Zijie Zhou
Publications
A Queueing-Theoretic Framework for Stability Analysis of LLM Inference with KV Cache Memory Constraints
The rapid adoption of large language models (LLMs) has created significant challenges for efficient inference at scale. Unlike traditional workloads, LLM inference is constrained by both computation and the memory overhead of key-value (KV) caching, which accelerates decoding but quickly exhausts GPU memory. In this paper, we introduce the first queueing-theoretic framework that explicitly incorporates both computation and GPU memory constraints into the analysis of LLM inference. Based on this framework, we derive rigorous stability and instability conditions that determine whether an LLM inference service can sustain incoming demand without unbounded queue growth. This result offers a powerful tool for system deployment, potentially addressing the core challenge of GPU provisioning. By combining an estimated request arrival rate with our derived stable service rate, operators can calculate the necessary cluster size to avoid both costly over-purchasing and performance-violating under-provisioning. We further validate our theoretical predictions through extensive experiments in real GPU production environments. Our results show that the predicted stability conditions are highly accurate, with deviations typically within 10%.
Position: LLM Serving Needs Mathematical Optimization and Algorithmic Foundations, Not Just Heuristics
This position paper argues that LLM inference serving has outgrown generic heuristics and now demands mathematical optimization and algorithmic foundations. Despite rapid advances in serving systems such as vLLM and SGLang, their algorithmic cores remain largely unchanged from classical distributed computing: request routing uses join-shortest-queue or round-robin, scheduling defaults to FIFO, and KV cache eviction follows LRU. These general-purpose policies ignore the distinctive structure of LLM inference--dynamically growing KV cache memory, prefill-decode phase asymmetry, unknown output lengths, and continuous batching constraints. We contend that the field must develop mathematical models capturing these characteristics, enabling the design of algorithms with provable performance guarantees across diverse workloads, rather than heuristics that may succeed in some scenarios but fail unpredictably in others. Emerging work at the intersection of operations research and ML systems demonstrates that principled methods can match or exceed heuristic performance while providing theoretical guarantees. We call on the community to recognize algorithmic design for LLM serving as a research frontier.
PolarMem: A Training-Free Polarized Latent Graph Memory for Verifiable Multimodal Agents
As multimodal agents evolve from passive observers to long-horizon decision-makers, they require memory systems that provide not just information availability but logical verifiability. A fundamental limitation of current architectures is the epistemic asymmetry inherent in probabilistic vision-language models and dense associative memories: they conflate semantic affinity with factual existence and structurally fail to encode negative constraints. To this end, we introduce PolarMem, a training-free Polarized Latent Graph Memory designed to ground agent reasoning in verifiable evidence. PolarMem transforms fuzzy perceptual likelihoods into discrete logical constraints through non-parametric distributional partitioning. Furthermore, it employs a polarized graph topology with orthogonal inhibitory connections to explicitly store verified negation as a primary cognitive state. At inference time, we enforce a logic-dominant retrieval paradigm, suppressing hallucinatory patterns that violate negative constraints. Extensive evaluation across eight frozen Vision--Language Models and six benchmarks demonstrates that PolarMem functions as a robust cognitive system, establishing a foundation for verifiable multimodal agents. Our code is available at https://github.com/czs-ict/PolarMem.
Theoretically Optimal Attention/FFN Ratios in Disaggregated LLM Serving
Attention-FFN disaggregation (AFD) is an emerging architecture for LLM decoding that separates state-heavy, KV-cache-dominated Attention computation from stateless, compute-intensive FFN computation, connected by per-step communication. While AFD enables independent scaling of memory and compute resources, its performance is highly sensitive to the Attention/FFN provisioning ratio: mis-sizing induces step-level blocking and costly device idle time. We develop a tractable analytical framework for sizing AFD bundles in an $r$A-$1$F topology, where the key difficulty is that Attention-side work is nonstationary-token context grows and requests are continuously replenished with random lengths-while FFN work is stable given the aggregated batch. Using a probabilistic workload model, we derive closed-form rules for the optimal A/F ratio that maximize average throughput per instance across the system. A trace-calibrated AFD simulator validates the theory: across workloads, the theoretical optimal A/F ratio matches the simulation-optimal within 10%, and consistently reduces idle time.