Explaining Cortical Adaptation with a Statistically Optimized - PowerPoint PPT Presentation

Explaining Cortical Adaptation with a Statistically Optimized Normalization Mo del Martin W ain wrigh t Eero Simoncelli Vision Sciences Cen ter for Neural Science Harv ard Univ ersit y Couran t Institute New Y ork Univ ersit y

In tro duction sensory systems are matc hed to their input statistics Hyp othesis� �A ttnea v e� ����� statistical indep endence of neural resp onses� More sp eci�cally� �Barlo w� ����� Role of image statistics � indep endence of resp onses m ust b e de�ned with resp ect to statistics of visual input � large b o dy of previous researc h on natural image statistics and cortical pro cessing �e�g� Field� ����� A tic k � Redlic h� ����� v an Hateren� ����� Ruderman� ����� Olshausen � Field� ����� Bell � Sejno wski� �����

Cortical adaptation and image statistics Statistics of visual input are constan tly c hanging �o v er seconds and�or min utes�� Question� Can cortical adaptation b e understo o d as optimal adjustmen t to statistics of recen t input� Sev eral authors ha v e tried to link input statistics to cortical adaptation ����� � �e�g�� Barlo w� ����� W ain wrigh t� Limitations of previous w ork� � simplistic mo dels of images �e�g�� Gaussian� � linear mo dels of neurons

Normalization mo dels � Divisiv e normalization� �� Compute linear resp onses f L g of receptiv e �elds at di�er� k en t spatial scales� p ositions� and orien tations� �� Compute a normalized resp onse b y a dividing � cell�s squared resp onse b y a sum of squared re� L sp onses of neigh b ors� � Normalization accoun ts for nonlinear b eha vior in neurons� �Bonds� ����� Geisler and Albrec h t� ����� Heeger� ����� � Normalization can b e deriv ed from natural image statistics� �Simoncelli� ����� Simoncelli and Sc h w artz� �����

Statistical view of normalization � normalization is a form of non�line ar pr e dictive c o ding � resp onses of neigh b oring mo del neurons are used to the pr e dict v ariance of a mo del neuron � mo del neuron is normalized b y the prediction � L R � � � �� P j � � � j L k k k � normalized resp onses are close to statistically indep enden t � f � g Key P oin t� � and are determined b y the k statistics of the visual en vironmen t�

Con trast adaptation � � Increase con trast increase � shift CRF righ t Environment A − 200 Rightward shift � L 0 R � � 10 A � � � � �L 0 A � Log response 200 − 1 − 200 0 200 10 Environment B − 400 � L R � � Environment A B − 2 � � 10 Environment B � � �L 0 B � 1 10 100 % Grating contrast 400 − 400 0 400

P attern adaptation � � Increase dep endency increase � decrease saturation Environment A − 200 Saturation change − 100 � L 0 � R � 10 A � � � � � L 0 A � 100 Log response 200 − 1 − 200 − 100 0 100 200 10 Environment B − 200 � − 100 L Environment A R � � B − 2 Environment B � 10 � � � � L 0 B � 100 1 10 100 % Grating contrast 200 − 200 − 100 0 100 200

Sim ulation of adaptation �� Compute parameters for an en� generic vironmen t of natural images� �� Compute parameters adapte d for a mixture of sine w a v e grating and natural images� �� Compute normalized resp onses to sin usoidal test stim uli using eac h set of parameters�

CRF� Di�eren t adapting con trasts Cell Mo del �Albrec h t et al�� ����� 100 100 Low contrast Low contrast Response (spikes/s) adapt adapt Response 10 10 High contrast High contrast adapt adapt 1 1 1 10 100 1 10 100 Contrast (%) Contrast (%)

CRF� Di�eren t test spatial frequencies Cell Mo del �Albrec h t et al�� ����� Optimal Test Non − optimal Test Optimal Test Non − optimal Test 100 100 100 100 Unadapted Unadapted Response (spike/s) Response Adapted 10 10 10 10 Adapted 1 1 1 1 2 10 50 2 10 50 2 10 50 2 10 50 Contrast (%) Contrast (%) Contrast (%) Contrast (%)

T uning curv es� Di�eren t adapting orien tations Cell Mo del �M uller � � Lennie� ����� Unadapted Unadapted 1 1 0.8 0.8 Adapt 14 Adapt 14 Response Response Adapt 0 0.6 Adapt 0 0.6 0.4 0.4 0.2 0.2 0 0 − 40 − 20 0 20 40 − 60 − 30 0 30 60 Orientation (deg) Orientation (deg)

Conclusions � Cortical adaptation can b e explained using a normalization mo del with parameters determined b y image statistics� � Suc h a mo del mak es a principled distinction b et w een con trast and pattern adaptation� � Mo del accoun ts for V� cell b eha vior under a v ariet y of adaptation conditions�

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