教育和學習︰ Up《grade》【四】

500px-GabrielHorn

傳說中大天使加百利之號角 Gabriel’s Horn 一旦響起,就是審判日 Judgment Day 的到來。然而卻沒有任何人見過這個號角 ?這也許正是義大利數學家埃萬傑利斯塔‧托里拆利 Evangelista Torricelli 想像創造托里拆利小號之原因︰它是一個表面積無限大但卻體積有限的三維物體,或許該是用著第五元素乙太才能構成的吧!!

羊角螺旋

Cornu_Spiral.svg

龍捲風

比方說︰『事實就是發生過了的事』? 如果曾經有一隻猴子真的敲打出了莎士比亞的哈姆雷特,那麽這是那隻猴子它自己能知道的事實嗎?假使連它自己都不能知道,人們會認為這是件發生過的事實嗎? 又假使歷史上根本沒有莎士比亞的哈姆雷特,然而未來將會有□□的○○,到那時有隻猴子曾使這事成真的了,難道真的可以歸結說過去曾經有一隻猴子真的敲打出 了□□的○○的嗎?

學習就像是個『羊角螺旋』的軌跡,一再的一次又一次覆裹著中心的主題,每次的回歸 ,總是帶著新的知識與舊的記憶。自古以來人類一直想方設法希望解開大自然的奧秘,也許終將能有一天,這個思想螺旋成了『龍捲風』,大到能含括天地萬物。

這樣的一個學習者將會如何建造自己知識之金字塔的呢?他會不會用『想像的實驗』去釐清『基本概念』之糾葛的呢?還是用『推導歸謬』的邏輯,去探測一個『自明假設』之深遠結論的呢?又或者會將在大自然中發現的方程式求解,然後『畫圖』與『演示』這個解之意義的呢?……

─── 《加百利之號角!!

 

假使 AI 只是場欺人的美夢,傳說中之 Oneiroi 會穿越『象牙之門』而來?

The gates of horn and ivory are a literary image used to distinguish true dreams (corresponding to factual occurrences) from false. The phrase originated in the Greek language, in which the word for “horn” is similar to that for “fulfil” and the word for “ivory” is similar to that for “deceive”. On the basis of that play on words, true dreams are spoken of as coming through the gates of horn, false dreams as coming through those of ivory.

 

是誰拿著『犄角』!吹響了號角?!

Why this name, Keras?

Keras (κέρας) means horn in Greek. It is a reference to a literary image from ancient Greek and Latin literature, first found in the Odyssey, where dream spirits (Oneiroi, singular Oneiros) are divided between those who deceive men with false visions, who arrive to Earth through a gate of ivory, and those who announce a future that will come to pass, who arrive through a gate of horn. It’s a play on the words κέρας (horn) / κραίνω (fulfill), and ἐλέφας (ivory) / ἐλεφαίρομαι (deceive).

Keras was initially developed as part of the research effort of project ONEIROS (Open-ended Neuro-Electronic Intelligent Robot Operating System).

“Oneiroi are beyond our unravelling –who can be sure what tale they tell? Not all that men look for comes to pass. Two gates there are that give passage to fleeting Oneiroi; one is made of horn, one of ivory. The Oneiroi that pass through sawn ivory are deceitful, bearing a message that will not be fulfilled; those that come out through polished horn have truth behind them, to be accomplished for men who see them.” Homer, Odyssey 19. 562 ff (Shewring translation).

 

果真能左右夢神俄涅洛伊之行事!?

祇聞日昨紅樓方建

Theano at a Glance

Theano is a Python library that lets you to define, optimize, and evaluate mathematical expressions, especially ones with multi-dimensional arrays (numpy.ndarray). Using Theano it is possible to attain speeds rivaling hand-crafted C implementations for problems involving large amounts of data. It can also surpass C on a CPU by many orders of magnitude by taking advantage of recent GPUs.

Theano combines aspects of a computer algebra system (CAS) with aspects of an optimizing compiler. It can also generate customized C code for many mathematical operations. This combination of CAS with optimizing compilation is particularly useful for tasks in which complicated mathematical expressions are evaluated repeatedly and evaluation speed is critical. For situations where many different expressions are each evaluated once Theano can minimize the amount of compilation/analysis overhead, but still provide symbolic features such as automatic differentiation.

Theano’s compiler applies many optimizations of varying complexity to these symbolic expressions. These optimizations include, but are not limited to:

  • use of GPU for computations
  • constant folding
  • merging of similar subgraphs, to avoid redundant calculation
  • arithmetic simplification (e.g. x*y/x -> y, --x -> x)
  • inserting efficient BLAS operations (e.g. GEMM) in a variety of contexts
  • using memory aliasing to avoid calculation
  • using inplace operations wherever it does not interfere with aliasing
  • loop fusion for elementwise sub-expressions
  • improvements to numerical stability (e.g. \log(1+\exp(x)) and \log(\sum_i \exp(x[i])))
  • for a complete list, see Optimizations

Theano was written at the LISA lab to support rapid development of efficient machine learning algorithms. Theano is named after the Greek mathematician, who may have been Pythagoras’ wife. Theano is released under a BSD license (link).

 

今天竟已成黃葉地呦??!!