work-storage-presentations-qualsJC-routing

\documentclass{seminar} \usepackage{color}

Routing in the brain

---

\begin{center}

Q: What happens in your brain when I say

"When you see the blue light, press the green button"

?

%%\Huge{\begin{equation*}\downarrow\end{equation*} } %%\begin{ugraph} %%"?" [fontsize=15 width=.2 height=.2 margin=0] %%\end{ugraph}

\begin{ugraph} size="1.7,1.7" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4 [fillcolor=blue];5;6;7;8;9;10;11 ;12 [fillcolor=green]

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{center}

---

Every neuron is not directly connected to every other neuron

\begin{center} \textcolor{red} {Not this:} \begin{ugraph} size=".6,.6" node [width=0.2 height=0.2 style=filled label=""]

1 [fillcolor=blue] 2 3 4 5 [fillcolor=green]

1 -- 2; 1 -- 3; 1 -- 4; 1 -- 5; 1 -- 6; 1 -- 7; 2 -- 1; 2 -- 3; 2 -- 4; 2 -- 5; 2 -- 6; 2 -- 7; 3 -- 1; 3 -- 2; 3 -- 4; 3 -- 5; 3 -- 6; 3 -- 7; 4 -- 1; 4 -- 2; 4 -- 3; 4 -- 5; 4 -- 6; 4 -- 7; 5 -- 1; 5 -- 2; 5 -- 3; 5 -- 4; 5 -- 6; 5 -- 7; 6 -- 1; 6 -- 2; 6 -- 3; 6 -- 4; 6 -- 5; 6 -- 7; 7 -- 1; 7 -- 2; 7 -- 3; 7 -- 4; 7 -- 5; 7 -- 6;

\end{ugraph}

But rather: \begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] 1;2;3;4 [fillcolor=blue];5;6;7;8;9;10;11 ;12 [fillcolor=green]

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{center}

---

But$\ldots$ it seems we can make arbitrary behavioral associations

\begin{center} \begin{ugraph} size="1.7,1.7" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4 [fillcolor=blue];5;6;7;8;9;10;11 ;12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph} \end{center}

---

Therefore, intermediate neurons must be able to "route" information depending on task

Blue light $\Rightarrow$ green button: \begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 6 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

Loud noise $\Rightarrow$ green button: \begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

7 [fillcolor=orange] 10 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

7--10 [style=bold color=red] 10--9 [style=bold color=red] 12--9 [style=bold color=red]

6--9;5--6;12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--4;3--10;11--1;11--3 \end{ugraph}

---

But how?

---

Packet-switching vs. circuit-switching

---

\begin{tabular}{l

& \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 2;3;4;5;6;7;9;10;11 ;12

l}

4 [fillcolor=blue] 6 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

M [shape=diamond width=.1 height=.1 label="" color=yellow fillcolor=yellow label="To: 12"]

4--6 6--M M--9 12--9

12--11;4--5;3--7;4--5;;4--3;5--2;2--9;;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--3 \end{ugraph}
\textbf{Packet switching}
\qquad Like the post office %% %% %% %% %% %% %% %%
\hline
& \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 6 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}
\textbf{Circuit switching}
\qquad Like the (old) telephone system \end{tabular}

---

Table of Contents

• Packet or circuit?
  • Packet
  • Circuit
• \textbf{Addressing}
  • \textbf{Absolute}
  • \textbf{Relative}
  • \textbf{Activity-based/temporary addressing}
  • \textbf{None}

---

\begin{center}

Absolute addressing

"every node has a unique name"

\begin{ugraph} size="1.0,1.0" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1 [label="Jyoti"] 2 [label="Erik"] 3 [label="Moe"] 4 [label="Flavio"] 5 [label="Philip"] 6 [label="Ev"] 7 [label="Emily"] 8 [label="Shantanu"] 9 [label="Ben"] 10 [label="Corinne"] 11 [label="Bassam"] 12 [label="Justin"]

7--10 10--9 12--9

6--9;5--6;12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--4;3--10;11--1;11--3 \end{ugraph}

\begin{ugraph} size="1.0,1.0" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{center}

---

• Must have a mechanism for allocating addresses
• Must be able to "pronounce" long addresses

---

• Absolute addressing
• \textbf{Relative addressing}

\begin{graph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] normalize=true edge [dir=none]

1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16

subgraph cluster_1 {rank=same;1;2;3;4} subgraph cluster_2 {rank=same;5;6;7;8} subgraph cluster_3 {rank=same;9;10;11;12} subgraph cluster_4 {rank=same;13;14;15;16}

2 [fillcolor=green] 11 [fillcolor=blue]

7->11 [style=bold color=red] 3->7 [style=bold color=red] 2->3 [style=bold color=red]

1->5; 2->6; 4->8 1->2; 3->4

5->9; 6->10; 8->12 5->6; 6->7; 7->8

9->13; 10->14; 11->15; 12->16 9->10; 10->11; 11->12

13->14; 14->15; 15->16

\end{graph} "go up 2 and 1 to the left"

\begin{graph} size="1.2,1.2" graph [rankdir=LR] node [width=0.2 height=0.2 style=filled fillcolor=lightgray] normalize=true edge [dir=none]

subgraph cluster_1 {rank=same;8;2;3} subgraph cluster_1 {rank=same;5;6} 11->5 [label="b"] 5->6 7->6 [label="g"] 8->2 3->5 3->6 [label="w"]

