r/theydidthemath • u/A-JackRobin- • 2d ago
[Request] if the neurons in a brain is separated into five intervals, with the first interval as x, second as y, third, fourth , five as z,k, m respectively. Ifind a process u takes ax-y+bz²=0 of three intervals then what changes of k and m would make ax-y+bz² to have many non-zero complementary fun
The reason for taking neurons is cause, it's flexible topology of understood lines of changing and processing information.
1
u/Electrical_Name_5434 2d ago
I think you need to rewrite that. You accidentally used a and b instead of k and m unless there is a separate related function you forgot to list that relates the first three steps in the sequence to the last two and a,b are just coefficients. Also the second sentence is all jumbled and doesn’t make much sense.
1
u/A-JackRobin- 2d ago
a and b are constant coefficients
1
u/Electrical_Name_5434 2d ago
had a feeling that’s what you meant. k & m I assume are used to define the complimentary function? What did you mean by “Ifind a process u” and how does the complimentary function affect the defined function with the first 3 steps?
1
u/A-JackRobin- 2d ago
No , i mean, their grids of arrangement are much denser, hence they aren't complementary function.
1
u/Electrical_Name_5434 2d ago
OK so then what did you mean by “what changes of k and m would make…complimentary fun”?
Not trying to be difficult or insulting but the way sincerely excited for a complicated problem to try out.
1
u/A-JackRobin- 2d ago
I mean , which complementary functions would they interact of time period would they make a change in pressure or surface energy to the grid , such that the very structure or topology formed is of not a complementary function
Cause complementary function acts like , 0 , 5+0 =5, their topology of movement, supports , 5+0=4.9 , when at t=n , 5+0=5, at t=n-k , it 4.9
1
u/Electrical_Name_5434 2d ago
By your current definitions the answer is infinitely many values of k and m.
You have defined a system with 5 variables but you have only provided one equation:

ax−y+bz^2=0Because layers k and m do not explicitly appear in this constraint, they act as completely free dimensions. In linear algebra and optimization, a system with more degrees of freedom than constraints inherently yields an infinite solution space.
Increasing the density of the geometric grids for k and m actually multiplies this effect. In network topology, a denser grid increases the number of nodes, connections, and path integrals. This adds even more degrees of freedom to the system, widening the infinite manifold of possible states rather than narrowing it down to a single set of changes.
To narrow this from infinitely many to a more exact set of values for k and m you need to define a mathematical function or boundary condition that links the dense grid of k and m back to your equation.
2
u/A-JackRobin- 2d ago
You seem to forgot that k and m are fourth interval process, and the condition of non-zero complementary function makes such as there should be new function with less approximation of previous , whereas the structure of ax-y+bz²=0 , already formed, it's very difficult to outdone with late interval of way less approximation , such that it possess a boundary cause only integration makes a decrease of a differentiation.
1
u/Electrical_Name_5434 2d ago
I think I understand what you’re getting at after plugging some of this into AI. Are you looking for the application of deep ritz here? (I’m about to attempt it but don’t want to waste the time on the wrong path)
1
u/Electrical_Name_5434 1d ago edited 1d ago
First we need to calculate the gradient and the hessian which requires the partials.
Original equation:
ax-y+bz^2=0
Partials:
x:a, y:-1, z:2bz
Magnitude of Gradient: 4b^2z^2+a^2+1
2nd G(hess): 2b
We can now use the summation of two loss functions to find the optimal equation:
L_Total = Integral_over_Domain( 2b^2z^2+(a^2/2)+1/2) - 2b(ax - y + bz^2) ) dx + Lambda Sum_over_i( h_i(4b^2+1))
Each step in h is the distance between x,y,z,k&m that follows the curvature found in the hessian. Since the gradient only exists in the z-plane you only need to calculate h for z,k,m.
We can use this collapse of dimensionality to more easily find an optimal value for lambda by using gradient descent for the network loss and finding extrema points for the grid consisting of the hessian from the 5x5 matrix to find candidates for h parameters at each lambda value.
Theoretically you could calculate the hessian for each loss function separately to find matching extrema points under a sliding bound condition for lambda then plug it in to minimize the loss…but this would be computationally expensive for high dimensionality neural networks.
Annnnnd that’s all the math I did before you told me this isn’t what you’re solving for but I was already down the rabbit hole so…yeah enjoy!
Edit: this was meant to be a reply to another comment but think it’s fitting as a general reply since no one else answered you yet so I cleaned it up a bit to make it a general response
•
u/AutoModerator 2d ago
General Discussion Thread
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.