Sliding Window Memory Scheduler

• Sliding window memory scheduler is a mechanism that manages a dynamic buffer of sequential data for stateless aggregation in both hardware SWAG engines and reinforcement learning systems.
• It employs a five-stage FPGA pipeline—comprising window buffering, sorting, merging, aggregation, and output—to ensure high-throughput access while efficiently handling insertions and deletions.
• Adaptive memory scheduling reduces compute and memory costs by dynamically selecting critical observations, leading to optimized performance across diverse applications.

A sliding window memory scheduler is a mechanism—prevalent in both low-latency hardware data processing engines and memory-constrained reinforcement learning—that manages a windowed buffer of sequential data, facilitating efficient, high-throughput access to subsets of time- or event-ordered elements for stateless aggregate computation or sequential decision-making. In hardware, this scheduler orchestrates the flow, sorting, and updating of memory-resident tuples in SWAG (Sliding Window Aggregation) engines; in learning systems, it designates which past observations are retained for policy input and which are evicted, whether through fixed heuristics or adaptive, policy-driven selection (Papaphilippou et al., 2024, Tasse et al., 22 Dec 2025).

1. Foundations and Formal Problem Setting

The sliding window concept generalizes to settings wherein only the most recent or most relevant history from a stream is material to current computation. In classical hardware streaming or database contexts, the window is defined by a parameter $WS$ (window size) and advanced by a stride $WA$ (window advance), over which aggregates such as sum, count, or median are performed (Papaphilippou et al., 2024). In non-Markovian reinforcement learning, the window comprises a finite stack of prior observations $[x_{t-k+1},\dots,x_t]$, with stack length $k$ selected to capture all environment dependencies up to minimal order $k^*$, i.e., $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$ being stationary (Tasse et al., 22 Dec 2025).

The central scheduling challenge is to maintain this window under stringent constraints on processing time, memory bandwidth, and on-chip RAM capacity, ensuring timely incorporation of new elements and eviction of stale data while supporting high-throughput aggregate or sequence computations.

2. Pipeline Architecture and Memory Layout in Hardware SWAG Engines

A canonical FPGA-based SWAG engine consists of five sequential pipeline stages: (a) a window buffer (a shift register of width $WA$), (b) a sorter (operating over $WS$ elements), (c) an insertion/deletion engine (performing WA-way merge and eviction), (d) an aggregation engine (such as a pipelined partial reduction-rolling aggregator), and (e) an output writer (Papaphilippou et al., 2024). The organization enables each window advance to push in $WA$ new tuples, evict $WA$ oldest, and propagate a fully sorted and updated window downstream for aggregation.

The window buffer is physically realized through interleaving the $WA$0-element buffer across $WA$1 on-chip BRAM banks (typically $WA$2 or $WA$3) to facilitate one read (eviction) and one write (insertion) per cycle without port contention. Each BRAM bank stores a round-robin stripe of 64-bit tuples; element $WA$4 is mapped to bank $WA$5 and slot $WA$6. Head and tail pointers track the positions for next eviction and next insertion, respectively, each advanced by $WA$7 every $WA$8 cycles. This architectural arrangement enables both high-frequency pipeline operation and large window sizes absent external DRAM, supporting window sizes up to $WA$9 on Xilinx UltraScale+ FPGAs (Papaphilippou et al., 2024).

3. Window Maintenance Algorithms and Scheduling Policies

The sliding window scheduler must guarantee: (a) that only the most recent $[x_{t-k+1},\dots,x_t]$0 tuples are present for aggregation, and (b) that insertions, deletions, and sorting do not induce throughput bottlenecks. The insertion/deletion stage merges a sorted run of $[x_{t-k+1},\dots,x_t]$1 new tuples into an existing $[x_{t-k+1},\dots,x_t]$2 sorted block, evicting the $[x_{t-k+1},\dots,x_t]$3 oldest. In-place merge algorithms—implemented via hardware binary search and block shifts—maintain window order at each step. Time complexity per window advance is $[x_{t-k+1},\dots,x_t]$4 for insertion and $[x_{t-k+1},\dots,x_t]$5 for eviction, yielding amortized per-tuple overhead $[x_{t-k+1},\dots,x_t]$6 when $[x_{t-k+1},\dots,x_t]$7 (Papaphilippou et al., 2024).

