We present the design and implementation of a new lifetime-aware tensor offloading framework for GPU memory expansion using low-cost PCIe-based solid-state drives (SSDs). Our framework, TERAIO, is developed explicitly for large language model (LLM) training with multiple GPUs and multiple SSDs. Its design is driven by our observation that the active tensors take only a small fraction (1.7% on average) of allocated GPU memory in each LLM training iteration, the inactive tensors are usually large and will not be used for a long period of time, creating ample opportunities for offloading/prefetching tensors to/from slow SSDs without stalling the GPU training process. TERAIO accurately estimates the lifetime (active period of time in GPU memory) of each tensor with the profiling of the first few iterations in the training process. With the tensor lifetime analysis, TERAIO will generate an optimized tensor offloading/prefetching plan and integrate it into the compiled LLM program via PyTorch. TERAIO has a runtime tensor migration engine to execute the offloading/prefetching plan via GPUDirect storage, which allows direct tensor migration between GPUs and SSDs for alleviating the CPU bottleneck and maximizing the SSD bandwidth utilization. In comparison with state-of-the-art studies such as ZeRO-Offload and ZeRO-Infinity, we show that TERAIO improves the training performance of various LLMs by 1.47 on average, and achieves 80.7% of the ideal performance assuming unlimited GPU memory.

In large language model (LLM) serving, each request accumulates persistent graphics processing unit (GPU) memory during service as its key-value cache grows with every generated token. Under high concurrency, aggregate memory usage therefore increases endogenously over time: the service process itself creates future capacity pressure. When memory capacity is exceeded, systems evict active requests, discarding cached state and restarting them later, which wastes computation and reduces throughput. We develop a discrete-time dynamical model of memory-constrained LLM inference that captures admission, memory growth, and eviction under continuous batching. In the saturated-input regime, the system admits both eviction-free fixed points and limit cycles with evictions. For homogeneous workloads, we show that the eviction-free equilibrium is unstable and that, except for a Lebesgue-measure-zero exact-capture set, the system converges to a unique worst-case limit cycle that is asymptotically stable outside this exceptional set, with throughput losses as large as 50%. For heterogeneous workloads, we prove a stability criterion in the two-class common-input setting and explain how the survival-polynomial mechanism generalizes to multiple classes and heterogeneous-input lengths. Under an input-dominated scaling regime, coprime decoding lengths stabilize the eviction-free equilibrium, while non-coprime lengths create synchronized modes that drive instability. These results characterize when workload heterogeneity desynchronizes completions and helps stabilize memory-constrained serving. More broadly, we identify service-induced congestion as a structural instability mechanism and derive scheduling design principles for sustaining high throughput.

We present the design and implementation of a new lifetime-aware tensor offloading framework for GPU memory expansion using low-cost PCIe-based solid-state drives (SSDs). Our framework, TERAIO, is developed explicitly for large language model (LLM) training with multiple GPUs and multiple SSDs. Its design is driven by our observation that the active tensors take only a small fraction (1.7% on average) of allocated GPU memory in each LLM training iteration, the inactive tensors are usually large and will not be used for a long period of time, creating ample opportunities for offloading/prefetching tensors to/from slow SSDs without stalling the GPU training process. TERAIO accurately estimates the lifetime (active period of time in GPU memory) of each tensor with the profiling of the first few iterations in the training process. With the tensor lifetime analysis, TERAIO will generate an optimized tensor offloading/prefetching plan and integrate it into the compiled LLM program via PyTorch. TERAIO has a runtime tensor migration engine to execute the offloading/prefetching plan via GPUDirect storage, which allows direct tensor migration between GPUs and SSDs for alleviating the CPU bottleneck and maximizing the SSD bandwidth utilization. In comparison with state-of-the-art studies such as ZeRO-Offload and ZeRO-Infinity, we show that TERAIO improves the training performance of various LLMs by 1.47 on average, and achieves 80.7% of the ideal performance assuming unlimited GPU memory.

We formalize and generalize the notation of Section 4.1 and prove the results. For the remainder of this section, we fix a dimension D (e.g. The D-dimensional SSM will be a map from a function u: D! to y: D!. Definition 2 (Indexing notation). Given a subset I [D], let I denote its complement [D]\I. Given a 2 N1 and b 2 N2, let a b 2 N1 N2 be defined as (a b)n1,n2 = an1bn2.

We describe a new software framework for fast training of generalized linear models. Theframework,named Snap Machine Learning (Snap ML), combines recent advances inmachine learning systems andalgorithms inanested manner to reflect the hierarchical architecture of modern computing systems.