Once an LLM has been trained, it can be deployed to respond to user requests. For instance, given a prompt like 'How can I live a more environmentally friendly life?', the model can generate multiple distinct answers by sampling the output space, producing four different outputs mathematically denoted as $\mathbf{y}_1, \dots, \mathbf{y}_4$:

• Output 1 ($\mathbf{y}_1$): Consider switching to an electric vehicle or bicycle instead of traditional cars to reduce carbon emissions and protect our planet.
• Output 2 ($\mathbf{y}_2$): Adopt a minimalist lifestyle. Own fewer possessions to reduce consumption and the environmental impact of manufacturing and disposal.
• Output 3 ($\mathbf{y}_3$): Go off-grid. Generate your own renewable energy and collect rainwater to become completely self-sufficient and reduce reliance on non-renewable resources.
• Output 4 ($\mathbf{y}_4$): Support local farm products to reduce the carbon footprint of transporting food, while enjoying fresh, healthy food.