Add CN2 object recognition

src/year1/cognition-and-neuroscience/metadata.json

@@ -6,6 +6,10 @@
         {
             "name": "CN module 1",
             "path": "module1/cn1.pdf"
+        },
+        {
+            "name": "CN module 2",
+            "path": "module2/cn2.pdf"
         }
     ]
 }

src/year1/cognition-and-neuroscience/module2/ainotes.cls

@@ -0,0 +1 @@
+../../../ainotes.cls

src/year1/cognition-and-neuroscience/module2/cn2.tex

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+\documentclass[11pt]{ainotes}
+\usepackage{biblatex}
+\addbibresource{./references.bib}
+
+\title{Cognition and Neuroscience\\(Module 2)}
+\date{2023 -- 2024}
+\def\lastupdate{{PLACEHOLDER-LAST-UPDATE}}
+
+\newtheorem*{casestudy}{Case study}
+
+\begin{document}
+    
+    \makenotesfront
+    \newpage
+
+    \input{./sections/_object_recognition.tex}
+    
+    \printbibliography[heading=bibintoc]
+
+\end{document}

src/year1/cognition-and-neuroscience/module2/references.bib

@@ -0,0 +1,22 @@
+@article{vision_monkey_svm,
+    title = {Fast Readout of Object Identity from Macaque Inferior Temporal Cortex},
+    author = {Chou P. Hung  and Gabriel Kreiman  and Tomaso Poggio  and James J. DiCarlo },
+    journal = {Science},
+    volume = {310},
+    number = {5749},
+    pages = {863-866},
+    year = {2005},
+    doi = {10.1126/science.1117593},
+}
+
+
+@article{vision_monkey_hcnn,
+    title = {Performance-optimized hierarchical models predict neural responses in higher visual cortex},
+    author = {Daniel L. K. Yamins  and Ha Hong  and Charles F. Cadieu  and Ethan A. Solomon  and Darren Seibert  and James J. DiCarlo },
+    journal = {Proceedings of the National Academy of Sciences},
+    volume = {111},
+    number = {23},
+    pages = {8619-8624},
+    year = {2014},
+    doi = {10.1073/pnas.1403112111},
+}

src/year1/cognition-and-neuroscience/module2/sections/_object_recognition.tex

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+\chapter{Object recognition}
+
+
+\begin{description}
+    \item[Vision] \marginnote{Vision}
+        Process that, from images of the external world, 
+        produces a description without irrelevant information (i.e. interference) useful to the viewer.
+
+        This description includes information such as what is in the world and where it is.
+
+        \begin{remark}
+            Vision is the most important sense in primates (i.e. in case of conflicts between senses, vision is usually prioritized).
+        \end{remark}
+
+        \begin{remark}
+            Vision is also involved in memory and thinking.
+        \end{remark}
+
+        \begin{remark}
+            The two main tasks for vision are:
+            \begin{itemize}
+                \item Object recognition.
+                \item Guiding movement.
+            \end{itemize}
+            These two functions are mediated by (at least) two pathways that interact with each other.
+        \end{remark}
+
+
+    \item[Vision Bayesian modeling] \marginnote{Bayesian modeling}
+        Vision can be modeled using Bayesian theory.
+        
+        Given an image $I$ and a stimulus $S$, an ideal observer uses some prior knowledge (expectation) of the stimulus ($\mathcal{P}(S)$)
+        and input sensory data ($\prob{I | S}$) to infer the most probable interpretation of the stimulus in the image:
+        \[ \mathcal{P}(S | I) = \frac{\mathcal{P}(I | S) \mathcal{P}(S)}{\mathcal{P}(I)} \]
+
+        \begin{remark}
+            Prior knowledge is learned from experience. 
+            It could be related to the shape of the object, the direction of the light or the fact that objects cannot overlap.
+        \end{remark}
+
+        \begin{remark}
+            If the image is highly ambiguous, prior knowledge contributes more to disambiguate it.
+        \end{remark}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.4\linewidth]{./img/vision_bayesian.png}
+        \end{figure}
+
+        \begin{description}
+            \item[Feed-forward processing] Involves the likelihood $\prob{I | S}$.