2 [fillcolor=green] 11 [fillcolor=blue]

7->11 [style=bold color=red label="a"] 3->7 [style=bold color=red label="f"] 2->3 [style=bold color=red label="z"]

\end{graph} "take edge a, then edge f, then edge z"

---

\bullet Each node must have a local name for each of its edges

---

• Absolute addressing
• Relative addressing
• \textbf{Activity-based/temporary addressing}

\begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] 1;2;3;4 [fillcolor=blue];5;6;7;8;9;10;11 ;12 [fillcolor=green]

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

"I'd like to talk to someone who is currently green, please"

\bullet Not a permanent address; if the the nodes change state, then the same "address" could go to a different place

---

• Absolute addressing
• Relative addressing
• Activity-based/temporary addressing
• \textbf{No addressing}

\begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] 1;2;3;4;5;6;7;8;9;10;11 ;12

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

There is no way for one node to describe another node

---

Addressing summary

\begin{tabular}{ll} \bullet Absolute addressing & \begin{ugraph} size=".5,.5" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

%% %% %% %% %%
\bullet Relative addressing & \begin{graph} size=".5,.5" graph [rankdir=LR] node [width=0.2 height=0.2 style=filled fillcolor=lightgray] normalize=true edge [dir=none]

subgraph cluster_1 {rank=same;8;2;3} subgraph cluster_1 {rank=same;5;6} 11->5 [label="b"] 5->6 7->6 [label="g"] 8->2 3->5 3->6 [label="w"]

2 [fillcolor=green] 11 [fillcolor=blue]

7->11 [style=bold color=red label="a"] 3->7 [style=bold color=red label="f"] 2->3 [style=bold color=red label="z"]

\end{graph} %% %% %% %% %% %% %%
\bullet Activity-based/temporary addressing & \begin{ugraph} size=".5,.5" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] 1;2;3;4 [fillcolor=blue];5;6;7;8;9;10;11 ;12 [fillcolor=green]

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph} %% %% %% %% %% %% %%
\bullet No addressing & \begin{ugraph} size=".5,.5" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] 1;2;3;4;5;6;7;8;9;10;11 ;12

12--9;12--11;1--6;8--9;4--5;6--8;9--6;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;4--6;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{tabular}

---

How you find things?

• Even with absolute addressing, a hard problem
• How are the words "When you see a blue light" translated into a path to the blue light detector?
• Giant symbolic lookup table?
  • Seems unlikely
• Imagination?
  • You've only recursed the problem

---

Table of Contents

• Packet or circuit?
  • Packet
  • Circuit
• Addressing?
  • Absolute
  • Relative
  • Activity-based/temporary addressing
  • None
• \textbf{Granularity?}
  • \textbf{Single neurons}
  • \textbf{Fixed ensembles}

---

Granularity

What is the smallest "routable"\footnote{we'd usually say "addressable", but we're not sure if there are addresses...} unit? Is it:

• a single neuron / (dynamic ensembles)
• static ensembles

---

Granularity: single neuron $/$ dynamic ensembles

Single neuron:

\begin{center} \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 6 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph} \qquad \qquad \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

7 [fillcolor=orange] 10 [fillcolor=red] 9 [fillcolor=red] 12 [fillcolor=green]

7--10 [style=bold color=red] 10--9 [style=bold color=red] 12--9 [style=bold color=red]

6--9;5--6;12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--4;3--10;11--1;11--3 \end{ugraph}

\end{center}

Dynamic ensembles:

\begin{center} \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 5 [fillcolor=blue]

6 [fillcolor=red] 9 [fillcolor=red] 2 [fillcolor=red] 8 [fillcolor=red]

12 [fillcolor=green] 11 [fillcolor=green] 1 [fillcolor=green]

10 [fillcolor=orange] 3 [fillcolor=orange] 7 [fillcolor=orange]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph} \qquad \qquad \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=pink] 5 [fillcolor=pink]

8 [fillcolor=tan4] 2 [fillcolor=tan4] 6 [fillcolor=tan4]

10 [fillcolor=purple] 9 [fillcolor=purple] 1 [fillcolor=purple]

12 [fillcolor=orange] 11 [fillcolor=orange]

4 [fillcolor=gold] 3 [fillcolor=gold] 7 [fillcolor=gold]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{center}

---

Granularity: static ensembles

\begin{center} \begin{tabular}{ll} \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 5 [fillcolor=blue]

6 [fillcolor=red] 9 [fillcolor=red] 2 [fillcolor=red] 8 [fillcolor=red]

12 [fillcolor=green] 11 [fillcolor=green] 1 [fillcolor=green]

10 [fillcolor=orange] 3 [fillcolor=orange] 7 [fillcolor=orange]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph} \qquad \qquad & \begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 5 [fillcolor=blue]

6 [fillcolor=red] 9 [fillcolor=red] 2 [fillcolor=red] 8 [fillcolor=red]

