All of these research topics sound amazing to me. Are you submitting research proposals for them?
Sent from my iPhone > On Nov 7, 2016, at 10:00 AM, axiom-developer-requ...@nongnu.org wrote: > > Send Axiom-developer mailing list submissions to > axiom-developer@nongnu.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://lists.nongnu.org/mailman/listinfo/axiom-developer > or, via email, send a message with subject or body 'help' to > axiom-developer-requ...@nongnu.org > > You can reach the person managing the list at > axiom-developer-ow...@nongnu.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Axiom-developer digest..." > > > Today's Topics: > > 1. Future research directions (Quantum Computing) (Tim Daly) > 2. Future research directions (Universal Numbers) (Tim Daly) > 3. Future research directions (Deep Neural Networks) (Tim Daly) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Mon, 7 Nov 2016 04:13:20 -0500 > From: Tim Daly <axiom...@gmail.com> > To: axiom-dev <axiom-developer@nongnu.org>, Tim Daly > <d...@axiom-developer.org> > Subject: [Axiom-developer] Future research directions (Quantum > Computing) > Message-ID: > <CAJn5L=+GffD7RZc8Aks7M4XdYC+z=q4sqdcdeaxszh4mqie...@mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Axiom is reaching a stable point where it can support research > in new areas. There is current work on Gustafson's Universal > Numbers (UNUMS) which promises to simplify the numeric > libraries. It seems to also promise some symbolic/numeric > computation. Time will tell. > > Another area, still at the read-the-literature stage is quantum > computing. IBM has made a 5-qubit machine available on the > web. Some effort was devoted to implementing known algorithms. > > Quantum computing had come a long way in the last few years. > There are several attempts to create a high level language for > expressing algorithms. > > Quipper is an interesting effort: > www.mathstat.dal.ca/~selinger/quipper > It is currently implemented on top of Haskell but it looks like > it could be implemented in Axiom. It uses Knill's QRAM model. > Some papers: > https://arxiv.org/pdf/1304.3390v1.pdf (Overview of the language) > https://arxiv.org/pdf/1304.5485v1.pdf (Introductory examples) > > My particular interest is twofold: Given my crypto background I'm > interested in the post-crypto quantum work. I'm also interested in > my observation that Hadamard gates are the basis for both unitary > quantum operations and shared-channel telecommunications. By > combining quantum crypto and shared-channel communication it > seems that there is a potential for ultra-secure communication. > > There are quantum computer simulators which could be embedded > into Axiom to support simulated quantum development. Since the > quantum operations are simple (unitary matrix operators) we could > create a syntax and language front end to express them. For instance, > being able to write a|Y> using the bra and ket notation. > > This is a NIST-supported exploding area of research with many dozens > of algorithms already available in the literature: > http://math.nist.gov/quantum/zoo/ > > Tim > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: > <http://lists.nongnu.org/archive/html/axiom-developer/attachments/20161107/a602b272/attachment.html> > > ------------------------------ > > Message: 2 > Date: Mon, 7 Nov 2016 04:32:31 -0500 > From: Tim Daly <axiom...@gmail.com> > To: axiom-dev <axiom-developer@nongnu.org>, Tim Daly > <d...@axiom-developer.org> > Subject: [Axiom-developer] Future research directions (Universal > Numbers) > Message-ID: > <CAJn5L=J3EvGEHzFUfwUnG86HE0hwzgvR9_ty00+gAgzU=vq...@mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Numeric computations have been locked into IEEE arithmetic > for a long time. The problems are well known. NAG's numeric > routines have a huge number of parameters to deal with these > issues. > > Axiom now has (growing) support for BLAS/LAPACK in native > form. This gives us the opportunity to explore alternative > number formats. BLAS routines could be adapted to use > interval arithmetic but initial experiments show that this tends > to generate wide, uninformative intervals. > > Gustafson[0] has proposed a universal number format (UNUMs) > which essentially allows two things. First, you can re-define the > width