MACHINE REASONING: A PERSPECTIVE AND POSSIBILITY Aik Beng NG, - - PowerPoint PPT Presentation
MACHINE REASONING: A PERSPECTIVE AND POSSIBILITY Aik Beng NG, Zhangsheng LAI, Mar 18 AI EXCEEDING HUMAN PERFORMANCE Timeline Estimates for AI Achieving Human Performance [1] Years from 2016 [1] Grace et al. When Will AI Exceed Human
Aik Beng NG, Zhangsheng LAI, Mar 18
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[1] Grace et al. “When Will AI Exceed Human Performance? Evidence from AI Experts” Journal of Artificial Intelligence Research 62, 2018, 729-754
Years from 2016 Timeline Estimates for AI Achieving Human Performance[1]
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[1] Grace et al. “When Will AI Exceed Human Performance? Evidence from AI Experts” Journal of Artificial Intelligence Research 62, 2018, 729-754
Years from 2016 Timeline Estimates for AI Achieving Human Performance[1]
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[2] He et al. “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification”. ICCV '15 Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV), 2015, Pages 1026-1034 [3] Chaochao Lu and Xiaoou Tang. “Surpassing Human-Level Face Verification Performance on LFW with GaussianFace”. AAAI'15 Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015, Pages 3811-3819 [4] The Challenge of StarCraft, DeepMind [5] Liu et al. “Artificial Intelligence–Based Breast Cancer Nodal Metastasis Detection”. Archives of Pathology & Laboratory Medicine In-Press., 2018 [6] Assael et al. “LipNet: End-to-End Sentence-level Lipreading”. arXiv:1611.01599v2 [cs.LG], 2016
Image Recognition[2] Face Recognition[3] Cancer Detection[5] Lip Reading[6] Starcraft II[4]
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“to identify something from prior knowledge”
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“again”, “once more” “understand through thought, experience, senses”, “to acquire knowledge”
“to identify something from prior knowledge”
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“to identify something from prior knowledge”
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“again”, “once more” “understand through thought, experience, senses”, “to acquire knowledge”
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“again”, “once more” “understand through thought, experience, senses”, “to acquire knowledge”
“to identify something from prior knowledge”
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
[7] Leon Bottou. “From machine learning to machine reasoning”. Machine Learning Volume 94 Issue 2, 2004, Pages 133-149
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[8] Adam Santoro, David Raposo, David G. Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Tim Lillicrap. "A simple neural network module for relational reasoning." In Advances in neural information processing systems, pp. 4974-4983, 2017.
Set of sentences (supporting facts) LSTM (sentence processing) Question LSTM (question embedding)
𝜄(𝑝𝑗, 𝑝
𝑘, 𝑟)
𝜄(𝑝𝑗, 𝑝
𝑘, 𝑟)
𝜄(𝑝𝑗, 𝑝
𝑘, 𝑟)
Σ
𝑔
𝜚(𝑝𝑗, 𝑝 𝑘, 𝑟) Answer
𝑃 𝑟
Relation Network (RN)
𝑆𝑂 𝑃 = 𝑔
𝜚
𝑗,𝑘
𝜄(𝑝𝑗, 𝑝
𝑘, 𝑟)
𝑥ℎ𝑓𝑠𝑓 𝑗𝑜𝑞𝑣𝑢 𝑗𝑡 𝑡𝑓𝑢 𝑝𝑔 objects 𝑃 = 𝑝1, 𝑝2, … , 𝑝𝑜 𝑏𝑜𝑒 𝑟𝑣𝑓𝑡𝑢𝑗𝑝𝑜 𝑓𝑛𝑐𝑓𝑒𝑒𝑗𝑜 𝑟 𝑏𝑜𝑒 𝑔
𝜚 𝑏𝑜𝑒𝜄 𝑏𝑠𝑓 𝑁𝑀𝑄𝑡
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“Fast and intuitionistic thinking”
“Slow and deliberate thinking”
decisions by constructing mental models or simulations of future possibilities.
Designed by Freepik
[9] Jonathan St. B.T. Evans. "In two minds: dual-process accounts of reasoning“. Trends in cognitive sciences 7, no. 10, 2003, 454-459
System 1
(also known as Type 1)
System 2
(also known as Type 2)
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“Fast and intuitionistic thinking”
within the resulting matrix. “Slow and deliberate thinking”
answer.
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“Fast and intuitionistic thinking”
within the resulting matrix.
“Slow and deliberate thinking”
answer.
