Large Language Models (LLMs) are impressive, but their size makes them expensive to run. Imagine trying to fit a supercomputer in your pocket – that's the challenge with running LLMs on everyday devices. A new technique called ResQ is changing the game. It shrinks LLMs down to a fraction of their original size, using a clever trick called 4-bit quantization. Essentially, it simplifies the math behind the model without losing much accuracy. This process is like converting a high-resolution image to a smaller file size – you lose some detail, but the overall picture is still recognizable. ResQ uses a combination of mathematical techniques, including Principal Component Analysis (PCA) and random rotations, to pinpoint the most important parts of the model to keep in higher precision. This targeted approach minimizes errors and preserves performance. Tests on popular LLMs like Llama 2 and Llama 3 show ResQ significantly outperforms other quantization methods. It delivers similar accuracy to the original models while using much less computing power. This breakthrough opens doors for running powerful LLMs on smaller devices, making AI more accessible and efficient. While challenges remain, ResQ is a crucial step towards a future where powerful AI is within everyone's reach.