a dozen prior datasets (BLINK, SpatialEval, 3DSR-Bench, VSI-Bench, etc.), augmented by the new SpatialPlus set (250,000 QAs), resulting in 41 tasks and 200,000 examples.

Annotation pipeline integrates perception engines (DepthAnything3, SpatialTracker), QA templating, and LLM rephrasing. L3 tasks include explicit chain-of-thought (CoT); L4 tasks discretize trajectories for agentic reasoning.

Evaluation metrics:

• L1–L2: MCQ accuracy, relative/numeric error, angular difference (orientation).
• L3–L4: Success rate, continuous trajectory metrics.
• GPT-Judge for open-ended answers.
• Aggregation uses bottom-up hierarchical weighting.

Measured interdependencies:

• L1 sub-abilities: Orthogonal ($r<0.2$ Pearson correlation).
• L3–L4: Strong positive correlation ($r>0.6$).

Experimental findings:

• Best overall: Gemini 2.5-Pro at 50.1%, GPT-4o at 31.9%, Qwen 3VL-235B at 40.0%.
• L1 geometric and orientation tasks yield highest scores, but L4 agentic competencies remain challenging (30–40%).
• Single-ability supervised fine-tuning (SFT) produces negative intra-level transfer but positive cross-level transfer, while multi-ability SFT unlocks synergy.
• Hierarchy-aware RL, penalizing unnecessary CoT in L1 and amplifying rewards in L3–L4, produces consistent improvements; naive RL (@think) introduces regressions in direct perception.

Significance: SpatialTree-Bench enables structured diagnosis of spatial reasoning, revealing that perceptual subskills are independently acquired while high-level agentic reasoning requires synergy. Hierarchy-aware training and inference (e.g., "auto-think") are recommended to balance intuitive skills and complex CoT (Xiao et al., 23 Dec 2025).

3. Remote Sensing: SpatialTree-Bench for Individual Tree Mapping

SpatialTree-Bench also denotes the evaluation suite for benchmarking individual tree detection and mapping in sub-meter aerial imagery (Gominski et al., 2023).

Datasets:

• Denmark: 23,600 trees, 712 km², RGB+NIR, 20 cm GSD.
• Rwanda: 98,800 trees, 340 km², RGB, 25 cm GSD.

Ground-truth annotation involves manual delineation of crowns; center–area ("disk") annotation is 5–10$\times$ faster than full segmentation.

Evaluation framework:

Matching Mode	Method	Details
One-to-one	Hungarian on $N \times M$	Pairs predictions and labels; strict
Many-to-one	Label rows replicated $K$	Captures overcount, merges
One-to-many	Prediction columns replicated	Captures undercount, splits
Composite	Balanced F1 ($bF1$)	Weighted sum: $\alpha$ for MO, $1-\alpha$ for OM; see below

Matching cost:

$$c_{ij} = \|p_i - \hat p_j\|_2 + \lambda \big| \mathrm{CA}_i - \widehat{\mathrm{CA}_j} \big|$$

with assignment constrained: $\|p_i-\hat p_j\|_2 < \gamma\,\mathrm{CD}_i$.

Composite $bF_1$:

$$\mathrm{bF1} = \alpha\, \mathrm{F1}^{\mathrm{MO}} + (1-\alpha)\, \mathrm{F1}^{\mathrm{OM}}$$

where $\alpha = 1/(1 + e^{2\epsilon})$, $\epsilon = (M-N)/N$.

Balanced localization/crown-area error defined analogously, increasing robustness to annotation noise.

Benchmarked approaches:

• Segmentation (UNet-R50, bin. mask + Tversky/Focal loss)
• Anchor-free heatmap detector (CenterNet-like; two heads: center, size)
• Segmentation-to-disk heatmap (single UNet-R50, L1 to Gaussianized heatmap)
• Point-based (P2P with anchor grid, Hungarian matching)
• Box detection (Faster R-CNN with ResNet-50 backbone)

Key experimental results:

Method	Denmark $bF1$@1	Rwanda $bF1$@1	Denmark nMAE (%)	Rwanda nMAE (%)
Segmentation	42.1	34.3	30.7	64.4
CenterNet	40.7	31.9	55.2	75.9
Heatmap (proposed)	41.8	31.4	33.4	78.5
P2P	49.6	35.3	26.4	68.7
Faster R-CNN	47.6	33.6	39.9	78.1

Ensembling and test-time augmentation (TTA) yield stronger boosts in the heatmap approach ($+20-28\%$ $bF_1$). Backbone comparison finds UNet-R50 is optimal for this setting; DeepLabV3, SegFormer, and TransUNet offer no further gains.

Significance: The heatmap approach, requiring only "disk" annotation, is annotation-efficient and achieves performance approaching that of segmentation. P2P excels in strict-detection regimes ($\gamma \leq 1$). Balanced matching and error metrics provide resilience to label uncertainty, substantiated by two-annotator agreement experiments (Gominski et al., 2023).

4. Algorithmic and Architectural Recommendations

Biological Simulations

• Use k-d trees (preferably MSAS) for local interaction, tightly bounded search radii, and $O(\log N)$ query complexity.
• Octrees offer simpler, partition-aligned implementations, suitable for distributed environments but with moderately higher cost.
• Avoid R-trees for high-throughput, point-based querying.

Multimodal LLMs

• Structure fine-tuning to combine foundational perceptual (L1) skills; avoid over-specialization in single abilities to prevent negative transfer.
• Reinforcement learning supervision should penalize elaborate reasoning on perception tasks and accentuate CoT for complex planning/simulation.
• Aggregate benchmarking results bottom-up to reflect the prerequisite dependencies between capabilities.

Remote Sensing

• Heatmap-based detection is annotation- and noise-efficient, enabling large-scale tree inventory with minimal ground-truthing effort.
• For strict detection and localization, point-based P2P methods are preferable.
• Balanced F1 and error metrics are essential for credible, noise-resilient model comparison.

5. Methodological Implications and Future Directions

SpatialTree-Bench typifies best practices in benchmarking complex spatial tasks:

• Integrating multiple task paradigms—detection, localization, reasoning, and agentic navigation—within a unified data and evaluation suite.
• Adopting robust statistical matching and error measures that decouple annotation uncertainty from algorithmic performance.
• Informing architecture design (both for ML models and spatial data structures) with domain-dependent, empirical tradeoff analysis.
• Providing scalable, reproducible baselines that support future extension to larger model sizes, richer input modalities, and more complex spatial environments, such as real-time simulation or integrated perception–control loops.

A plausible implication is that capability-centric, hierarchical benchmarking (as in the MLLM instantiation) is increasingly important for diagnosing and fostering transferability of spatial reasoning in next-generation models and perception systems.

• "Evaluation of spatial trees for simulation of biological tissue" (Dmitrenok et al., 2016).
• "SpatialTree: How Spatial Abilities Branch Out in MLLMs" (Xiao et al., 23 Dec 2025).
• "Benchmarking Individual Tree Mapping with Sub-meter Imagery" (Gominski et al., 2023).