Scale-Dependent Memory Optimization

• Scale-dependent memory optimization is a dynamic strategy that tailors memory allocation and management to match the scale of the problem, model, or system.
• It employs techniques like low-rank approximations, adaptive cache management, and hardware–software co-design to minimize resource usage while preserving performance.
• Real-world applications include high-dimensional optimization, neural network inference, and systems design, with proven theoretical guarantees and measurable efficiency improvements.

Scale-dependent memory optimization refers to algorithmic, architectural, and systems-level strategies that explicitly adapt memory usage and memory management mechanisms based on problem, model, or system scale. Rather than prescribing uniform memory efficiencies across all scenarios, scale-dependent approaches differentiate and optimize memory for distinct regimes—such as increased problem dimensionality, larger model sizes, deeper optimization trajectories, or rapidly expanding working sets in both data and compute-centric applications. This paradigm is motivated by the observation that memory constraints and optimal allocation schemes change drastically as models, buffers, or systems grow, and that both computational and performance bottlenecks often shift at different scales. Scale-dependent memory optimization therefore encompasses data structures, iterative methods, model compression, cache management, and hardware–software co-design, each adapted to maximize efficiency, performance, and robustness under evolving scale constraints.

1. Memory-Efficient Algorithm Design and Factorization

Central to scale-dependent memory optimization is the replacement of full-matrix or full-trajectory state with factorized, low-rank, or selective representations. In high-dimensional continuous optimization, the Limited Memory CMA-ES (LM-CMA-ES) (Loshchilov, 2014, Loshchilov, 2015) avoids storing an explicit $n \times n$ covariance matrix and instead reconstructs the necessary Cholesky factor from $m \ll n$ direction vectors. The update equation,

$A^{(t+1)} = a A^{(t)} + b^{t} p_c^t (v^t)^\top,$

where $A$ is the Cholesky factor and $p_c^t$, $v^t$ are evolution paths and inverse directions, enables sampling with $O(mn)$ time and space. The performance–efficiency trade-off is governed by $m$; for large $n$, modest $m$ (e.g. 20–30) suffices to capture critical dependencies in fully non-separable problems, offering strong convergence with minimal memory.

Analogously, subspace adaptation schemes in large-scale Riemannian meta-optimization (Yu et al., 25 Jan 2025) decompose gradient adaptation into row- and column-wise components using small LSTMs. This enables optimizer sharing across parameter blocks of different sizes and reduces memory footprint by up to six orders of magnitude. For convex optimization, sample-based variants of Frank–Wolfe replace $n \times n$ SDP iterates by single random vectors with matching covariance, reducing storage from $O(n^2)$ to $O(n)$ without compromising theoretical guarantees (Shinde et al., 2020).

These methods exemplify a key principle: full, dense state maintenance quickly becomes infeasible at scale, but low-rank or selective statistics—appropriately constructed—can approximate dynamics or solution properties with significantly lower memory cost, permitting large-scale applications infeasible under naïve approaches.

2. Adaptive and Differentiated Memory Management

Memory allocation and cache management schemes increasingly exploit the heterogeneity of memory demands across scale and workload characteristics. RecShard (Sethi et al., 2022) partitions embedding tables and their constituent rows in neural recommendation (DLRM) models according to statistical access patterns, CDF/ICDF profiles, and per-feature usage. This allows hot rows to reside in high-bandwidth memory (HBM) while cold rows are relegated to slower tiers (UVM), yielding over 6× higher throughput and orders-of-magnitude less access to bottlenecked memory.

In the context of transformer inference, Scissorhands (Liu et al., 2023) compresses KV caches in LLMs by retaining only tokens with persistent importance, as determined by attention scores—an approach justified both empirically and by formal bounds on attention contribution preservation. Discarding low-importance entries offers up to 5× reduction in memory usage, with negligible loss in perplexity or downstream accuracy, and compounds synergistically with low-bit quantization techniques.

Similarly, for visual autoregressive models, ScaleKV (Li et al., 26 May 2025) utilizes attention selectivity metrics to categorize transformer layers as “drafters” (requiring broad context and larger cache) or “refiners” (focusing on local details and supporting aggressive cache reduction). This scale-aware allocation achieves 10× KV cache reduction while maintaining pixel-level fidelity.

Mario (Liu et al., 22 Sep 2024) further demonstrates at the hardware systems level that dynamic page interleaving/tiering and runtime policies, informed by scale-dependent workload characterization and PMU metrics, maximize throughput or minimize tail latency in CXL memory configurations as system and working set scale increases.

3. Impact of Problem and Model Scale on Memory Trade-offs

The optimal memory optimization strategy is inextricably tied to the scale of the problem, model, or system. In reasoning-oriented LLM inference, recent results (Kim et al., 13 Oct 2025) show a bifurcation: for models below an “effective 8-bit 4B size” threshold, allocating memory to higher model capacity (i.e., more weights or higher precision) is advantageous for accuracy, whereas, above this scale, allocating memory to longer token generations and parallel decoding batches yields better performance. This trade-off is also decisive in the choice between KV cache quantization versus eviction, and in the deployment of parallel scaling and cache management policies.

