1/ A ∞-wide NN of *any architecture* is a Gaussian process (GP) at init. The NN in fact evolves linearly in function space under SGD, so is a GP at *any time* during training. https://t.co/v1b6kndqCk With Tensor Programs, we can calculate this time-evolving GP w/o trainin any NN

2/ In this gif, narrow relu networks have high probability of initializing near the 0 function (because of relu) and getting stuck. This causes the function distribution to become multi-modal over time. However, for wide relu networks this is not an issue.
3/ This time-evolving GP depends on two kernels: the kernel describing the GP at init, and the kernel describing the linear evolution of this GP. The former is the NNGP kernel, and the latter is the Neural Tangent Kernel (NTK).
4/ Once we have these two kernels, we can derive the GP mean and covariance at any time t via straightforward linear algebra.
5/ So it remains to calculate the NNGP kernel and NT kernel for any given architecture. The first is described in https://t.co/cFWfNC5ALC and in this thread
https://t.co/6RO7VZDQNZ
6/ The NTK for any architecture is calculated in https://t.co/v1b6kndqCk and in this thread
https://t.co/OOoOMdPOsR

More from Data science

Wellll... A few weeks back I started working on a tutorial for our lab's Code Club on how to make shitty graphs. It was too dispiriting and I balked. A twitter workshop with figures and code:


Here's the code to generate the data frame. You can get the "raw" data from https://t.co/jcTE5t0uBT


Obligatory stacked bar chart that hides any sense of variation in the data


Obligatory stacked bar chart that shows all the things and yet shows absolutely nothing at the same time


STACKED Donut plot. Who doesn't want a donut? Who wouldn't want a stack of them!?! This took forever to render and looked worse than it should because coord_polar doesn't do scales="free_x".
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🌺कैसे बने गरुड़ भगवान विष्णु के वाहन और क्यों दो भागों में फटी होती है नागों की जिह्वा🌺

महर्षि कश्यप की तेरह पत्नियां थीं।लेकिन विनता व कद्रु नामक अपनी दो पत्नियों से उन्हे विशेष लगाव था।एक दिन महर्षि आनन्दभाव में बैठे थे कि तभी वे दोनों उनके समीप आकर उनके पैर दबाने लगी।


प्रसन्न होकर महर्षि कश्यप बोले,"मुझे तुम दोनों से विशेष लगाव है, इसलिए यदि तुम्हारी कोई विशेष इच्छा हो तो मुझे बताओ। मैं उसे अवश्य पूरा करूंगा ।"

कद्रू बोली,"स्वामी! मेरी इच्छा है कि मैं हज़ार पुत्रों की मां बनूंगी।"
विनता बोली,"स्वामी! मुझे केवल एक पुत्र की मां बनना है जो इतना बलवान हो की कद्रू के हज़ार पुत्रों पर भारी पड़े।"
महर्षि बोले,"शीघ्र ही मैं यज्ञ करूंगा और यज्ञ के उपरांत तुम दोनो की इच्छाएं अवश्य पूर्ण होंगी"।


महर्षि ने यज्ञ किया,विनता व कद्रू को आशीर्वाद देकर तपस्या करने चले गए। कुछ काल पश्चात कद्रू ने हज़ार अंडों से काले सर्पों को जन्म दिया व विनता ने एक अंडे से तेजस्वी बालक को जन्म दिया जिसका नाम गरूड़ रखा।जैसे जैसे समय बीता गरुड़ बलवान होता गया और कद्रू के पुत्रों पर भारी पड़ने लगा


परिणामस्वरूप दिन प्रतिदिन कद्रू व विनता के सम्बंधों में कटुता बढ़ती गयी।एकदिन जब दोनो भ्रमण कर रहीं थी तब कद्रू ने दूर खड़े सफेद घोड़े को देख कर कहा,"बता सकती हो विनता!दूर खड़ा वो घोड़ा किस रंग का है?"
विनता बोली,"सफेद रंग का"।
तो कद्रू बोली,"शर्त लगाती हो? इसकी पूँछ तो काली है"।
The chorus of this song uses the shlokas taken from Sundarkand of Ramayana.

It is a series of Sanskrit shlokas recited by Jambavant to Hanuman to remind Him of his true potential.

1. धीवर प्रसार शौर्य भरा: The brave persevering one, your bravery is taking you forward.


2. उतसारा स्थिरा घम्भीरा: The one who is leaping higher and higher, who is firm and stable and seriously determined.

3. ुग्रामा असामा शौर्या भावा: He is strong, and without an equal in the ability/mentality to fight

4. रौद्रमा नवा भीतिर्मा: His anger will cause new fears in his foes.

5.विजिटरीपुरु धीरधारा, कलोथरा शिखरा कठोरा: This is a complex expression seen only in Indic language poetry. The poet is stating that Shivudu is experiencing the intensity of climbing a tough peak, and likening

it to the feeling in a hard battle, when you see your enemy defeated, and blood flowing like a rivulet. This is classical Veera rasa.

6.कुलकु थारथिलीथा गम्भीरा, जाया विराट वीरा: His rough body itself is like a sharp weapon (because he is determined to win). Hail this complete

hero of the world.

7.विलयगागनथाला भिकारा, गरज्जद्धरा गारा: The hero is destructive in the air/sky as well (because he can leap at an enemy from a great height). He can defeat the enemy (simply) with his fearsome roar of war.