Rogers, Timothy T., Ma hew A. Lambon Ralph, Peter Garrard, Sasha Bozeat, James L. McClelland, John R. Hodges, and Karalyn Pa erson. âStructure and ...
Are semantic representations of words radically distributed? 1 Cox ,
Christopher
Mark
1 Seidenberg ,
Jeffery
2 Binder ,
Rutvik
2 Desai
& Timothy
1 Rogers
1-University of Wisconsin—Madison, 2-Medical College of Wisconsin
Introduction
fMRI Dataset:
Multivariate: Methods
• Neuroimaging studies of seman0c memory o3en suggest localiza0on of conceptual domains in cortex. • Connec0onist models of seman0c memory propose: ‣ A voxel can encode informa0on about >1 domain. ‣ Adjacent voxels may encode different informa0on. ‣ Distal regions can contribute to one representa0on. ‣ Experience determines what a given voxel encodes. • We argue that univariate analyses are ill suited to detect such radically distributed signals should they exist in fMRI datasets. [1] • We use sparse logis-c regression (LASSO) to test the localist and distributed hypotheses with less bias.
Par-cipants: 14 right handed subjects scanned at the Medical College of Wisconsin. S-muli: 1200 le]er strings (900 words, 300 nonwords obeying English phonology). 600 words were concrete, 300 abstract. Of the concrete nouns: 94 animals 145 ar-facts Task: Respond to the ques0on "Is it something physical you can experience with your senses?" by bu]on-‐press for every s0mulus. Procedure: Le]er strings presented one at a 0me at ji]ered intervals in random order over the course of 10 scanner runs with no repe00ons in a rapid event-‐related design. Imaging and Preprocessing: Par0cipants were scanned in a GE 3T scanner with a 2-‐second TR. The first 6 TRs from each run were discarded. Func0onal data was 0me-‐shi3ed, registered to the anatomy and scaled prior to deconvolu0on. Cor-cal Masks: Surface reconstruc0ons for each subject's anatomy were created and used to select only cor0cal voxels (i.e. space between pial and white ma]er ribbons) from the volumes of beta coefficients for each word and subject (Freesurfer[3]).
Deconvolu-on: Mul0ple linear regression with gamma variate HRF. GLM analysis included a regressor for each word and nonword s0mulus, resul0ng in 1200 volumes with beta coefficients at each voxel for each subject. Classifica-on Tasks: In separate tasks, LASSO[4] is used to discover a sparse solu0on given λ to classify 900 words as animal/non-‐animal or ar-fact/non-‐ar0fact. Voxel Pre-‐selec-on: Applied cor0cal mask to the beta-‐volumes for each par0cipant. Cross Valida-on: The words were separated into 10 blocks, each balanced for number of animals, ar-facts, and abstract words. Cross valida0on was performed at two levels: one to pick a good value of λ from 10 pre-‐specified choices without peeking, and another to evaluate the chosen λ for all train-‐test combina0ons of the 10 blocks of words.
Least Absolute Shrinkage and Selec0on Operator (LASSO)[5] regression applies an L1-‐norm regularizer to p find a sparse solu-on. � argmin l(β) + λ||β||1 , where ||β||1 =
j=1
SUMMARY: LASSO sa0sfies two condi0ons, which can be parametrically priori0zed; (1) minimize predic0on error (2) while keeping the sum of the absolute values of β low. For large enough λ many βi's are zero-‐-‐-‐the solu0on is sparse.
Simulation: Methods Created 1-‐D brains with 128 voxels for 30 “subjects”, with three structures.
Distributed Diff. Distrib.
Subj 1
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‣Noise added to each voxel N (µ = 0, σ = 1). ‣Signal strength = 2. ‣When applying a blur, FWHM = 4 voxels. ‣Analyzed either by univariate method (t-‐test) or LASSO.
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Max ! best Sparsity Helped Sparsity Hurt
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t(13)=6.03, sd=.16, p 2.16, k > 20
References: 1.Rogers, Timothy T., Ma]hew A. Lambon Ralph, Peter Garrard, Sasha Bozeat, James L. McClelland, John R. Hodges, and Karalyn Pa]erson. “Structure and Deteriora0on of Seman0c Memory: A Neuropsychological and Computa0onal Inves0ga0on.” Psychological Review 111(1): 205–235, 2004 2.Cox, RW. AFNI: So3ware for analysis and visualiza0on of func0onal magne0c resonance neuroimages. Computers and Biomedical Research, 29:162-‐173, 1996. 3.Cor0cal reconstruc0on and volumetric segmenta0on was performed with the Freesurfer image analysis suite, which is documented and freely available for download online (h]p://surfer.nmr.mgh.harvard.edu/). 4.Tomioka, R., Suzuki, T., Sugiyama, M. and Kashima, H. A Fast Augmented Lagrangian Algorithm for Learning Low-‐Rank Matrices. Proc. of the 27th Annual Interna0onal Conference on Machine Learning (ICML 2010), Haifa, Israel, 2010 5.Has0e, T., Tibshirani, R, and Friedman, J. “ The Elements of Sta0s0cal Learning: Data Mining, Inference, and Predic0on”. Second Edi0on, 2009 6.Chao, Haxby, and Mar0n. “A]ribute-‐based neural substrates in temporal cortex for perceiving and knowing about objects”. Nature Neuroscience, 2(10):913-‐919, 1999
• LASSO provides evidence of r a d i c a l l y d i s t r i b u t e d a n d overlapping code in areas implicated by disorder.[1] • Each solu0on is likely a subset of the full system. • Elastic nets blend LASSO and ridge r e g r e s s i o n , s p a r s i t y a n d inclusiveness. • C o n st ra i n i n g re g re s s i o n i n Adapted from Our results, different ways changes the Chao, Haxby, including voxels Martin in solution of >3 preferred solution; different brain and (1999) [6] participants regions may encode semantics in different ways. • Tuning elastic nets to prefer solutions of different types should identify regions thought to represent semantics in a corresponding way.