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive
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Type theory is a branch of mathematical symbolic logic that formalizes the idea that each term if of some definitive type. We write 𝑏 ∶ 𝐵 which can be interpreted in two ways:
2019 ∶ ℕ 1; 0.75; 2.3; 18.3 ∶ Vec(ℝ, 4) Lemma simple : forall (n : nat), n = n.
simple : forall (n : nat), n = n. Lemma impossible : forall (n : nat), n = n+1. ?? : forall (n : nat), n = n+1.
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Dependent pair types (∑-types) are types with two components where the type of the second component is allowed to vary depending on the choice of the first component.
Types that depend on a term
(𝑑:𝐷𝑝𝑚𝑝𝑠)
(red, apple) : ∑(𝑑:𝐷𝑝𝑚𝑝𝑠) 𝐺𝑠𝑣𝑗𝑢𝑡(𝑑) (silver, ??) : ∑(𝑑:𝐷𝑝𝑚𝑝𝑠) 𝐺𝑠𝑣𝑗𝑢𝑡(𝑑) The dependent pair type is written as ∑(𝑦:𝐵) 𝐶(𝑦) with term 𝑏, 𝑐 ∶ ∑(𝑦:𝐵) 𝐶(𝑦), given 𝑏 ∶ 𝐵 and 𝑐 ∶ 𝐶(𝑏). projT1 (red, apple) = red projT2 (red, apple) = apple
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(Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
Tom Betty
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(Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞)
Andy Betty
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Andy Betty Tom Betty
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(??, ??) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
?? Tom
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Mother’s Husband is Father
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Mother’s Husband is Father findFather : forall (x : Person) (y : ), ℍ -> Person prfFather : forall (x : Person) (y : ) (z : ℍ), 𝐺𝑏𝑢ℎ𝑓𝑠
𝑦(𝑞𝑠𝑝𝑘𝑈1 𝑨)
where =
𝑞:𝑄𝑓𝑠𝑡𝑝𝑜
𝑁𝑝𝑢ℎ𝑓𝑠
𝑦(𝑞)
ℍ =
𝑞:𝑄𝑓𝑠𝑡𝑝𝑜
𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝑞𝑠𝑝𝑘𝑈1 (𝑧)(𝑞) (??, ??) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
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Mother’s Husband is Father infFather : forall (x : Person) (y : ), ℍ -> ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠
𝑦(𝑞)
where =
𝑞:𝑄𝑓𝑠𝑡𝑝𝑜
𝑁𝑝𝑢ℎ𝑓𝑠
𝑦(𝑞)
ℍ =
𝑞:𝑄𝑓𝑠𝑡𝑝𝑜
𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝑞𝑠𝑝𝑘𝑈1 (𝑧)(𝑞) (??, ??) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
Merge findFather and prfFather
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Mother’s Husband is Father infFather : forall (x : Person) (y : ), ℍ -> ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠
𝑦(𝑞)
(??, ??) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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Goal Window
1 subgoal (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) (Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞) ______________________________________(1/1) . ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
Proof Window
Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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Goal Window
2 subgoals (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) (Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞) ______________________________________(1/2) .∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) ______________________________________(2/2) .∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒??(𝑞)
Proof Window
Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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Goal Window
1 subgoal (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) (Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞) ______________________________________(1/1) .∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞)
Proof Window
Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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Goal Window
No more subgoals.
Proof Window
Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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Goal Window
father_of_Tom is defined
Proof Window
Theorem father_of_Tom : sigT (Father Tom).
exact (Betty, birthcert). exact (Andy, marriagecert). Defined.
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We have constructed the term, father_of_Tom = (Andy, prfFather Tom (Betty, birthcert) (Andy, marriagecert)) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) Using represented information (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) (Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞) And the encoded knowledge infFather : forall (x : Person) (y : ), ℍ -> ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠
𝑦(𝑞)
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) (Andy, marriagecert) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐼𝑣𝑡𝑐𝑏𝑜𝑒𝐶𝑓𝑢𝑢𝑧(𝑞)
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive (Betty, birthcert) : ∑𝑞:𝑄𝑓𝑠𝑡𝑝𝑜 𝑁𝑝𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞) infFather : forall (x : Person) (y : ), ℍ -> ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠
𝑦(𝑞)
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive
father_of_Tom = (Andy, prfFather Tom (Betty, birthcert) (Andy, marriagecert)) : ∑𝑞:𝑄𝑓𝑝𝑞𝑚𝑓 𝐺𝑏𝑢ℎ𝑓𝑠𝑈𝑝𝑛(𝑞)
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“A plausible definition of ‘reasoning’ could be ‘algebraically manipulating previously acquired knowledge in order to answer a new question’.” [7]
Natural Representations Modular and Composable Constructive