+            \item[Feed-back processing] Involves the prior $\mathcal{P}(S)$.
+        \end{description}
+
+        \begin{remark}
+            Perception integrates both feed-forward and feed-back processing.
+        \end{remark}
+
+
+    \item[Vision levels] \marginnote{Vision levels}
+        A visual scene is analyzed at three levels:
+        \begin{descriptionlist}
+            \item[Low level]
+                Processes simple visual attributes captured by the retina such as local contrast, orientation, color, depth and motion.
+
+            \item[Intermediate level] 
+                Low-level features are used to parse the visual scene (i.e. local features are integrated into the global image).
+                This level is responsible for identifying boundaries and surfaces belonging to the same object and 
+                discriminating between foreground and background objects.
+                % \begin{example}
+                %     Local orientation is integrated into global contours, local features are assembled into surfaces, 
+                %     the shapes of surfaces are identified, \dots
+                % \end{example}
+
+            \item[High level] 
+                Responsible for object recognition.
+                
+                Once the objects have been recognized, they can be associated with memories of shapes and meaning.
+
+                \begin{casestudy}[Agnosia]
+                    Patients with agnosia have their last level of vision damaged.
+                    They can see (e.g. avoid obstacles) but cannot recognize object or get easily confused.
+                \end{casestudy}
+        \end{descriptionlist}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.6\linewidth]{./img/vision_levels.png}
+        \end{figure}
+\end{description}
+
+
+
+\subsection{Pathways}
+
+\begin{description}
+    \item[Retino-geniculo-striate pathway] \marginnote{Retino-geniculo-striate pathway}
+        Responsible for visual processing.
+        It includes the:
+        \begin{itemize}
+            \item Retina.
+            \item Lateral geniculate nucleus (LGN) of the thalamus.
+            \item Primary visual cortex (V1) or striate cortex.
+            \item Extrastriate visual areas (i.e. beyond the area V1).
+        \end{itemize}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.35\linewidth]{./img/vision_pathway.png}
+        \end{figure}
+
+        
+    \item[Ventral pathway] \marginnote{Ventral pathway}
+        Responsible for object recognition.
+        It extends from the area V1 to the temporal lobe (feed-forward processing).
+
+        \begin{remark}
+            This pathway emphasizes color.
+        \end{remark}
+
+        \begin{remark}
+            The connection from the frontal lobe encodes prior knowledge (feed-back processing).
+        \end{remark}
+
+    \item[Dorsal pathway] \marginnote{Dorsal pathway}
+        Responsible for movement guiding.
+        It connects the V1 area with the parietal lobe and then with the frontal lobe.
+
+        \begin{remark}
+            This pathway is colorblind.
+        \end{remark}
+\end{description}
+
+\begin{remark}
+    The ventral and dorsal pathways are highly connected and share information.
+\end{remark}
+
+\begin{remark}
+    All connections in the ventral and dorsal pathways are reciprocal (i.e. bidirectional).
+\end{remark}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.4\linewidth]{./img/ventral_dorsal_pathways.png}
+\end{figure}
+
+
+\section{Neuron receptive field}
+\begin{description}
+    \item[Single-cell recording] \marginnote{Single-cell recording}
+        Technique to record the firing rate of neurons.
+        A fine-tipped electrode is inserted into the animal's brain to record the action potential of a single neuron.
+        
+        This method is highly invasive but allows to obtain high spatial and temporal readings of the neuron firing rate while distinguishing excitation and inhibition.
+
+        \begin{remark}
+            On a theoretical level, neurons can fire a maximum of $1000$ times per second.
+            This may actually happen in exceptional cases.
+        \end{remark}
+
+    
+    \item[Receptive field] \marginnote{Receptive field}
+        Region of the visual scene at which a particular neuron will respond if a stimulus falls within it. 
+
+        \begin{remark}
+            The receptive field of a neuron can be described through a Gaussian.
+        \end{remark}
+
+        \begin{casestudy}
+            A monkey is trained to maintain fixation at a point on a screen.
+            Then, stimuli are presented in various positions of the visual field.
