Certified means an exact certificate and a second checker. Everything else is labelled. If a certified claim cannot be rebuilt from the repo, that is a bug.
We also showed that if part of a secret prime leaks, the first bits are worth more than the last bits.
If the two primes were generated sloppily so p−1 and q−1 share a large factor, there is a proven method that beats the 2021 record. Ordinary keys are not generated that way.
This is not the algorithm that factors RSA in the real world. That one is much faster.
It’s the fastest factoring method that comes with a proof. Under the rules that method uses: N^(1/3) cells, N^(1/5) with today’s packing, N^(1/6) even with perfect packing.
N^(1/6) needs a pattern in the start positions that isn’t there. 2048-bit N^(1/6) is still ~2^341. Not an exploit.
The estimate’s effort setting then reads 417 / 642 / 900 instead of 406 / 624 / 874.
A standard simulator, run to the end, gives the same three numbers. What’s new is the proof that nothing obeying the rule does better, and a certificate a second program re-checks.
Not a claim the new standard is safer or weaker.
The old estimate used a straight line. The line starts where no allowed shape can — 6% too short.
You shall not pass. Unless you change the rules. Then you shall.
A fast an effective framework, which helped me put a UI around a prototype agent driven ML paper to code tool I put together...
There is also clearly a deep semantic analysis taking place on the image content, such as understanding iconography and the contextual meaning of it for a given document
How does this multimodal capability appear to work? An interesting differential is the reported token length of the retrieved pdf document. In contrast, the underlying text represents around 12k tokens.
It is only once a paper has been searched for via the Bing index that the picture content becomes indexed.
This capability does not appear to exist for local documents summarized via the Bing chat extension in edge, which is only able to reason atop the textual content in a pdf.
The GPT-4 accessible today is still limited to a 4k token context, which begins to cause it to forget as a task progresses and it runs out of context. However, with a 32k context available in preview, this is clearly the future of R&D. And it already has ideas on improvement...
GPT-4 then developed a Bayesian optimization system to model & sample hyperparameters for further improvement. The investigation was grounded in code, forming & testing hypotheses, and using larger datasets to evaluate algorithmic changes to enhance ML performance.
The benchmarks (written by GPT-4) evaluated accuracy, training time & inference times. A 50% speedup was observed using LRA & sparse matrices! This led to GPT-4 expanding the evaluation to a CNN with the MNIST dataset, resulting in a similar 30% speedup vs traditional approaches.
Exploring ways to improve ML model inference speed, GPT-4 via ChatGPT+ identified Low Rank Approximation & sparse matrices as a promising approach. It rapidly created Python programs to benchmark performance on the classic Iris dataset with a simple linear neural network.
I observed the system changing strategies based on tool outcomes, showing that it can adapt and learn from its mistakes. As these systems continue to progress, applying this technology in synbio, materials science, and other scientific grand challenges is borderline sci-fi.
It used the python interpreter to systematically debug the code it was generating, including working through problems such as accessing API keys, out of date documentation, and even debugging the quality of the output from the code generation tool it wrote!
