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Mathematical Reasoning in Latent Space [article]

Dennis Lee, Christian Szegedy, Markus N. Rabe, Sarah M. Loos and Kshitij Bansal
2019 arXiv   pre-print
Since our corpus of mathematical formulas includes a wide variety of mathematical disciplines, this experiment is a strong indicator for the feasibility of deduction in latent space in general.  ...  Predicting the embedding of a formula generated by some rewrite rule is naturally viewed as approximate reasoning in the latent space.  ...  We raise the question whether hard algorithms could be omitted from this process and mathematical reasoning performed entirely in the latent space.  ... 
arXiv:1909.11851v1 fatcat:qct3x6qw4zerzdoe6iqzlagidq

Page 18 of Psychological Abstracts Vol. 90, Issue 1 [page]

2003 Psychological Abstracts  
—Most computer systems that deal with issues of space reason about distance by us- ing a metric.  ...  Moreover, it is shown how latent state-trait theory can guide the selection of the number of chains in latent Markov models as well as in latent mixed Markov models. 157. Guesgen, Hans W.  ... 

Attending to Feeling: It May Matter More than You Think

Carol R. Aldous
2014 Creative Education  
Recent advances in cognitive neuroscience reveal that reasoning and decision-making are comprised of both cognitive (thinking) and non-cognitive (feeling, intuiting) components.  ...  The cognitive and non-cognitive measures involved five aspects: a strategic, a systematic, a spatial-verbal, a free-flowing and a feeling approach to reasoning.  ...  Strategic Approach to Reasoning (Strat) Ten indicators were used in the formation of the latent variable Strat.  ... 
doi:10.4236/ce.2014.510091 fatcat:gzvkrnzbczh7tjp5sucwpchdte

Quantum Local Causality in Non-Metric Space

Fosco Ruzzene
2018 Journal of Applied Mathematics and Physics  
This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time.  ...  Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect.  ...  For a switch in apparatus-setting at B along 2 n , on an orienta- tion-by-orientation basis it is reasoned that [32]: ( ) ( ) 2 1 1 1 latent in orientation actual in orientation 1 B B  ... 
doi:10.4236/jamp.2018.66100 fatcat:4656shdqnvednjvnlbb2gzvb5u

Generate and Verify: Semantically Meaningful Formal Analysis of Neural Network Perception Systems [article]

Chris R. Serrano and Pape M. Sylla and Michael A. Warren
2020 arXiv   pre-print
In this work, we propose a notion of global correctness for neural network perception models performing regression with respect to a generative neural network with a semantically meaningful latent space  ...  That is, against an infinite set of images produced by a generative model over an interval of its latent space, we employ neural network verification to prove that the model will always produce estimates  ...  If we are interested in global correctness with respect to semantically meaningful specifications, then the images over which we reason will need to be drawn from a semantically meaningful latent space  ... 
arXiv:2012.09313v1 fatcat:3t7fbdxjk5ft7lzxuvgjuwia2i

Page 386 of School Science and Mathematics Vol. 59, Issue 520 [page]

1959 School Science and Mathematics  
Tue LATENT Roots The mathematical derivation and interpretation of the discrimi- nant equations are numerous (2, 7, 8, 9, 10, 11), so those details need not be gone into here.  ...  fifth roots were more inaccurate, only the first three roots and their associated vectors are used in describing the discrimi- nant space.  ... 

The Dawning of Computational Psychoanalysis

Giuseppe Iurato
2014 International Journal of Cognitive Informatics and Natural Intelligence  
the so-called latent semantic space.  ...  In latent semantic indexing, the original vector space representation of documents is replaced by a representation in the low-dimensional latent space, and the similarity is computed based on that representation  ... 
doi:10.4018/ijcini.2014100104 fatcat:dslx7typuveqjldpkf6h6csjpe

Page 342 of Rambler; A Catholic Journal and Review of Home and Foreign Literature Vol. 2, Issue Part VI [page]

1860 Rambler; A Catholic Journal and Review of Home and Foreign Literature  
as presiding over and directing the immediate ob- ject, and giving it its order or latent reason, and its beauty or latent love.  ...  The soul, though imagining space, and perceiving all objects in space, does not recognise its reality.  ... 