+
+            It has been seen that a particular neuron fires vigorously only when a stimulus is presented in a particular area of the screen.
+
+            The response is the strongest at the center of the receptive field and gradually declines when the stimulus moves away from the center.
+
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.55\linewidth]{./img/receptive_field_monkey.png}
+            \end{figure}
+        \end{casestudy}
+
+        \begin{remark}
+            Neurons might only react to a specific type of stimuli in the receptive field (e.g. color, direction, \dots).
+
+            \begin{casestudy}
+                It has been seen that a neuron fires only if a stimulus is presented in its receptive field while moving upwards.
+            \end{casestudy}
+        \end{remark}
+
+    
+    \item[Retinotopy] \marginnote{Retinotopy}
+        Mapping of visual inputs from the retina (i.e. receptive field) to the neurons.
+
+        There is a non-random relationship between the position of the neurons in the visual areas (V1, V2, V4):
+        their receptive fields form a 2D map of the visual field in such a way that 
+        neighboring regions in the visual image are represented by adjacent regions of the visual cortical area
+        (i.e. the receptive fields are spatially ordered).
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.3\linewidth]{./img/retinotopy.png}
+            \caption{\parbox[t]{0.45\linewidth}{Mapping from the visual field to the neurons in the primary visual cortex (V1)}}
+        \end{figure}
+
+        \begin{description}
+            \item[Eccentricity] \marginnote{Eccentricity}
+                The diameter of the receptive field is proportional to the wideness of the visual angle.
+
+                \begin{figure}[H]
+                    \centering
+                    \includegraphics[width=0.35\linewidth]{./img/eccentricity.png}
+                    \caption{\parbox[t]{0.45\linewidth}{Relationship between visual angle and receptive field diameter}}
+                \end{figure}
+
+            \item[Cortical magnification] \marginnote{Cortical magnification}
+                The neurons (retinal ganglion cells, RGCs) responsible for the center of the visual field (fovea)
+                have a visual angle of about $0.1^\circ$ while the neurons at the visual periphery reach up to $1^\circ$ of visual angle.
+
+                Accordingly, more cortical space is dedicated to the central part of the visual field.
+                This densely packed amount of smaller receptive fields allows for the highest spatial resolution at the center of the visual field.
+
+                \begin{figure}[H]
+                    \centering
+                    \includegraphics[width=0.4\linewidth]{./img/cortical_magnification.png}
+                    \caption{Cortical magnification in V1}
+                \end{figure}
+
+                \begin{remark}
+                    The brain creates the illusion that the center and the periphery of vision are equal.
+                    In reality, the periphery has less resolution and is colorblind.
+                \end{remark}
+        \end{description}
+
+    \item[Hierarchical model of receptive field]
+        The processing of some information in the visual image is done through an incremental convergence of information
+        in a hierarchy of receptive fields of neurons.
+        Along the hierarchy the size of the receptive field increases.
+\end{description}
+
+
+\section{Retina cells}
+
+\begin{description}
+    \item[Photoreceptor] \marginnote{Photoreceptor}
+        Specialized neurons that are hyperpolarized in bright regions and depolarized in dark regions.
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.3\linewidth]{./img/photoreceptor.png}
+        \end{figure}
+
+        \begin{remark}
+            They are the first layer of neurons in the retina.
+        \end{remark}
+
+
+    \item[Retinal ganglion cell (RGC)] \marginnote{Retinal ganglion cell (RGC)}
+        Neurons of the visual cortex with a circular receptive field.
+        They are categorized into:
+        \begin{descriptionlist}
+            \item[ON-center] \marginnote{ON-center cells}
+                RGCs that are activated in response to a bright stimulus in the center of the receptive field.
+            \item[OFF-center] \marginnote{OFF-center cells}
+                RGCs that are activated in response to a dark stimulus in the center of the receptive field.
+        \end{descriptionlist}
+
+        \begin{remark}
+            They are the last layer of neurons in the retina, before entering LGN of the thalamus.
+        \end{remark}
+
+        The receptive field of RGCs is composed of two concentric areas. 
+        The inner one acts according to the type of the cell (ON-center/OFF-center)
+        while the outer circle acts antagonistically to the inner area.
+
+        \begin{remark}
+            A uniform stimulus that covers the entire receptive field of an RGC produces a weak or no response.
+        \end{remark}
+
+        \begin{remark}
+            RGCs are not responsible for distinguishing orientation or lines.
+        \end{remark}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.6\linewidth]{./img/on_off_center.png}
+            \caption{Responses of an ON-center RGC}
+        \end{figure}
+
+        \begin{remark}
+            The response of RGCs can be described by two Gaussians: 
+            one is positive with a narrow peak and represents the response at the center 
+            while the other is negative with a wide base and covers both the inner and outer circles.
+            Their difference represents the response of the cell (receptive field profile).
+
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.2\linewidth]{./img/visual_gaussian.png}
+            \end{figure}
+        \end{remark}
+
+        \begin{description}
+            \item[Band-pass behavior] \marginnote{Band-pass behavior}
+                The visual system of humans has a band-pass behavior: it only responds to a narrow band of intermediate frequencies
+                and is unable to respond to spatial frequencies that are too high or too low 
+                (as they get canceled by the two antagonistic circles).
+
+                \begin{figure}[H]
+                    \centering
+                    \includegraphics[width=0.2\linewidth]{./img/visual_frequencies.png}
+                \end{figure}
+        \end{description}
+\end{description}
+
+
+
+\section{Area V1 cells}
+
+
+\subsection{Simple cells}
+\marginnote{Simple cells}
+
+Neurons that respond to a narrow range of orientations and spatial frequencies.
+
+This is the result of the alignment of different circular receptive fields of the LGN cells (which in turn receive their input from RGCs).
+
+\begin{figure}[H]
+    \centering
+    \begin{subfigure}{0.45\linewidth}
+        \centering
+        \includegraphics[width=0.9\linewidth]{./img/v1_simple_cell.png}
+    \end{subfigure}
+    \begin{subfigure}{0.45\linewidth}
+        \centering
+        \includegraphics[width=0.9\linewidth]{./img/v1_simple_cells_visual.png}
+    \end{subfigure}
+\end{figure}
+
+\begin{casestudy}
+    In monkeys, the neurons of the LGN have non-oriented circular receptive fields.
+    Still, simple cells are able to perceive specific orientations.
+\end{casestudy}
+
+\begin{description}
+    \item[Simple cells model] 
+        The stages of computation in simple cells are:
+        \begin{enumerate}
+            \item Linear filtering through a weighted sum of the image intensities done by the receptive field (i.e. convolutions).
+            \item Rectification (i.e. thresholding with non-linearity) to determine if the neuron has to fire.
+        \end{enumerate}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.4\linewidth]{./img/simple_cell_model.png}
+        \end{figure}
+\end{description}
+
+
+\subsection{Complex cells}
+\marginnote{Complex cells}
+
+Neurons with a rectangular receptive field larger than simple cells.
+They respond to linear stimuli with a specific orientation and move in a particular direction (position invariance).
+
+\begin{remark}
+    At this stage, the position of the stimulus is not relevant anymore as the ON and OFF zones of the previous cells are mixed.
+\end{remark}
+
+\begin{figure}[H]
+    \centering
+    \begin{subfigure}{0.45\linewidth}
+        \centering
+        \includegraphics[width=0.9\linewidth]{./img/complex_cell.png}
+    \end{subfigure}
+    \begin{subfigure}{0.45\linewidth}
+        \centering
+        \includegraphics[width=0.6\linewidth]{./img/complex_cell_stimuli.png}
+    \end{subfigure}
+\end{figure}
+
+\begin{description}
+    \item[Complex cell model]
+        The stages of computation in complex cells are:
+        \begin{enumerate}
+            \item Linear filtering of multiple receptive fields.
+            \item Rectification for each receptive field.
+            \item Summation of the response.
+        \end{enumerate}
+
+        \begin{figure}[H]
+            \centering
+            \includegraphics[width=0.4\linewidth]{./img/complex_cell_model.png}
+        \end{figure}
+\end{description}
+
+
+\subsection{End-stopped (hypercomplex) cells}
+\marginnote{End-stopped cells}
+
+Neurons whose receptive field has an excitatory region surrounded by one or more inhibitory regions all with the same preferred orientation.
