There are a number of generalisations of this transference technique. In a paper of Green and myself, we extended the above theorem to progressions of longer length (thus transferring Szemerédi’s theorem to the primes). In a series of papers (culminating in a paper to appear shortly) of ...
for medium-sized and large , where are natural numbers and is the divisor function (actually our methods can also treat a generalisation in which is non-integer, but for simplicity let us stick with the integer case for this discussion). Our methods also allow for one of the divisor functio...
P. What does it mean to understand a neural network? Preprint at arXiv https://arxiv.org/abs/1907.06374 (2019). Saxe, A., Bhand, M., Mudur, R., Suresh, B. & Ng, A. Y. Unsupervised learning models of primary cortical receptive fields and receptive field plasticity. Adv. Neural ...
This method is a more accurate way of measuring website performance, especially when compared to the previous options. By taking a selection of your end users and measuring how long it takes for them to access your pages, you can use the averages of these results to make generalisations abo...
(e.g. those in Writing and Marketing) than for others, like those in Finance & Legal or Software and Tech work. (B) Skill Premia: Here we see that relative to specialisation – the diagonal of the matrix – generalisation is profitable across skill and worker domains. But we clearly see...
Reasoning, axiomatisation, and generalisation are still big open questions in Graph ML. Throughout the year, we have seen continued advances in GNN architectures inspired by algorithmic reasoning, as well as more robust out-of-distribution generalisation on graph-structured tasks. We now have Knowled...
In particular, we first perform independent prompting on both sketch and photo branches of an SBIR model to build highly generalisable sketch and photo encoders on the back of the generalisation ability of CLIP. We then devise a train- ing paradigm to adapt the learned encoders for ...
Another limitation of our study is in the heterogeneity of STS and the diverse biological behaviour of the 450 histological subtypes, which makes generalisations difficult. Furthermore, we are unable to present an optimal schedule for the follow-up of soft tissue sarcomas of the limb. However, ...
Let , , , be as in that theorem. It will be convenient to normalise the weights by to make their mean value comparable to . From Theorem 1 and summation by parts we have whenever does not consist entirely of ones. We now take a closer look at what happens when does consist entirely...
Even when does pretend to be a Dirichlet character , we can still say something: if the limits exist for each (which can be guaranteed if we pass to a suitable subsequence), then is the uniform limit of periodic functions , each of which is –isotypic in the sense that whenever are ...