multivariable calculus – Gradient of $ -y ^ T log left (f left (W x; gamma, beta right) right) $ w.r.t. $ left {W, gamma, beta right } $?

How to calculate the gradient of
begin {align}
L left (W, gamma, beta right): = -y ^ T log left (f left (W x; gamma, beta right) right)

in memory of $ left {W, gamma, beta right } $, from where $ x in mathbb {R} ^ n $, $ W in mathbb {R} ^ {m times n} $, and $ y in mathbb {R} ^ m $, but $ y_i in {0,1 } $, $ f (z; gamma, beta) $ is parameterized with $ gamma $ and $ beta $?

The definition of
$$ eqalign {
f (z; gamma, beta) & = gamma left (z- mu (z) right) \ left ( sigma (z) + epsilon right) ^ {- 1/2} + beta cr
mu (z) & = alpha 1 ^ Tz cr
sigma (z) & = alpha sum_ {k = 1} ^ m left (ex[k] – mu (z) right) ^ 2 equiv alpha 1 ^ T left[ left( z- mu(z) right) odot left(z – mu(z) right) right] cr
from where $ 1 ^ T $ is a row vector with all, $ odot $ is an elementwise multiplication and $ alpha $ and $ epsilon $ are known scalars.

Thanks in advance for your help

dd wrt – What would be the best / easiest option for my home network setup? openwrt vs ddwrt vs. pfsense

Current TPLink TL-WDR4300 routers with original firmware have a very limited parental control.
It only has 4 entries for trusted devices. So my ability is to either turn on parental control, ie only 4 devices can be connected. Not only for me, I also have to give my wife Chromecast access

I only know 3 possibilities:

I need:

What hardware do I have:

I bought the last one for Pfsense. But honestly, I would prefer to use it for Ubuntu Docker containers because it's quiet and low power.

About me: A developer with little knowledge of networks. Have a good experience with Ansible / Docker and prefer UI scripts.

I tend to think about going to Openwrt with Tplink Archer C7 (by ISP as a gift for 3 years). I think I should be able to flash it, in the worst case with UART.

The only thing is that I'm scared of spending time and figuring out that I had to go with peacock and spend the time learning pfsense.

Matrix Calculus – Derivation of $ { rm Re} left { rm tr} left [Z^H left( AX right) right] right } $ w.r.t. $ X in mathbb {C} ^ {m times n} $.


Let's say I have a function
$$ f = { rm Re} left { rm tr} left [Z^H left( AX right) right] right } , $$
where the matrices are $ Z in mathbb {C} ^ {k times n} $, $ A in mathbb {C} ^ {k times m} $, and $ X in mathbb {C} ^ {m times n} $,

I want the derivative w.r.t. $ X $i.e. $ frac { partial f} { partial X} $,


Start with the differential, followed by derivation.

Since $ { rm tr} (A ^ H B): = A ^ *: B $,
begin {align}
& = d ; { rm Re} left {Z ^ *: A ; X right } \
& = d ; { rm Re} left {Z: A ^ * ; X ^ * right } \
& = { rm Re} left {A ^ H ; Z: ; dX ^ * right }. \
end {align}

Then the gradient
begin {align}
frac { partial f} { partial X ^ *}
& = { rm Re} left {A ^ H ; Z right }.
end {align}

Is that correct? Thank you in advance.

dd wrt – QoS: MAC priority for clients behind a repeater

I've set up a wireless network with a Linksys router (DD-WRT) as an AP and a TP-Link repeater to expand coverage.

To manage the bandwidth for specific users, I have set up QoS rules on the AP (DD-WRT) with MAC priority:

however The AP only shows the MAC of the repeater and the MACs of the users within the AP area. The MAC addresses of users behind the repeater are not listed:
AP Client MACs

Repeater client MACs

The purple MAC is not listed in the AP client list. It refers to a device that is connected via the TP-Link repeater.

Q: How can I set up MAC priority for repeater clients? Am I simply adding the purple MAC in the AP-MAC priority list even though it is not listed as a client? I want to set a certain priority, rather than prioritizing all clients behind the repeater, by adding the repeater's MAC to the AP's MAC priority list, as is happening now.

If there is (only) one (more complicated) way to accomplish this task, I would like to know how, but probably knowledge expires, how to leak through port forwarding and other things.