+
+This type of cell responds to short segments, long curved lines (as the tail of the curve that ends up in the inhibition region is not the preferred orientation)
+or to angles.
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.5\linewidth]{./img/end_stopped_cell.png}
+    \caption{End-stopped cell with a vertical preferred orientation}
+\end{figure}
+
+
+\subsection{Ice cube model}
+
+Each 1 mm of the visual cortex can be modeled through an ice cube module 
+that has all the neurons for decoding all the information (e.g. color, direction, \dots) in a specific location of the visual scene (i.e. each cube is a block of filters).
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.3\linewidth]{./img/ice_cube.png}
+\end{figure}
+
+
+
+\section{Extrastriate visual areas}
+
+\begin{description}
+    \item[Extrastriate visual areas] Areas outside the primary visual cortex (V1).
+        They are responsible for the actual object recognition task.
+\end{description}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.55\linewidth]{./img/ventral_pathway.png}
+    \caption{Ventral pathway}
+\end{figure}
+
+
+\begin{description}
+    \item[Visual object] \marginnote{Visual object}
+        Set of visual features (e.g. color, direction, orientation, \dots) perceptually grouped into discrete units.
+
+    \item[Visual recognition]
+        Ability to assign a verbal label to objects in the visual scene.
+        \begin{description}
+            \item[Identification] \marginnote{Identification} 
+                Recognize the object at its individual level.
+            \item[Categorization] \marginnote{Categorization} 
+                Recognize the object as part of a more general category.
+        \end{description}
+
+        \begin{remark}
+            In humans, categorization is easier than identification.
+            Stimuli originating from distinct objects are usually treated as the same on the basis of past experience.
+
+            % This behavior is motivated from a survival point of view.
+        \end{remark}
+\end{description}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.7\linewidth]{./img/object_recognition.png}
+    \caption{Processes that start after an object has been recognized}
+\end{figure}
+
+\begin{remark}
+    For survival reasons, after an object has been recognized, 
+    its emotional valence is usually the first thing that is retrieved to determine if the object is dangerous.
+\end{remark}
+
+
+Object recognition requires both the following competing properties:
+\begin{descriptionlist}
+    \item[Selectivity] \marginnote{Selectivity}
+        Different responses to distinct specific objects.
+
+    \item[Consistency] \marginnote{Consistency}
+        Similar responses to transformations (e.g. rotation) of the same object (generalization).
+\end{descriptionlist}
+
+\begin{description}
+    \item[Core object recognition] \marginnote{Core object recognition}
+        Ability to rapidly ($< 200$ ms) discriminate a given visual object from all the other possible objects.
+        \begin{remark}
+            Primates perform this task exceptionally well even if the object is transformed.
+        \end{remark}
+
+        \begin{remark}
+            200 ms is the time required to move the eyes. Experiments on core object recognition don't want candidates to move their eyes.
+        \end{remark}
+\end{description}
+
+
+\subsection{Area V4}
+\marginnote{Area V4}
+
+Intermediate cortical area responsible for visual object recognition and visual attention.
+It facilitates figure-ground segmentation of the visual scene enabling both bottom-up and top-down visual processes.
+
+
+\subsection{Inferior temporal cortex (IT)}
+\marginnote{Inferior temporal cortex (IT)}
+
+Responsible for object perception and recognition.
+It is divided into three areas:
+\begin{itemize}
+    \item Anterior IT (AIT).
+    \item Central IT (CIT).
+    \item Posterior IT (PIT).
+\end{itemize}
+
+\begin{remark}
+    It takes approximately 100 ms for the signal to arrive from the retina to the IT.
+\end{remark}
+
+\begin{remark}
+    The number of neurons decreases from the retina to the IT.
+    V1 can be seen as the area that sees everything and decides what to further process.
+\end{remark}
+
+\begin{remark}
+    Central IT and anterior IT do not show clear retinotopy.
+    Posterior IT shows some sort of pattern.
