Most prospective students are required to submit a PhD proposal. It is important to understand that this project proposal does not bind you to do the project, if you are admitted. However, it should be written as though it does. The proposal is important input to the department’s decison to admit a student to the program and to award a scholarship.
Here are some tips how to write it:
The project proposal is a should be a narrative about a field of research (rather than individual papers) and identify important recent trends in research. It should briefly explain how a particular field of research is connected to wider research fields (e.g. how are Spiking Neural Networks connected to Neural Networks to Machine Learning to AI). This is best done by using a “funnel” approach. You start by describing a general research field (AI) and then narrow down very quickly to some specialised field (“Spiking Neural Networks”). In this narrowing down text, there should be many citations. This need not be longer than 2 paragraphs, perhaps shorter.
Once you narrowed down, you can write in more detail about the particular challenges in your chosen subfield. Here it is important to develop a narrative of what people are currently (the last 3 years or so) doing, and what is missed. You should not describe individual papers, but describe questions, challenges and trends. Citations are evidence for your narrative. Avoid too detailed descriptions of what is in specific papers. A typical sentence could be:
“The authors of [34] describe a new method to solve XXX; however, it was later shown [35] that their method did not scale to larger problems. Another solution was proposed by [36] showing promising performance on a range of benchmark problems, but a problem of the approach is that it has a high computational cost and still relies on ….”
This narrative about the research field should then directly lead to a research question. State the research question explicitly.
The second part of the proposal is an indication of what you plan to do during your PhD. Following this write a short plan of what you want to do: In Year 1, I will do this, then in Year 2 I will do this, etc. Detail is not as important here, rather it is an indication that your project is feasible within three years. Make sure that you indicate methods such that the reader understands what your approach will be, for example simulations, proofs, mathematical derivations and so on.
It is also good to indicate outcomes: What will your proposed contribution be? A new algorithm? A new theory?