Bank-interleave scheduling is managed through a deterministic, latency-aware rotation: at cycle $[x_{t-k+1},\dots,x_t]$8, read bank is $[x_{t-k+1},\dots,x_t]$9, write bank is $k$0, where $k$1 reflects pipeline latency. This guarantees that read and write ports on each bank are accessed in a disjoint schedule, eliminating data hazards with minimal control overhead.

4. Complexity, Resource Utilization, and Performance Metrics

For hardware-accelerated SWAG, aggregate resource utilization scales as

• $k$2, with $k$3 and $k$4
• $k$5, with $k$6 and $k$7
• $k$8

Peak measured throughputs on real hardware (Xilinx ZU3EG Ultra96, $k$9 MHz, $k^*$0, $k^*$1) are 1 Gtup/s, with on-chip resource usage of 128 BRAM tiles, 36k LUTs, and 50k FFs, and a speedup of $k^*$2 over ARM64 CPU for $k^*$3k-tuple sorts. Compared to prior FPGA SWAG approaches, these designs achieve $k^*$4 tuple-rate with similar BRAM and $k^*$5 fewer LUTs, all without off-chip DRAM (Papaphilippou et al., 2024).

5. Sliding Window Scheduling for Learning Agents: Frame Stacking and Adaptive Stacking

In sequential decision-making, a “sliding window memory scheduler” (or frame stacker) governs the retention of observation tuples for function approximation in non-Markovian environments. Fixed-size FIFO frame stacking, in which the most recent $k^*$6 elements are preserved, incurs costs scaling as $k^*$7 or $k^*$8 (for Transformers) in inference and update. However, the necessary window length $k^*$9 may far exceed the minimal sufficient $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$0, resulting in sharp growth of both compute and storage costs as $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$1 (Tasse et al., 22 Dec 2025). This effect is particularly pronounced in environments where relevance is sparse but long-range dependency is high, such as T-Mazes and hidden-cue tasks.

Adaptive Stacking (AS) generalizes the sliding window scheduler by introducing a policy-driven “memory action” which jointly selects which slot to evict in a bounded stack, exploiting the fact that only a sparse subset $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$2 observations are necessary for optimal action. The resulting policy achieves full-history optimality when $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$3, as formalized in convergence theorems and empirically validated across diverse memory tasks (Tasse et al., 22 Dec 2025).

6. Comparative Evaluation and Empirical Findings

Experiments in (Tasse et al., 22 Dec 2025) demonstrate that adaptive memory scheduling via AS attains optimal returns with reduced stack sizes and dramatically lower memory regret compared to fixed windowing. In Passive-T-Maze with maze length $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$4, a fixed stack requires $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$5 while $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$6 suffices for AS, yielding a 9× reduction in stack size. For Transformer-based policies, this translates to a quadratic reduction in per-step compute: from $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$7 to $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$8. Across MLP, LSTM, and Transformer architectures, the savings in both working memory and computation scale with $\Pr(x_{t+1}, r_{t+1} \mid x_{t:t-k^*}, a_t)$9 or $WA$0, with no deterioration in final performance or generalization (Tasse et al., 22 Dec 2025).

A representative empirical table (Passive-T-Maze, MLP policy):

Memory Scheme	Stack Size $WA$1	Compute Cost/Step	Memory Cost	Final Return	Memory Regret
FS($WA$2)	18	$WA$3	$WA$4	Optimal	~0.02
AS($WA$5)	2	$WA$6	$WA$7	Optimal	~0.01
FS($WA$8)	2	$WA$9	$WS$0	Fail	>0.8

In FetchReach, AS($WS$1) achieves 90% success, outperforming both FS(4) (<20%) and FS($WS$2) (≈10%).

7. Application Domains and Broader Relevance

Sliding window memory schedulers are foundational in a spectrum of domains: high-performance database analytics, low-latency operating system monitoring, streaming data mining in securities and medical sensors, and learning-based autonomous agents exposed to long- or variable-lag dependencies (Papaphilippou et al., 2024, Tasse et al., 22 Dec 2025). Their utility arises from both providing explicit, bounded memory resources for stateless windowed computation and enabling flexible, policy-adaptive control of memory under learning-theoretic constraints. This architecture is especially significant in hardware datastream aggregation, where real-time guarantees and on-chip resource frugality are critical, and in learning agents, where variable-order memory control underpins scalability and sample efficiency in non-Markovian settings.

The confluence of deterministic hardware scheduling and meta-learned memory control illustrates the interdisciplinary interplay between systems and learning, with sliding window schedulers serving as a bridging abstraction for scalable, efficient computation in both engineered and autonomous systems.