+\end{remark}
+
+\begin{remark}
+    Receptive field scales by a factor of $\sim 3$ after passing through each cortical area.
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.4\linewidth]{./img/receptive_field_growth.png}
+    \end{figure}
+\end{remark}
+
+\begin{remark}
+    It is difficult to determine which stimuli trigger the neurons in the IT and
+    what actual stimuli trigger the IT is still unclear.
+
+    Generally, neurons in this area respond to complex stimuli, often biologically relevant objects (e.g. faces, hands, animals, \dots).
+    
+    \begin{figure}[H]
+        \centering
+        \begin{subfigure}{0.35\linewidth}
+            \centering
+            \includegraphics[width=0.95\linewidth]{./img/vision_complexity.png}
+            \caption{Stimuli that trigger specific neurons of the ventral pathway}
+        \end{subfigure}
+        \begin{subfigure}{0.6\linewidth}
+            \centering
+            \includegraphics[width=0.95\linewidth]{./img/it_response.png}
+            \caption{Responses of a specific IT neuron to different stimuli}
+        \end{subfigure}
+    \end{figure}
+\end{remark}
+
+
+\begin{casestudy}[IT neurons in monkeys]
+    Several researchers observed that a group of IT neurons in monkeys respond selectively to faces.
+    The response is stronger when the full face is visible and gets weaker if it is incomplete or malformed.
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.4\linewidth]{./img/monkey_it_faces.png}
+    \end{figure}
+
+    It also has been observed that an IT neuron responds to hands presented at various perspectives and orientations.
+    A decrease in response is visible when the hand gets smaller and it is clearly visible when a glove is presented.
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.95\linewidth]{./img/monkey_it_hands.png}
+    \end{figure}
+\end{casestudy}
+
+\begin{casestudy}[IT neuron response to a melon]
+    An IT neuron responds to a complex image of a melon.
+    However, it has been shown that it also responds to simpler stimuli that represent the visual elements of the melon.
+
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.4\linewidth]{./img/it_melon.png}
+    \end{figure}
+\end{casestudy}
+
+\begin{description}
+    \item[View-dependent unit] \marginnote{View-dependent unit}
+        The majority of IT neurons are view-dependent and respond only to objects at specific points of view.
+
+    \item[View-invariant unit] \marginnote{View-invariant unit}
+        10\% of IT neurons are view-invariant and respond regardless of the position of the observer.
+\end{description}
+
+\begin{figure}[H]
+    \centering
+    \begin{subfigure}{0.48\linewidth}
+        \centering
+        \includegraphics[width=0.95\linewidth]{./img/object_recognition_process.png}
+    \end{subfigure}
+    \begin{subfigure}{0.48\linewidth}
+        \centering
+        \includegraphics[width=0.95\linewidth]{./img/it_view_independent_response.png}
+        \caption{View-invariant unit}
+    \end{subfigure}
+\end{figure}
+
+
+\begin{description}
+    \item[Gnostic unit] \marginnote{Gnostic unit}
+        Neuron in the object detection hierarchy that gets activated by complex stimuli (i.e. objects with a meaning).
+\end{description}
+
+\begin{casestudy}[Jennifer Aniston cell]
+    An IT neuron of a human patient only responded to pictures of Jennifer Aniston or to its written name.
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.5\linewidth]{./img/aniston_cell.png}
+    \end{figure}
+\end{casestudy}
+
+
+
+\subsection{Local vs distributed coding}
+
+
+\begin{description}
+    \item[Local coding hypothesis] \marginnote{Local coding hypothesis}
+        IT neurons are gnostic units that are activated only when a particular object is recognized.
+
+    \item[Distributed coding hypothesis] \marginnote{Distributed coding hypothesis}
+        Recognition is due to the activation of multiple IT neurons.
+        \begin{remark}
+            This is the most plausible hypothesis.
+        \end{remark}
+\end{description}
+
+
+\begin{casestudy}[Neurons in vector space]
+    The response of a population of neurons can be represented in a vector space.
+    It is expected that transformations of the same object produce representations that lie on the same manifold. 