of the exponent and mantissa fields to match the problem. > Second, you can define exact intervals to generate exact results. > > Efforts are underway to create a new UNUM number format which, > hopefully, can be used in any context that DFLOAT can be used > (e.g. in polynomials). > > In the longer but still near term Intel has bought Altera so it now > owns about 45% of the Field Programmable Gate Array (FPGA) > market. They have used their manufacturing to shrink the die size > by many generations and incorporated the FPGA onto the latest > Intel processor chip. What this likely means is the ability to define > new, novel instructions "on the fly" from your program. That would > allow "hardware UNUM support". > > Ultimately this has the potential to allow strong symbolic/numeric > computation that does not suffer from overflow/underflow problems > and allows "symbolic epsilons". These symbolic epsilons can > eliminate the rounding-error / cancellation problems, leading to > more exact arithmetic and dynamic error analysis. > > Tim > > [0] Gustafson, John "The End of Error" 13-978-1-4822-3986-7 (2015) > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: > <http://lists.nongnu.org/archive/html/axiom-developer/attachments/20161107/5f80eb25/attachment.html> > > ------------------------------ > > Message: 3 > Date: Mon, 7 Nov 2016 05:00:51 -0500 > From: Tim Daly <axiom...@gmail.com> > To: axiom-dev <axiom-developer@nongnu.org>, Tim Daly > <d...@axiom-developer.org> > Subject: [Axiom-developer] Future research directions (Deep Neural > Networks) > Message-ID: > <CAJn5L=LCcOUF2Cgx4Q=4uqgbwwpvot6q5x59jvfasdwu9q0...@mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > There is an explosion of research on Deep Neural Networks. > OpenAI (https://openai.com/blog/) has 1 billion (US) dollars > in support. They are doing focused work on reinforcement > learning. Baidu, Google, Facebook, etc. are all deeply in the > game. > > Specifying Neural Networks to solve problems is easy. See > https://www.youtube.com/watch?v=sEciSlAClL8 which explains > the steps and the code to get 99+% accuracy on the MNIST > dataset (handwritten digits). > > Tensorflow includes primitives, such as 2d convolution, > matrix multiplication, symbolic derivatives, RELU (rectified > linear unit which is just zero for negative values and linear > otherwise), sigmoid functions, atan functions, etc. The actual > computation is just linear matrix computations, XW+B where > X are the data, W are the weights, and B are the biases. > > Latest "best practices" shows that deep neural networks are > best implemented by repeating layers of XW+B followed by > a non-linear (e.g. RELU, Sigmoid, Atan) step. > > Axiom has the ability to do all of these tasks, making it a good > platform for further research. In particular, there seems to be > little "algorithmic analysis". The DNN area and NN research > in general seems to be a collection of "tricks" (e.g. dropout). > This is troubling since there is no easy way to predict the > actual result, and rather frightening when the DNN is driving > your car. > > In theory what a DNN computes can be computed using a > single layer NN. Can Axiom be used to "collapse" the layers > by combining and spreading derivatives? A single layer NN > with complicated derivatives seems easier to analyze than a > multilayer iterated structure. The complicated derivatives could > be "grouped" into similar classes and the shape of the higher > order curves explored using symbolic expressions. This would > give a clearer view of what the NN will do, where the high > dimensional "valleys" lie, and where the system is sensitive. > Such an ability to do analysis could reshape the industry. > > Tim > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: > <http://lists.nongnu.org/archive/html/axiom-developer/attachments/20161107/9ff6ee93/attachment.html> > > ------------------------------ > > Subject: Digest Footer > > _______________________________________________ > Axiom-developer mailing list > Axiom-developer@nongnu.org > https://lists.nongnu.org/mailman/listinfo/axiom-developer > > > ------------------------------ > > End of Axiom-developer Digest, Vol 155, Issue 1 > *********************************************** _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer