GPUs are inherently better at handling large batch sizes and parallel computations due to their design. CPUs, on the other hand, have fewer cores and are better suited for sequential computations. Hence, you observe a performance drop when you switch from GPU to CPU.

Here are some ways you can improve the performance on CPUs:

1. Reduce Batch Size: While it's advantageous to use large batch sizes on a GPU, it's the opposite with CPUs. When using CPUs, you should use smaller batch sizes. Although this means more iterations, it will help you avoid memory-related slowdowns.

2. Optimize Model: If possible, consider pruning or quantizing your model. Pruning is the process of removing less significant weights, while quantization reduces the precision of the weights. Both of these techniques make the model smaller and quicker, although at the cost of some accuracy.

3. Use ONNX Runtime: ONNX (Open Neural Network Exchange) is a open format to represent deep learning models. With ONNX, AI developers can more easily move models between state-of-the-art tools and choose the combination that is best for them. ONNX Runtime is a performance-focused engine for ONNX models, which has been optimized for both cloud and edge and works on both Linux and Windows.

4. Use Distillation: If your model is very large, you might want to consider using a technique known as distillation. This is a process in which a smaller model is trained to mimic the behavior of the larger one, leading to smaller and faster models that are capable of similar performance.

5. Parallelize: Even if a single core of a CPU is not as powerful as a GPU core, modern CPUs usually have multiple cores. You can use parallel processing libraries like Ray or multiprocessing in Python to distribute the load across all cores.

6. Libraries Optimized for CPU: PyTorch has an extension library called torch.utils.bottleneck which can help you to find the bottlenecks in your model. Additionally, Intel has optimized several deep learning operations in PyTorch for CPU usage specifically. To use these, you simply need to install the MKL (Math Kernel Library) version of PyTorch.

7. JIT Compilation: PyTorch provides a Just-In-Time (JIT) compiler that can optimize your model's speed and reduce its memory consumption. It can be especially beneficial for deployment where constant model interpretation can lead to overhead.

Remember that these are guidelines and the exact steps you'll need to take will depend on your specific model and application. It might be necessary to experiment with several of these options and profile the performance to see what works best for your needs.
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