Why Optimizer States Dominate Training Memory

Model parameters alone do not determine the VRAM footprint of training runs. Each optimizer maintains additional state tensors alongside the weights and gradients. For optimizers like Adam, two full-size buffers track the running mean and variance of gradients. With billions of parameters, these states require as much or more memory than the model itself. This calculator quantifies how much memory is consumed by parameters $\mathrm{M\_w}$, gradients $\mathrm{M\_g}$, and optimizer states $\mathrm{M\_o}$ so that practitioners can gauge hardware needs or choose lighter optimizers.

Computing Parameter and Gradient Memory

The memory for model weights depends on parameter count $P$ and precision $b$ in bits. Weight memory is $\mathrm{M\_w}=P\backslash times10^9\backslash timesb/8$ bytes. Because backpropagation stores gradients of the same size, gradient memory is $\mathrm{M\_g}=\mathrm{M\_w}$. Many large-model training setups already double memory from weights and gradients before optimizer states are considered. Mixed-precision training reduces $b$ to 16 or even 8 bits for weights and gradients, yet states are often kept at 32-bit precision for stability.

Optimizer State Variants

Different optimizers require varying numbers of auxiliary buffers per parameter. The simplest form of stochastic gradient descent (SGD) stores no extra state beyond weights and gradients, so $\mathrm{M\_o}=0$. SGD with momentum adds one velocity vector, implying $\mathrm{M\_o}=\mathrm{M\_w}$. Adam and AdamW maintain first and second moments, requiring two buffers: $\mathrm{M\_o}=2\backslash times\mathrm{M\_w}\backslash times\backslash frac\{\mathrm{b\_o}\}\{b\}$ where $\mathrm{b\_o}$ is the state precision. AdaGrad tracks accumulated squared gradients ($\mathrm{M\_o}=\mathrm{M\_w}\backslash times\backslash frac\{\mathrm{b\_o}\}\{b\}$), while RMSProp uses both a decaying average and an optional momentum term resulting in two or three buffers depending on implementation. The calculator assumes two.

Total Memory Requirement

The total memory for a single replica is $\mathrm{M\_t}=\mathrm{M\_w}+\mathrm{M\_g}+\mathrm{M\_o}$. Dividing by $\mathrm{10^9}$ converts bytes to gigabytes. To see if a model fits into available hardware, we compare $\mathrm{M\_t}$ with the per-GPU memory capacity $G$. The minimum number of GPUs needed without sharding is $N=\backslash lceil\mathrm{M\_t}/G\backslash rceil$. Optimizer selection can therefore double or triple the GPU count.

Example Calculation

Consider a 7-billion-parameter model in 16-bit precision trained with Adam at 32-bit state precision. Each parameter requires two bytes, so weight memory is $\mathrm{M\_w}=7\backslash times2=14$ GB and gradients add another 14 GB. Two 32-bit state tensors consume $\mathrm{7\backslash times4\backslash times2=56}$ GB. The total memory is 84 GB. If training on 80 GB GPUs, the model barely fits on one device without activations. Real workloads would need pipeline or tensor parallelism to distribute model and activations across multiple GPUs.

Optimizer	State Buffers	State Memory (GB)	Total Memory (GB)
SGD	0	0	28
SGD + Momentum	1	14	42
Adam	2	56	84

Impact of Precision Choices

Many optimizers store states in 32-bit precision even when weights use half precision. This halved $b$ but unchanged $\mathrm{b\_o}$ means optimizer memory dominates. Emerging research explores 8-bit optimizers that quantize moment estimates, reducing $\mathrm{b\_o}$ and reclaiming significant memory. Plugging in $\mathrm{b\_o}=8$ demonstrates potential savings: for Adam with 7B parameters, state memory drops from 56 GB to 14 GB, lowering total memory to 42 GB. Such reductions make single-GPU fine-tuning more accessible and cut communication overhead in distributed training.

Sharded and Offloaded Optimizers

Modern libraries like ZeRO partition optimizer states across devices or offload them to host memory. Sharding divides $\mathrm{M\_o}$ by the number of shards, while offloading transfers it out of VRAM at the cost of bandwidth. The calculator’s naive assumption of fully replicated states highlights the worst-case requirement; actual systems may achieve lower per-GPU memory, yet still pay costs in communication and host memory usage. Knowing the baseline helps evaluate whether sharding strategies are necessary.

Training vs. Inference Memory

Inference only needs weights and, optionally, a key–value cache for attention, omitting gradients and optimizer states entirely. If $\mathrm{M\_t^\{train\}}$ is the training memory and $\mathrm{M\_t^\{infer\}}=\mathrm{M\_w}$ (ignoring cache), the ratio $R=\mathrm{M\_t^\{train\}}/\mathrm{M\_t^\{infer\}}$ indicates how much additional memory training requires. For Adam, $R$ is roughly six with 32-bit states, meaning training consumes six times the memory of inference. This insight guides capacity planning for both development and deployment phases.

Future Trends

As models grow to trillions of parameters, traditional optimizer state replication becomes untenable. Research into state-efficient optimizers (e.g., Lion, Adafactor) and techniques like optimizer state factorizations will continue. Memory calculators help compare new methods quantitatively. By allowing different precision and optimizer combinations, this tool encourages exploration of hybrid approaches that balance convergence speed with hardware limits.

Conclusion

Optimizer states can account for the majority of memory in large-scale training. By entering model size, precision, and optimizer choice, practitioners quickly see how many gigabytes are consumed by each component and how many GPUs are required. The ability to experiment with half-precision weights or 8-bit optimizers reveals trade-offs between memory, communication, and numerical stability. With transparent memory accounting, teams can better plan training runs, budget hardware, and adopt innovations that reduce VRAM pressure without compromising performance.