cfgauss2718

11 ms·

1.
by cfgauss2718 2y ago
Even if you could get around the payload and energy density (power autonomy) constraints, which are very stringent, this seems like a dead product. Sure, it’s a cool project for some controls engineers. But I can scarcely imagine the deafen
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by cfgauss2718 2y ago
We know from the No Communication theorem that quantum entanglement does not transmit information between classical observers who have no role in preparing the initial state of the entangled elements. Why should one think that this No Commu
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Lectures on the Geometrical Anatomy of Theoretical Physics(youtube.com)
1 points by cfgauss2718 2y ago|1 comments
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by cfgauss2718 2y ago
This series by lecturer Frederic P. Schuller is astounding work of thorough mathematical exposition delivered with clarity and charisma. This body serves as an exemplary introduction and tutorial on mathematics spanning propositional logic,
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by cfgauss2718 2y ago
In quantum field theory (standard model of particle physics), photons are the quanta of a field (naturally identified with the quantized electromagnetic field, or U(1) gauge field), which evolves in a nonlinear way that is coupled not only
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by cfgauss2718 2y ago
I think are overstating the strength of the No Communication Theorem. It does not state that communication via quantum entanglement is impossible in all cases; the theorem is weaker. From the article you linked: “Being only a sufficient con
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by cfgauss2718 2y ago
I love when grammatical mistakes become unintentional puns
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by cfgauss2718 2y ago
Here’s maybe a useful example. Consider a scalar potential function F on R^3 that describes some nonlinear spring law. At a point p=(x,y,z), the differential dF can be thought of as a (1,0) tensor measuring the spring force. It acts on a pa
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by cfgauss2718 2y ago
Can you provide some examples of important tensors in physics for which the underlying vector space is infinite dimensional? I’m most familiar with the setting of tensor fields on manifolds, in which case the vector bundle consists of finit
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by cfgauss2718 2y ago
Yes, the “multi linear map” definition is accessible to an undergraduate who has taken linear algebra. However, the more common meaning of tensor in physics, like the metric tensor of spacetime, requires some more sophisticated background t
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by cfgauss2718 2y ago
Here here! Functions do not depend on your choice of coordinates, only the components of tensors do! I think this is why it’s important to keep covariance and contravariance in mind. While tensor(fields) do not depend on coordinates intrins
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by cfgauss2718 2y ago
I think the point above is that in physics tensor is usually overloaded, and those practicing physicists when they speak of tensors are more often referring to tensor fields, and most often this is in a context with more geometric structure
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by cfgauss2718 2y ago
Very well, let’s just agree that in physics (r,s) tensors usually refer to sections of the tensor product of some fixed number of copies of the tangent bundle (r copies) and cotangent bundle (s copies) of a smooth manifold (almost always ps
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by cfgauss2718 2y ago
Agreed, I can’t help but feel there is some overcompensation driving the style of writing. It was difficult to finish.
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by cfgauss2718 2y ago
There are some interesting parallels to ideas in this article and IIT. The focus on parsimony in networks, and pruning connections that are redundant to reveal the minimum topology (and the underlying computation)is reminiscent of parts of
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by cfgauss2718 2y ago
Nothing about this research violates conservation of energy. The article as written is advocating using excess solar or wind energy as input to this CO2->CH4 conversion process (which is electrolysis based) so that some of that energy ca
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by cfgauss2718 2y ago
On a glance, the Chichilinsky theorem assumption of smoothness for the mapping between voter preferences And the vote result (the relation phi) seems burdensome. For example, many people might be effectively summarized as single issue voter
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by cfgauss2718 2y ago
The multiverse may be a consequence of Everett’s theory, but the reality shattering nature of that consequence warrants scrutiny of the theory. Consider one of Xeno’s paradoxes. One may postulate that to go from A to B that first one passes
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by cfgauss2718 2y ago
How is the answer “everything that can happen does happen, just in an alternate universe that is identical except for the outcome of one single measurement” a parsimonious answer to the measurement problem? To quote Sam Harris, many-worlds
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by cfgauss2718 2y ago
Sympy is a poor tool to learn because it simply doesn’t scale to problems one most often encounters, even in schooling. Frankly, CAS are so general and unintelligent that problems with well known and elegant closed-form solutions, when pres
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by cfgauss2718 3y ago
If one thinks of a metric as a “distance measure”, which is to say, how similar is some input x to the “feature” encoded by a layer f(x), and if this feature corresponds to some submanifold of the data, then naturally this manifold will hav
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by cfgauss2718 3y ago
Yes of course any positive definite matrix can be used as a metric on the corresponding Euclidean space - but that doesn’t mean it’s necessarily useful as a metric. Hence I think it’s useful to distinguish things which could be a metric (in
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by cfgauss2718 3y ago
This NFM is a curious quantity . It has the flavor of a metric on the space of inputs to that layer. However, the fact that W’W remains proportional to DfDf’ seems to be an obvious consequence of the very form of f… since Df is itself Ds’WW
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by cfgauss2718 3y ago
You raise a fair point, I do think that it’s important to understand how the properties of the data manifest in the least-squares solution to Ax=b. Without that, the only insights we have are from analysis, while we would be remiss to overl
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by cfgauss2718 3y ago
Indeed, hopefully they can be diverted from interest in LLMs towards actual science, like the neuroscience which revealed the existence of said mirror neurons.
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by cfgauss2718 3y ago
Your point is a salient one. It would be useful if we could provide guarantees/bounds on generalization, or representation power, or understand how brittle a model is to shifts in the data distributions. Are these questions of the kind
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by cfgauss2718 3y ago
I agree with your interpretation. There is something there to be learned for sure, but I’m doubtful whatever that thing is will be a breakthrough in machine learning or optimization, nor that it will come by applying the tools of analysis.
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by cfgauss2718 3y ago
I haven’t read the manuscript yet, and am not sure that I will. However I don’t agree with the question. Gradient descent, the properties of the loss function are the “how”. It seems like you want to know how some properties of the data are
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by cfgauss2718 3y ago
By minimizing a loss functional with respect to a bunch of numbers that amount to entries in matrices (or tensors, whatever) using an approximate hill climbing approach. I’m not sure what insights there are to be gained here, it doesn’t see
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by cfgauss2718 3y ago
Am I the only person who saw this headline and thought WOW, 12 inch transistors!?

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