+
+    In the first stages of vision processing, various manifolds are tangled.
+    Object recognition through the visual cortex aims to untangle the representations of the objects.
+
+    \begin{figure}[H]
+        \centering
+        \begin{subfigure}{0.48\linewidth}
+            \centering
+            \includegraphics[width=0.95\linewidth]{./img/tangled_vectors.png}
+        \end{subfigure}
+        \begin{subfigure}{0.48\linewidth}
+            \centering
+            \includegraphics[width=0.95\linewidth]{./img/tangled_joe_sam.png}
+        \end{subfigure}
+    \end{figure}
+\end{casestudy}
+
+
+\begin{casestudy}[Classifier from monkey neurons \cite{vision_monkey_svm}]
+    An animal maintains fixation at the center of a screen on which images of different categories are presented very quickly (100 ms + 100 ms pause)
+    at different scales and positions.
+
+    The responses of IT neurons are taken with some offset after the stimulus (to give them time to reach the IT)
+    and converted into vector form to train one binary classifier (SVM) for each category (one-vs-all).
+
+    Once trained, testing was done on new stimuli.
+    Results show that the performance increases linearly with the logarithm of the number of sites (measured neurons).
+    It can be concluded that:
+    \begin{itemize}
+        \item Categorization is easier than identification.
+        \item The distributed coding hypothesis is more likely.
+    \end{itemize}
+
+    \begin{figure}[H]
+        \centering
+        \begin{subfigure}{0.3\linewidth}
+            \centering
+            \includegraphics[width=0.65\linewidth]{./img/monkey_svm_results.png}
+        \end{subfigure}
+        \begin{subfigure}{0.6\linewidth}
+            \centering
+            \includegraphics[width=0.25\linewidth]{./img/monkey_svm_results2.png}
+            \caption{Accuracy on multiple units (MUA), a single unit (SUA) and readings made on the cortex, not inside (LFP)}
+        \end{subfigure}
+    \end{figure}
+
+    Time-wise, it has been observed that:
+    \begin{itemize}
+        \item Performance gets worse if the measurement of the neurons spans for too long 
+            (no explanation was given in the original paper, probably noise is added up to the signal for longer measurements).
+        \item The best offset from the stimulus onset at which the measures of the IT neurons should be taken is 125 ms.
+    \end{itemize}
+
+    \begin{figure}[H]
+        \centering
+        \includegraphics[width=0.5\linewidth]{./img/monkey_svm_time.png}
+    \end{figure}
+
+    It has also been observed that the visual ventral pathway, which is responsible for object recognition, also encodes information on the size of the objects.
+    This is not strictly useful for recognition, but a machine learning algorithm is able to extract this information from the neural readings.
+    This hints at the fact that the ventral pathway also contributes to identifying the location and size of the objects.
+\end{casestudy}
+
+
+\begin{casestudy}[Artificial neural network to predict neuronal activity \cite{vision_monkey_hcnn}]
+    Different neural networks are independently trained on the task of image recognition.
+    Then, the resulting networks are compared to the neuronal activity of the brain.
+
+    The network should have the following properties:
+    \begin{itemize}
+        \item Provide information useful to support behavioral tasks (i.e. act as the IT neurons).
+        \item Layers of the network should have a corresponding area on the ventral pathway (mappable).
+        \item It should be able to predict the activation of single and groups of biological neurons (neurally predictive).
+    \end{itemize}
+
+    \begin{descriptionlist}
+        \item[Dataset] 
+            A set of images is divided into two sets:
+            \begin{descriptionlist}
+                \item[Train set] To train the neural networks.
+                \item[Test set] To collect neuronal data and evaluate the neural networks.
+            \end{descriptionlist}
+
+            Images have different levels of difficulty (low to high variation) and are presented on random backgrounds.
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.2\linewidth]{./img/vision_nn_difficulty.png}
+            \end{figure}
+
+
+        \item[Neuronal data]
+            Neuronal data are collected from the area V4 and IT in two macaque monkeys.
+            They are tasked to maintain fixation at the center of a screen on which images are presented for 100 ms followed by a 100 ms blank screen.
