---
title: L3-Based Resource Allocation
url: https://www.emergentmind.com/topics/l3-based-resource-allocation-5bd51265-37f0-4acc-abe1-ece854673605
type: topic
---

# L3-Based Resource Allocation

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 language model deployments [2504.17584].

## 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 [2504.17584].

## 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 [2504.17584].

## 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.

Source: https://www.emergentmind.com/topics/l3-based-resource-allocation-5bd51265-37f0-4acc-abe1-ece854673605