For optimization methods such as LM-CMA-ES and subspace-adaptive Riemannian methods, scaling up the number of direction vectors or learned subspace adaptors directly determines the balance between memory footprint and quality of solution approximation. In memory slices architectures (Asgari et al., 2018), the number of slices and their memory–compute ratio govern the linear or superlinear scaling of performance with increased problem size and data volume.

A plausible implication is that, for large-scale, memory-intensive applications, static, one-size-fits-all memory efficiency mechanisms are fundamentally inadequate. Instead, scale-dependent design—explicitly recognizing thresholds and structural transitions—yields superior performance and system utilization.

4. Applications and Case Studies

Several domains exhibit the practical benefits of scale-dependent memory optimization:

• Derivate-free optimization in high-dimensions: LM-CMA-ES enables efficient optimization of problems with $n$ up to $10^6$ using less than 10 MB of working memory, as shown on separable and non-separable black-box benchmarks (1404.55201511.00221).
• Neural network training and inference: In large DLRMs, RecShard’s partitioned embedding placement limits bottlenecked memory movement, directly impacting training cost and throughput (Sethi et al., 2022). In video compressive sensing, multi-group reversible 3D convolutional blocks permit memory-efficient deep learning for high-resolution videos, reducing training memory from >17 GB (in BIRNAT) to about 1.35 GB and enabling end-to-end reconstruction of full-HD scenes (Cheng et al., 2021).
• LLM deployment: Quantization and KV cache compression/eviction, whose trade-offs are scale-dependent (Kim et al., 13 Oct 2025), are necessary for practical, high-throughput inference.
• Systems and architecture design: The modular memory slices paradigm (Asgari et al., 2018) and composable, locally-integrated memory architectures (Liu et al., 28 Aug 2025) scale bandwidth and locality-aware compute almost linearly with added units, outperforming naive scaling of monolithic DRAM.

These examples illustrate that a scale-sensitive approach is not only about resource efficiency but also about enabling real-world deployment and new applications otherwise blocked by prohibitive memory or compute bottlenecks.

5. Theoretical Guarantees and Analytical Formulations

Several of the reviewed methods are supported by explicit theoretical analysis:

• Sample-based SDP optimization (Shinde et al., 2020) provides convergence and feasibility bounds, demonstrating that storing only a vector $z_t$ (with $E[z_t z_t^\top] = X_t$) for each iterate achieves near-optimality for semidefinite relaxations.
• Cholesky factor recursions in LM-CMA-ES have closed-form updates (Equation (1) in (Loshchilov, 2014)), guaranteeing that sampling properties are preserved even without an explicit covariance matrix.
• Memory–performance predictions for system-level policies (e.g., Mario) employ lightweight linear models linking PMU counters to latency/throughput, validated with 91–94% fit accuracy across hundreds of workloads (Liu et al., 22 Sep 2024).

Such formalism ensures that scale-dependent optimization is not merely an engineering heuristic but an analytically tractable and reliable methodology.

6. Comparisons, Limitations, and Misconceptions

Many traditional memory-saving techniques (e.g., fixed 4-bit quantization, full-matrix optimizers, or heuristics treating all features, rows, or layers equivalently) are shown to be suboptimal or even counterproductive as scale increases. Recent results (Kim et al., 13 Oct 2025) highlight that standard memory-optimal choices for non-reasoning models (such as aggressive weight quantization) can fail dramatically for reasoning tasks. Similarly, memory slices and hardware–software codesign approaches (Asgari et al., 2018, Liu et al., 28 Aug 2025) demonstrate that simply scaling main memory, or pushing all data into a single tier, leads to energy and bandwidth crises due to fundamental physical and signaling constraints.

A persistent misconception is that maximizing model size or context always improves performance; however, when faced with exponential growth of caches, long prompts, or disproportionately skewed access patterns, only scale-aware allocation and differentiated pruning achieve tractable efficiency.

7. Future Directions

Scale-dependent memory optimization continues to evolve, with ongoing research focusing on:

• Meta-optimizers and hybrid compression that adapt to context, workload, or model architecture dynamically;
• Architectural innovations exploiting modular memory slices, hierarchical caches, and tight compute–memory integration using 2.5D/3D packaging (Liu et al., 28 Aug 2025);
• Unification of algorithmic and systems-level optimization, for example, embedding memory modeling and allocation statically at compile time (e.g., via advanced DSA (Lamprakos et al., 7 Apr 2025));
• Online adaptation—for autonomous agents, scalable online continuous-memory encoding and retrieval (Wu et al., 10 Oct 2025) demonstrate how an expanding memory bank and retrieval strategy can robustly improve long-horizon performance in variable environments.

A plausible implication is that as models and systems continue to scale, memory optimization will increasingly require cross-layer mechanisms that are sensitive to both present scale and anticipated evolution, blurring traditional boundaries between algorithms, architectures, and system software.

---

Scale-dependent memory optimization thus represents a unifying framework that underpins advances in large-scale optimization, learning systems, high-performance architecture, and resource-aware deployment. State-of-the-art approaches selectively leverage structure, adaptivity, and rigorous modeling to fundamentally reshape the balance between memory consumption, computational efficiency, and application scalability.