12 [fillcolor=green] 11 [fillcolor=green] 1 [fillcolor=green]

10 [fillcolor=orange] 3 [fillcolor=orange] 7 [fillcolor=orange]

4--6

6--9 12--9

3--11 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1 \end{ugraph}

\begin{graph} size=".5,.5" graph [rankdir=LR] [node style=filled label=""] 1 [fillcolor=blue label=""] 2 [fillcolor=green label=""] 1->2 \end{graph} & \begin{graph} size=".5,.5" graph [rankdir=LR] [node style=filled label=""] 1 [fillcolor=orange label=""] 2 [fillcolor=green label=""] 1->2 \end{graph} \end{tabular}

---

\begin{graph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray label=""] edge [color=gray dir=none]

gr [fillcolor=green] subgraph cluster_r {rank=source; red [fillcolor=red]} blue [fillcolor=blue] subgraph cluster_o {rank=sink; or [fillcolor=orange]}

blue->red blue->or

gr->red gr->or

or->red

\end{graph}

\end{center}

---

Granularity cont'd

Are there well-defined \textbf{boundaries} between inaccessible "\textbf{internal} module information" and "\textbf{public} information" \ldots

\smallskip

\ldots or is the system so dynamic and fluid that \textbf{any information anywhere} in a neural system can be used by anyone else?\footnote{This doesn't necessarily imply that all of that information is \emph{consciously} available}

\scriptsize{(if the latter, then we might need to route at a single-neuron granularity)}

---

Table of Contents

• Packet or circuit?
• Addressing?
• Granularity?
  • Single neurons
  • Fixed ensembles
• \textbf{Specialized routing components?}
  • \textbf{Yes, specialized "routers"}
  • \textbf{No, routing is a basic function of neurons}

---

Specialized routing components?

\begin{tabular}{l

Specialized routers? & Or not?

l}

\begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 6 [shape=diamond fillcolor=red] 9 [shape=diamond fillcolor=red] 12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

2 [shape=diamond fillcolor=pink] 7 [shape=diamond fillcolor=pink]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

&

\begin{ugraph} size="1.2,1.2" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 6 [ fillcolor=red] 9 [ fillcolor=red] 12 [fillcolor=green]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

Or routing modules?

\begin{ugraph} size="1,1" node [width=0.2 height=0.2 style=filled fillcolor=lightgray] edge [color=gray] 1;2;3;4;5;6;7;8;9;10;11 ;12

4 [fillcolor=blue] 5 [fillcolor=blue]

6 [shape=diamond fillcolor=red] 9 [shape=diamond fillcolor=red] 2 [shape=diamond fillcolor=red] 8 [shape=diamond fillcolor=red]

12 [fillcolor=green] 11 [fillcolor=green] 1 [fillcolor=green]

10 [fillcolor=orange] 3 [fillcolor=orange] 7 [fillcolor=orange]

4--6 [style=bold color=red] 6--9 [style=bold color=red] 12--9 [style=bold color=red]

12--11;1--6;8--9;4--5;6--8;2--8;9--1;3--7;4--5;9--1;4--3;5--2;2--9;2--1;3--2;3--4;7--5;6--5;3--10;10--9;7--10;11--1;11--3 \end{ugraph}

\end{tabular}

---

Table of Contents

• Packet or circuit?
• Addressing?
• Granularity
• Specialized routing components?
• \textbf{Topology?}

---

Topology?

• Can any module access any other module?
• How many hops needed?
  • Graph diameter
  • Hypercube: log_degree(N)
  • log_1000(10^12) = 4

---

Topology cont'd

• Clique topology between modules?

---

Plasticity for setup of circuit-switched connections

\bullet (Hebbian) "cell assemblies"\footnote{Theory in Biosciences, special issue on cell assemblies. Volume 122, Issue 1, Pages 1-103 (2003)}

---

Oscillations for setup of circuit-switched connections

---

Routing control signals

• "Meta-data"
• Addresses
• Separated in space (i.e. coming in on different synapses)
• Separated in time (as "header")
• Multiplexed onto primary signal

---

Routing-centric computation

\begin{center}

NAND

\begin{graph} size="2,2" i1 [label="input 1" shape=plaintext] i2 [label="input 2" shape=plaintext] output [shape=plaintext] 11 [label="1" shape=plaintext] 12 [label="1" shape=plaintext] 0 [shape=plaintext] s1 [label="switch"] s2 [label="switch"]

i1->s1 [style=bold color=gold] 11->s1 i2->s2 [style=bold color=gold] 12->s2 0->s2 s2->s1

s1->output

\end{graph} \end{center}

---

The hippocampus

• During sleep
• As a memory of cross-module bindings

---

Discussion

• How do you think the blue light detector gets in touch with the green button motor program?
• What is the addressing scheme, if any?
• How are connections actually switched, if they are?

---

This presentation is copyright 2005 Bayle Shanks but you may reuse any part of it under the Creative Commons by-sa version 2 copyright licence. Please ask me if you'd like the EasyLatex? source, or if you'd like to use it under other licensing terms.

\cfig{somerights20.eps}