+
+            For each stimulus, the firing rate is obtained as the average of the number of spikes in the interval 70 ms - 170 ms after the stimulus onset.
+
+
+        \item[Neural network training] 
+            Hierarchical convolutional neural networks (HCNN) are used for the experiments.
+            They are composed of linear-nonlinear layers that do the following:
+            \begin{enumerate}
+                \item Filtering through linear operations of the input stimulus (i.e. convolutions).
+                \item Activation through a rectified linear threshold or sigmoid.
+                \item Mean or maximum pooling as nonlinear aggregation operation.
+                \item Divisive normalization to output a standard range.
+            \end{enumerate}
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.7\linewidth]{./img/vision_nn_network.png}
+            \end{figure}
+
+            The HCNNs have a depth of 3 or fewer layers and are trained independently from the neuronal measurements.
+            For evaluation, models are divided into groups following three different criteria:
+            \begin{itemize}
+                \item Random sampling.
+                \item Selection of models with the highest performance on the high-variation images.
+                \item Selection of models with the highest IT neural predictivity.
+            \end{itemize}
+
+            Resulting HCNNs are also used to create a new high-performance architecture through hierarchical modular optimization (HMO)
+            by selecting the best-performing modules from the trained networks (as each layer is modular).
+
+
+        \item[Evaluation method]
+            Evaluation is done using the following approach:
+            \begin{itemize}
+                \item Object recognition performances are assessed using SVM classifiers:
+                    \begin{itemize}
+                        \item For neural networks, the output features of a stimulus are obtained from the activations at the top layers.
+                        \item For neuronal readings, the output features of a stimulus are obtained by converting the firing rates into vector form.
+                    \end{itemize}
+                
+                \item To measure the ability of a neural network to predict the activity of a neuron,
+                    a partial least squares regression model is used to find a combination of weights at the top layers of the network
+                    that best fits, using as metric the coefficient of determination ($R^2$), the activity of the neuron on a random subset of test images.
+
+                \item An ideal observer is used as a baseline.
+                    It has all the categorical information to make correct predictions but it does not use a layered approach.
+            \end{itemize}
+
+
+        \item[Results]
+            It has been observed that:
+            \begin{itemize}
+                \item The HMO model has human-like performances.
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=0.7\linewidth]{./img/vision_nn_performance_hmo.png}
+                    \end{figure}
+
+                \item The higher the categorization accuracy, the better the model can explain the IT.
+                    
+                    Moreover, forcefully fitting a network to predict IT as the main task 
+                    predicts the neuronal activity worse than using a model with high categorization accuracy.
+
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=0.7\linewidth]{./img/vision_nn_neural_prediction.png}
+                    \end{figure}
+
+                \item None of the parameters of the neural networks can independently predict the IT better than performance (i.e. the network as a whole).
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=0.5\linewidth]{./img/vision_nn_params_prediction.png}
+                    \end{figure}
+
+                \item Higher levels of the HMO model yield good prediction capabilities of IT and V4 neurons.
+                    More specifically:
+                    \begin{itemize}
+                        \item The fourth (last) layer of the HMO model predicts well the IT.
+                        \item The third layer of the HMO model predicts well the area V4.
+                    \end{itemize}
+                    \begin{figure}[H]
+                        \centering
+                        \begin{subfigure}{0.6\linewidth}
+                            \centering
+                            \includegraphics[width=\linewidth]{./img/vision_nn_prediction_it.png}
+                            \caption{Results on IT}
+                        \end{subfigure}
+                        \begin{subfigure}{0.38\linewidth}
+                            \centering
+                            \includegraphics[width=\linewidth]{./img/vision_nn_prediction_v4.png}
+                            \caption{Results on V4}
+                        \end{subfigure}
+                        \caption{
+                            \parbox[t]{0.78\linewidth}{
+                                (A) Actual neuronal activity (black) and predicted activity (colored).\\
+                                (B) $R^2$ value over the population of single IT neurons.\\
+                                (C) Median $R^2$ over the population of IT neurons.
+                            }
+                        }
+                    \end{figure}
+            \end{itemize}
+    \end{descriptionlist}
+\end{casestudy}