Locality-aware Generation Ordering

Updated 4 July 2025

Locality-aware generation ordering is a family of techniques that optimize the sequence of computational tasks by leveraging spatial, temporal, and network locality.
It employs methods such as domain-aware task queuing, locality-sensitive ordering, and adaptive reordering to minimize remote accesses and improve memory utilization.
This approach delivers practical benefits, including reduced cache misses, lower network traffic, and accelerated parallel processing in high-performance and generative systems.

Locality-aware generation ordering refers to a family of algorithmic and architectural techniques designed to optimize the sequence and structure of computational tasks, data generation, or model prediction steps to exploit locality—whether in data, computation, hardware memory, or distributed systems. The central goal is to reduce costly remote accesses, maximize contextual support, and enhance efficiency by aligning the order of processing with the spatial, temporal, or network locality inherent in the problem or hardware.

1. Principles and Motivations

At its core, locality-aware generation ordering aims to improve system efficiency by ensuring that elements processed in sequence—be it tasks, data blocks, output tokens, or spatial regions—are "local" with respect to each other in the underlying topology or metric. The motivation across domains includes:

Reducing remote accesses: On systems like ccNUMA, accessing remote memory domains incurs significant latency penalties. Grouping and ordering tasks to maximize local accesses can preserve bandwidth and performance (0902.1884).
Improving memory utilization: Reordering mesh computations or data traversals to minimize cache misses and reuse distance can yield substantial speedups on modern multi-level memory hierarchies (1606.00803, 1902.07928).
Minimizing network traffic: In distributed systems and P2P overlays, appropriately sequencing block dissemination and replica placement can dramatically reduce traffic redundancy and response times (1007.2902, 1907.11997).
Modeling spatial coherence: In generative modeling of spatial data (images, meshes), generating locally adjacent structures sequentially allows easier modeling of dependencies and better global coherence (2501.14317, 2507.01957).
Dynamic algorithmic guarantees: In computational geometry and doubling metrics, maintaining dynamic orderings that preserve locality enables fast updates to proximity structures and spanners (1809.11147, 2408.14617).

2. Methodological Techniques

Locality-aware generation ordering has been instantiated across varied systems using distinct but related methods:

Domain-aware task queueing: Tasks are sorted into separate queues based on their memory or spatial locality. Threads or processes with a particular affinity preferentially process tasks in their local queue, as in the locality queues for ccNUMA (0902.1884).
Locality-sensitive orderings: In computational geometry and metric spaces, Locality-Sensitive Orderings (LSOs) are constructed so that, for any pair of points, there is a total ordering where all points "local" to the pair are contiguous. Algorithmic structures such as quadtrees, shifted grids, and net tree covers underpin these dynamic orderings (1809.11147, 2408.14617).
Local-neighbor reordering: For irregular data structures like meshes or graphs, explicit vertex or face orderings are computed (e.g., by recursive traversal prioritizing unprocessed neighbors) to minimize cache misses and maximize data reuse (1606.00803).
Parallel decoding strategies: In autoregressive models for image or sequence generation, scheduling groups of tokens to maximize contextual locality (proximity to already-generated outputs) while minimizing intra-group dependency allows efficient and high-quality parallel prediction (2507.01957). Scheduling algorithms systematically partition positions so each step generates spatially proximate, context-supported tokens.
Data-driven adaptive ordering: Recent generative models discover or learn optimal non-monotonic or locality-maximizing generation orders from data—for text, images, or code—sometimes via variational inference over permutation matrices (2110.15797). Context-awareness is achieved by conditioning the order on input structure and content.
Local neighborhood aggregation: In feature representations for detection and understanding (e.g., zero-shot HOI), adapters aggregate neighborhood patch information before proceeding to higher-level relational and global features, forming an implicit local-to-global generation structure (2505.19503).

3. Empirical Performance and Theoretical Guarantees

The efficacy of locality-aware generation ordering is validated through both empirical benchmarks and analytic results:

