L3-Based Resource Allocation

• L3-based resource allocation is a hardware-software co-design approach that integrates DIMM-PIM and GPU architectures to efficiently manage large-scale LLM inference workloads.
• It partitions resources and schedules tasks using adaptive algorithms and mathematical formulations to balance compute, memory, and PCIe data transfer requirements.
• Empirical results demonstrate up to 6.1× throughput improvement and nearly linear scaling with increased DIMM capacity and PIM bandwidth.

L3-based resource allocation refers to the class of hardware-software co-design systems that leverage L3 architecture—DIMM-PIM integration coupled with adaptive coordination—to orchestrate and allocate resources efficiently for large context LLM inference workloads. The L3 system unifies GPU-based transformer computation with scalable, high-bandwidth host-side memory processing, fundamentally changing how memory capacity and compute resources are provisioned and utilized in large-scale LLM deployments (Liu et al., 24 Apr 2025).

1. Architectural Foundations of L3 Design

The L3 architecture integrates a multi-GPU server (such as NVIDIA DGX-A100) with PIM-enabled host-side DIMMs. Within this platform:

• GPU Nodes: Hold all model weights and execute the batched fully-connected (FC) operations from each transformer layer, utilizing high-bandwidth HBM2e memory.
• PIM-Enabled DIMMs: Organize DRAM channels (e.g., 16 × DDR4-3200) to support two tiers of Processing Units (PUs): a rank-level PU on the buffer chip and bank-level PUs, one per DRAM bank. The rank-level PU handles in-flight bit relayout, softmax, and chip-wise accumulation; bank-level PUs conduct QK and SV GEMV operations, central to multi-head attention (MHA).
• PCIe Communication: Q/K/V vectors are transferred GPU→DIMM for MHA and attention results delivered back DIMM→GPU. Notably, only per-token Q/K/V vectors and attention outputs cross PCIe, avoiding full KV cache movement.

This hierarchical design enables key/values (K/V) caches for all token requests to be distributed and processed directly on DIMM-PIM, scaling both capacity and internal bandwidth linearly with the number of DIMMs while avoiding severe memory bottlenecks typical of GPU-only or DDR4-only approaches.

2. Resource Partitioning and Scheduling Objectives

L3-based resource allocation is tasked with maximizing transformer inference throughput (tokens/sec) by efficiently orchestrating computation and memory resources subject to fundamental constraints:

• Memory Capacity: Aggregate K/V cache per batch,

$$\sum_{i=1}^m (2 \times Dh \times L_i) \leq C_\mathrm{total}$$

where $m$ is the batch size, $Dh$ the head dimension, $L_i$ the per-request remaining token length, and $C_\mathrm{total}$ the combined DIMM-PIM KV capacity.

• PCIe Bandwidth: Transfer requirements per iteration,

$$B_\mathrm{pcie} \geq \max\left(\sum_{i\in\mathrm{decode}} 3Dh, \sum_{i\in\mathrm{prefill}} 2Dh\right),$$

ensuring that data movement for Q/K/V is not a bottleneck.

• Compute Balance: Partition requests into sub-batches $S_0$ and $S_1$; minimize max compute time between GPU and PIM pipeline:

$$\min_{S_0, S_1, c} [\mathrm{idle}_\mathrm{GPU} + \mathrm{idle}_\mathrm{PIM}]$$

by balancing execution such that $$T_\mathrm{GPU}(S, c) \approx T_\mathrm{PIM}(S', c')$$.

The adaptive scheduler computes estimations for each resource, solves an allocation program (often integer or greedy search), and launches pipelined operations to maximize overlap and minimize idle periods across devices.

3. Mathematical Formulations and Optimization

Resource allocation is formalized using a bipartite flow model:

• Memory/Bandwidth Mapping:

$$\begin{array}{ll} \max & \sum_{i,r} w_{i,r} \cdot x_{i,r} \ \text{s.t.} & \sum_{r} x_{i,r} \leq C_i \quad \forall\,i\ & \sum_{i} x_{i,r} \leq B_r \quad \forall\,r\ & x_{i,r} \in \{0,1\} \end{array}$$

where $x_{i,r}=1$ if request $i$’s KV is mapped to rankset $r$.

• Timing Models:

$T_\mathrm{PIM} = \alpha \sum L_i + \beta \sum L_i$

$$T_\mathrm{GPU} = \gamma |S| + \delta \left(\sum L_i - c\right) + \epsilon c$$

capturing latency for decode-MHA, PCIe comm, batched FC, and chunked FC per sub-batch.

• Lagrangian Relaxation:

$$\mathcal{L}(S_0, S_1, c_0, c_1, \lambda) = \max_j [T_\mathrm{GPU}(S_j, c_j), T_\mathrm{PIM}(S_{1-j}, c_{1-j}) ] + \lambda (\sum_{i\in S_0 \cup S_1} \mathrm{KV\_size}(i) - C_\mathrm{total})$$

providing a penalty for exceeding memory constraints.

Pseudocode for each scheduler iteration predicts timings, balances load, and dynamically adjusts chunking to optimize overlap (Liu et al., 24 Apr 2025).

4. Communication Strategies and Hardware Coordination

L3-based allocation achieves high utilization through multiple synergistic optimizations:

• Rankset-Level Overlap: Only one rankset per channel interacts over PCIe at a time; other ranksets continue local MHA computations, preserving up to 75% PIM compute during transfers (for 4 ranks/channel).
• Asynchronous Offload/Onload: QKV payloads are timed to arrive just-in-time for their sub-batch; prefill KV is offloaded during GPU FC computation. PIM-side double buffering mitigates PCIe-induced stalls.
• Load-Balanced Mapping: KV caches are stripe-mapped per-layer across ranksets to prevent transfer bottlenecks.

These strategies allow L3 to decouple bread-and-butter transformer operations from device bottlenecks, facilitating almost linear scaling as memory and bandwidth resources are increased.

5. Empirical Performance and Scaling Properties

L3 resource allocation demonstrates significant empirical acceleration relative to prior architectures:

Model	GPU	HBM-PIM	R-PIM	L3
OPT-66B	1.0	1.3	0.7	4.5
GPT-89B	1.0	1.5	0.8	5.3
GPT-175B	1.0	1.2	0.5	6.1

L3 achieves up to 6.1× throughput increase over GPU-only, with batch size increases (up to 14.3× for decoding) and per-token latency reduced to 29–53% of GPU-only levels for large batches. Scaling both DIMM capacity and PIM bandwidth yields nearly linear gains, contrasting with sub-2× improvements from augmenting either component alone (Liu et al., 24 Apr 2025).

6. Significance and Future Directions

L3-based resource allocation systems resolve key memory bottlenecks in long-context LLM inference by distributing the KV cache and attention computation across scalable, PIM-integrated host memory. Their adaptive scheduling, bandwidth-aware data movement, and compute-communication overlap broaden the feasible space for batch size and context window, enabling high-throughput operation without latency trade-offs.

Current L3 implementations provide a template for future high-performance LLM inference infrastructure, particularly as model and context sizes continue to outpace the capacity/bandwidth scaling of classic accelerator stacks. Further development is expected in (a) expanding per-device scaling laws, (b) more granular scheduling heuristics, and (c) co-designing with advanced interconnects and memory hierarchies to address remaining bottlenecks and edge-case domain constraints.