mkvn/quantization-cache-amplification

Quantization as Cache Amplification

Trillion-Parameter Mixture-of-Experts Inference on a Commodity Laptop

Kavin Kumar, Neural Metrics

📄 Read the paper — 11 pages

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What this is

Weight quantization is usually justified as footprint reduction. This work argues that for offloaded mixture-of-experts inference that framing misses the leverage. The binding resource is not storage capacity but the fraction of expert slots resident in DRAM — and storage traffic depends on that fraction through a cache hit rate that is both concave and, for recency-based policies, discontinuous.

The central measured result: a least-recently-used expert cache hits exactly zero whenever its capacity falls below the k·L expert slots a single token touches. A token routes to k experts in each of L layers and revisits none of them until the next token — a cyclic reference string, the classical worst case for LRU. On real OLMoE-1B-7B traces (k=8, L=16, so 128 slots) we measure 0.0% hit rate at 2%, 5% and 10% capacity, jumping to 25.3% the moment capacity reaches 128. Quantization is what carries a system across that threshold.

Everything here was measured on one laptop: NVIDIA RTX A500 (4 GB VRAM), 32 GB DRAM, consumer NVMe, Windows 11.

Headline numbers

Result	Value
LRU hit rate below per-token working set	0.0% (measured, all capacities tested)
LRU hit rate at working set (128 slots)	25.3%
Popularity-pinned hit rate at 10% capacity	22.9% (vs 0.0% for LRU)
Codec @ 2.01 bits, WikiText-2 PPL	12.17 (bf16 reference: 8.11)
Frequency-conditioned allocation @ 1.51 bits	22.02 vs 25.54 uniform — 13.8% better at identical rate
NVMe random read @ expert-block granularity	6.01 GB/s (≥ sequential)
GPU device bandwidth	88.2 GB/s

Ablations (all at 1.51 bits, WikiText-2 PPL)

Configuration	PPL
RVQ + RHT + LDLQ (full codec)	25.54
— without block-LDL error feedback	7,701.98
— without incoherence processing	352.10
RTN uniform @ 2.25 bits (scalar baseline)	22,793.90

Both codec components are load-bearing, and error feedback matters more than rotation.

Contents

Path	Contents
paper/	Paper PDF + full LaTeX source and figures
code/codec.py	Sub-2-bit codec: randomized Hadamard transform, residual VQ, block-LDL error feedback
code/quant_model.py	Layer-sequential quantization + perplexity for OLMoE-1B-7B
code/trace_routing.py	Captures per-token expert routing traces
code/cache_policy.py	LRU / popularity-pinned / hybrid cache simulation
code/bench_io.py	Page-cache-bypassing NVMe, PCIe and DRAM benchmarks
code/project_1t.py	1T reference configuration and throughput roofline
results/routing_trace.npy	Raw routing traces: int16[16, 49152, 8] — the top-8 expert indices selected at every layer for 49,152 held-out tokens
results/*.json	Every measurement artefact behind the paper's numbers

Using the routing traces

import numpy as np
T = np.load("results/routing_trace.npy")   # [layers=16, tokens=49152, topk=8]
# distinct expert slots touched by one token:
print(T.shape[0] * T.shape[2])             # 128 -> the LRU threshold

Every number in the paper is generated programmatically from results/ via code/gen_numbers.py and code/gen_tables.py; nothing is transcribed by hand.

Scope — please read

No trillion-parameter model was executed. No 1T checkpoint was downloaded, quantized, or run. The 1T figures (196 GB at 1.5 bits, 1.81–3.08 tokens/s) are an analytical projection composing measured host parameters with a cache model validated against real 7B-scale routing traces. They are not benchmark results and should not be cited as such. The paper's Limitations section states this, and identifies the weakest assumption: that the Zipf exponent of expert popularity (measured s = 0.65 at 64 experts/layer) is scale-invariant up to 320 experts/layer. A full sensitivity curve across the entire hit-rate range is included precisely because that assumption cannot be foreclosed.

The paper also reports a negative result that constrains any system in this class: sustaining the storage stream while materializing fp16 weights would require ~116 GB/s of device bandwidth against 88.2 GB/s measured, so dequantization must be fused into the GEMM rather than staged through VRAM. No fused kernel was implemented here.

Quality cost is stated plainly rather than buried: sub-2-bit operation on a 1.3B-active-parameter MoE is expensive (8.11 → 22.02 PPL at 1.51 bits), which is why the systems analysis is parameterized by rate rather than asserting a single favourable operating point.

Model used

allenai/OLMoE-1B-7B-0924 — 6.9B total / 1.3B active, 16 layers, 64 experts/layer, top-8. Evaluation on WikiText-2.