Throughput and scale: On ccNUMA systems, associating tasks with local domains and scheduling them via locality queues restores parallel efficiency and nearly matches the best possible static locality (0902.1884). In mesh smoothing, reordering can reduce L2/L3 cache misses by up to 84% and speedup execution by 75× in strong scaling (1606.00803). In mesh generation, shell-based token ordering enables models to generate up to 5,000 faces, tripling the feasible mesh size relative to non-locality-aware baselines (2501.14317).
Network traffic reduction: Locality-aware network coding in P2P systems reduces inter-domain redundancy by over 50%, demonstrating that the generation order of coded blocks, combined with neighbor selection, is as crucial as the available locality information itself (1007.2902). In decentralized storage, considering node heterogeneity (latency, availability, bandwidth) in replica ordering can improve both utility and locality by ~1.1–1.2× versus single-objective methods (1907.11997).
Autoregressive generation acceleration: For image models, locality-aware generative ordering enables a reduction in sequential steps from 256 to 20 (256×256 images) without degrading generation quality, providing at least a 3.4× latency decrease (2507.01957).
Cache-oblivious universality: For broad classes of algorithms, including sorting and matrix multiplication, locality-aware ordering as achieved via cache-oblivious designs is proven to be asymptotically optimal for any memory hierarchy rewarding spatial or temporal locality, eliminating the need for hardware-specific tuning (1902.07928).
Dynamic metric algorithms: In geometric/metric settings, dynamic LSOs allow efficient $O(\log n)$ update algorithms for fault-tolerant spanners and nearest neighbor queries in arbitrary doubling metrics, a generalization beyond Euclidean geometry (2408.14617).

4. Architectural and Design Considerations

Implementing locality-aware generation ordering involves practical architectural decisions:

Queue and scheduling overhead: Task-level ordering benefits from mapping overhead only when the computational granularity is sufficient; for fine-grained tasks, queue locking and scheduling may dominate (0902.1884).
Topology and heterogeneity: Effectiveness depends on the underlying hardware or network topology. Unpredictable task or data movement, or lack of stable locality in workloads, can diminish gains (0902.1884, 1907.11997).
Coordination among blocks: In parallel models, intra-group dependencies must be explicitly managed—specialized attention masks or algorithmic scheduling ensures that jointly decoded tokens can see adequate context without conflicting dependencies (2507.01957).
Compatibility with dynamic data: For computational geometry and metric data structures, robust net-tree covers and pairwise index trees enable fast updating under insertions and deletions, preserving locality guarantees (2408.14617).
Adaptive and context-aware ordering: Some modern generative models infer orders adaptively from data, optimizing for local or salient content prediction, which can improve fine detail or editing capabilities (2110.15797).

5. Applications and Broader Implications

Locality-aware generation ordering is applicable across:

High-performance scientific computing: Stencil solvers, mesh algorithms, and other memory-bound numerical applications (0902.1884, 1606.00803).
Distributed systems and networking: P2P data dissemination, replication in DHTs, and traffic localization (1007.2902, 1907.11997).
Geometry and graphics: Mesh generation, smoothing, and rendering pipelines, as well as dynamic spatial data structures (2501.14317, 1809.11147, 2408.14617).
Generative modeling: Efficient autoregressive generation for images, text, 3D volumes, and meshes, supporting high-resolution, editing, and interactive use cases (2110.15797, 2507.01957, 2409.20332).
Vision and interaction reasoning: Zero-shot detection in vision-language systems, where fine-grained locality is crucial (2505.19503).

The locality-aware approach supports scalability, ensures efficient computation or bandwidth usage, facilitates parallelization without loss of quality, and enables robust adaptation across heterogeneous platforms and dynamic environments.

6. Summary Table: Techniques, Domains, and Impact

Technique / Domain	Locality Mechanism	Quantitative Impact
Task scheduling on ccNUMA	Local queues/affinity-aware ordering	4× speedup, 10% from ideal (0902.1884)
Mesh processing / smoothing	RDR/BFS neighbor-based ordering	30–75× speedup, 84% fewer L3 misses (1606.00803)
P2P content distribution	LANC block scheduling, network coding	>50% traffic reduction (1007.2902)
Generative mesh and image models	Shell-based, token grouping, adaptive	3× mesh size, 3–13× fewer gen. steps (2501.14317, 2507.01957)
Dynamic spatial data (geometry, metrics)	Locality-sensitive orderings, tree covers	$O(\log n)$ updates; optimal spanner maintenance (2408.14617)

7. Future Directions and Open Challenges

While locality-aware generation ordering is foundational for many domains, ongoing research addresses challenges including:

Extending LSOs and cache-oblivious techniques to more general metrics and high-dimensional spaces (1809.11147, 2408.14617).
Efficiently learning or adapting optimal data- or content-aware orders in generative models under dynamic, multimodal, or adversarial inputs (2110.15797).
Further reducing system overheads and improving robustness to irregular, unpredictable workloads.
Integrating locality-aware strategies into end-to-end neural and hybrid systems without sacrificing universality or generalizability.

Locality-aware generation ordering remains a key enabling paradigm for scalable, efficient, and robust computation, bridging performance-critical hardware realities with algorithmic and modeling advances across computational science, geometry, machine learning, and distributed systems.