# solvers.InferenceScalingModel { #mlsysim.solvers.InferenceScalingModel }

```python
solvers.InferenceScalingModel()
```

Models inference-time compute scaling (Wall 12: Reasoning/CoT Cost).

This model quantifies the cost of 'System-2 thinking' — inference-time
compute scaling via chain-of-thought (CoT) reasoning, where the model
generates K intermediate reasoning steps before producing the final answer.
Each step incurs the full cost of autoregressive decoding.

Literature Source:
1. Wei et al. (2022), "Chain-of-Thought Prompting Elicits Reasoning in
   Large Language Models."
2. Snell et al. (2024), "Scaling LLM Test-Time Compute Optimally Can Be
   More Effective Than Scaling Model Parameters."
3. OpenAI (2024), "Learning to Reason with LLMs." (o1 reasoning model.)

## Methods

| Name | Description |
| --- | --- |
| [solve](#mlsysim.solvers.InferenceScalingModel.solve) | Solves for inference-time reasoning cost. |

### solve { #mlsysim.solvers.InferenceScalingModel.solve }

```python
solvers.InferenceScalingModel.solve(
    model,
    hardware,
    reasoning_steps=8,
    context_length=2048,
    precision='fp16',
    efficiency=0.5,
)
```

Solves for inference-time reasoning cost.

#### Parameters {.doc-section .doc-section-parameters}

| Name            | Type                | Description                                          | Default    |
|-----------------|---------------------|------------------------------------------------------|------------|
| model           | TransformerWorkload | The language model used for reasoning.               | _required_ |
| hardware        | HardwareNode        | The target hardware node.                            | _required_ |
| reasoning_steps | int                 | Number of reasoning steps K (each generates tokens). | `8`        |
| context_length  | int                 | Input context length in tokens.                      | `2048`     |
| precision       | str                 | Numerical precision.                                 | `'fp16'`   |
| efficiency      | float               | Compute efficiency factor (0.0 to 1.0).              | `0.5`      |

#### Returns {.doc-section .doc-section-returns}

| Name   | Type             | Description                                             |
|--------|------------------|---------------------------------------------------------|
|        | Dict\[str, Any\] | Total reasoning time, cost per query, and token counts. |