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Sensation and Perception (II) (24 internal constrains (Evolutionary…
Sensation and Perception (II)
24
internal constrains
Evolutionary inheritance
Brain divisions
Relative size of brain divisions is similar in related species
gain flexibility by
regionalization of brain divisions
Neocortex is constrained to a particular architecture.
Species lost of one sensory modality still preserve the corresponding regions.
imprinted on
individual by
Developmental programs
canalization
Certain developmental programs are robust to genetic variations, and they channel neural systems into
stereotyped architecture
.
developmental noise
Due to stochasticity in signal transduction and gene expression.
compensations
redundant functions by multiple mechanisms
Metabolic constrains
The highest costs are
from maintaining ionic gradients.
Post incentives to neural architectures that minimize metabolic costs
the intrinsic properties of neurons match the signals
Wiring economy principle
connected neurons are located near each other
keep redundancy low
undersampling (e.g. photoreceptor)
adaptation or gain control
lateral inhibition among neurons with correlated activity
Electrical noise
ion-channel gating
Noise is not canceled out
by averaging across channels
SNR is proportional to \( \sqrt{N} \)
Channel opening is low in hyperpolarized potentials,
leading to poor SNR.
individual channels are not independent
synaptic vesicle release
release of synaptic vesicles is stochastic
compensation
pool redundant signals from independent sensors
apply a filter that discards noise
:!!:
Histogram equalization
distribute signals as uniformly as possible within the available coding space
Neural electronics
Limits on Speed
Fast membrane time constants
are metabolically costly.
Many neurons have relatively slow membrane time constants.
Limits on Dynamic Range
spike rates and vesicular release rates cannot be negative
firing rates cannot be arbitrarily large
synapses cannot be arbitrarily strong
Limits from Linear Summation
Inputs from dendrites are weighted and summed quasi-linearly.
Stimuli must be linear separable so as to be categorized by neural responses.
compensation
begin with high dimensional stimulus representation
Sparse recoding
by normalization or compressive non-linearity
Normalization
tends to equalize the total population firing rates evoked by different stimuli.
Compressive non-linearity
tends to make a responsive neuron fire at a fixed rate.
27
Probabilistic Inference
Scene Analysis
Involve multiple types of representation with different functions.
Cannot simply be accounted by a feedforward processing.
Meaningful behavior requires having a model of the world and one's place in it.
The goal of intermediate levels of representation is to disentangle from the raw input stream aspects of the scene appropriate for driving behavior.
:red_flag:
Inference
Problem of disentangling
Disentangling problems are
ill-posed
.
Not enough info. provided by the sensory data to
uniquely
recover the properties of interest.
Aspects of the scene needed to drive behavior can only be
inferred
but not
deduced
.
Different aspects of scene structure usually require to be estimated simultaneously; the inference of one variable affects the other.
Intrinsic images
stacks of 2D maps that are in register with the original intensity image, where each pixel location is labeled according to its shape, reflectance, or and illumination properties.
The computation of each maps involves propagating information between maps to obey photometric constraints and within map to obey continuity and occlusion constraints.
introduce the idea of a structured representation (cf. a flat and monolithic representation of image properties such as Gabor filter).
Surface representation
Intermediate representations are organized around
surfaces
in 3D environment.
Any further higher level processing is based on this representation (and not the 2D image).
Inferential computation
Bayes's rule
\( P(H|D)=\frac{P(D|H)P(H)}{P(D)} \)
where H is the hypothesis and D is data.
reasoning in the face of uncertainty
from data (image) to hypothesis (scene properties) is ill-posed.
Can be resolved by the priors (e.g. reflectance and shape).
The resulting posterior distribution rates the different parameter (reflectance and shape) values of the image in terms of prob. of being the correct interpretation.
Sparse coding
Visual sparse coding model
the spatial distribution of light intensities \(I(\overrightarrow{x})\) within a local region of the image may be represented in terms of a superposition of some basis patterns \(\phi (\overrightarrow{x})\)
\( I(\overrightarrow{x})=\sum_i a_i \phi_i (\overrightarrow{x})+n(\overrightarrow{x}) \)
Sparsity is enforced by imposing a prior over the coefficients, \(P(a)\), that encourages values to be zero.
\(a_i\) are found by maximizing the posterior prob.
Neural responses of a population of neurons that maximize the posterior prob. can be computed by
\( \tau \dot{u}_i+u_i=\sum_{\overrightarrow{x}} \phi_i (\overrightarrow{x})I(\overrightarrow{x})-\sum_j G_{ij}a_{ij} \)
\(a_i=g(u_i)\)
where \(u_i\) is each neuron's membrane voltage, \(G_{ij}\) is a feedback term that depends on the overlap bw basis patterns, and \(g()\) is a thresholding func.
the neuron's actual response is determined by the context in which other neurons are also responding.
If the basic pattern of one unit is better matched to the image than another, it will attempt to "explain awat the other unit's activity.
Here are all local image analysis
Hierarchical representation
Consider aggregating info. globally across the scene
At each stage, the variables being represented are influenced by both bottom-up and top-down inputs.
Priors are shaped by variables from next-higher level population.
e.g. \(P(a|b)\) is a prior for V1 neurons where b is a variable at V2.
Disambiguation
facilitate activity of the neurons at lower levels consistent with representation at higher levels and suppress those that are inconsistent.
emphasize feedback connection
35
Functional Architecture of VTC
Marr's framwork
Computation
the computational goal of VTC
shape
is the critical visual attribute for object recognition
system needs to be
robust to change in object appearance
w/o losing the ability to discriminate bw similar exemplars
support recognition and perception at
several levels of abstraction
there are classes of stimuli that may require specialized computations in addition to the domain-general computations
Representation
represent info. to support visual recognition
shape tuning
VTC responds strongly to shapes and objects compared to textures, noise, or scrambled objects
variability and tolerance
complete tolerance is unnecessary
as long as representations for different exemplars are untangled or linearly separable
VTC is
sensitive to small change that affect perceived identity
(e.g. viewpoint) but more tolerant to changes such as contrast and size
categorical info.
identified at different spatial scales
from the level of distributed responses across entire VTC, to activations in focal clusters, to responses of single neurons
exhibit a
hierarchical info structure
responses and perception
VTC responses are stronger when subjects perceive objects compared to when they are shown but not perceived
Implementation
relationship bw organizational and computational principles
large-scale map
several large-scale, superimposed functional map tile the entire VTC
maps display a common
lateral-to-medial spatial arrangement
the lateral-medial gradient is tied to anatomy
fined-scale cluster
within each large-scale components there is a series of fined-scale functional representations
tightly couple with anatomy
show consistent topology relative to other fined-scale clusters
superimposition
retinotopic maps superimpose with functional clusters within Medial VTC
retinotopic maps are yet to be identified in lateral VTC, but there's regularity in the arrangement of clusters relative to one another and to anatomy
"The enemy of art is the absence of limitations."