Page 342 of Rambler; A Catholic Journal and Review of Home and Foreign Literature Vol. 2, Issue 6 [page]

1860 Rambler; A Catholic Journal and Review of Home and Foreign Literature  
as presiding over and directing the immediate ob- ject, and giving it its order or latent reason, and its beauty or latent love.  ...  The soul, though imagining space, and perceiving all objects in space, does not recognise its reality.  ... 

Why Defining the Construct Matters: An Examination of Teacher Knowledge Using Different Lenses on One Assessment

Chandra H. Orrill, Allan S. Cohen
2016 The Mathematics Enthusiast  
In this paper, we analyze teachers' performance on the Learning Mathematics for Teaching assessment of Proportional Reasoning.  ...  We use a single assessment to illustrate the differences in results that can arise based on the ways in which the domain of interest is conceptualized. Suggestions for test development are provided.  ...  We also wish to thank Eric Gold, Dave Kamin, Tim Marum, Rob Nanna, Dennis Robinson, Ryan Robidoux, and Kaitlyn Walsh Rodrigues for their assistance in the initial analysis of the LMT-PR assessment.  ... 
doi:10.54870/1551-3440.1367 fatcat:nqt37lcuerbenfftw3zx3svajm

Sex Differences in Spatial Cognition, Computational Fluency, and Arithmetical Reasoning

David C. Geary, Scott J. Saults, Fan Liu, Mary K. Hoard
2000 Journal of Experimental Child Psychology  
Moreover, the results suggested that the male advantage in arithmetical reasoning is mediated by the male advantages in both computational fluency and spatial cognition.  ...  Alternative explanations for the male advantage in arithmetical reasoning, as measured by the ability to solve complex word problems, include a male advantage in spatial cognition and a male advantage  ...  variable to the Arithmetical Reasoning latent variable in both samples and the path from IQ to the Arithmetical Reasoning latent variable in the female sample.  ... 
doi:10.1006/jecp.2000.2594 pmid:11063633 fatcat:ortiwp7w2zcjrouacpy5yf55qm

Nonparametric item response theory axioms and properties under nonlinearity and their exemplification with knowledge space theory

Ali Ünlü
2007 Journal of Mathematical Psychology  
latent trait.  ...  The reason for this and conditions under which the implication holds are specified, based on a new, simpler proof of the fact that in the unidimensional case MLR implies SO.  ...  Acknowledgments The research reported in this paper was partly supported by the Austrian Science  ... 
doi:10.1016/j.jmp.2007.07.002 fatcat:jewod2scrjhtticfagakhgu4fu

Spectral Composition of Semantic Spaces [chapter]

Peter Wittek, Sándor Darányi
2011 Lecture Notes in Computer Science  
Spectral theory in mathematics is key to the success of as diverse application domains as quantum mechanics and latent semantic indexing, both relying on eigenvalue decomposition for the localization of  ...  their respective entities in observation space.  ...  Among the reasons are the following: -The semantic space methodology makes semantics computable allowing a definition of semantic similarity in mathematical terms.  ... 
doi:10.1007/978-3-642-24971-6_7 fatcat:jjmx7flu6fb5tdeqa5wjx3pfqq

Modelling dynamical systems using manifest and latent variables

Jan C. Willems
2000 Mathematics and Computers in Simulation  
Subsequently, the notions of controllability and observability are cast in this setting.  ...  This allows to obtain behavioral equations involving only manifest variables, starting from models that contain also latent variables.  ...  Further, the state space representation problem: obtaining a special latent variable representation in which the latent variables capture the memory of a system.  ... 
doi:10.1016/s0378-4754(00)00209-3 fatcat:zgtu722fpfg4hlmz5zejagkjou

Examining Students' Proportional Reasoning Strategy Levels as Evidence of the Impact of an Integrated LEGO Robotics and Mathematics Learning Experience

Araceli Martinez Ortz
2015 Journal of Technology Education  
We have begun to meet this challenge with one topic in mathematics, proportional reasoning.  ...  between measure spaces.  ... 
doi:10.21061/jte.v26i2.a.3 fatcat:l5dy7b7vkbc37pvngekp7b2ma4
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