Download Nature 411, 189 - 193 (2001)

Daniel Amit 1938-2007
Systems of spin-like elements may dynamically relax
governed by the
Hamiltonian
towards increasingly complex “discrete” attractor states
J ij  constant
(Ising model)
ferromagnetic
J ij  disordered
(e.g., S.K. model)
+ spin-glass state
J ij    i  j
(Hopfield model)
+ memory states

A
B
C
D
Daniel Amit, Hanoch Gutfreund and Haim Sompolinsky
showed how to extend the mathematical analysis of spin-glasses
into a new “statistical physics” of Hopfield attractor networks
No. Almost.
They derived the free-energy
and the saddle-point equations
that describe the equilibrium
reached by relaxational dynamics
DS (disordered state)
SG (spin glass)
yielding finally a phase-diagram
+RS (retrieval memory state)
storage load
=p/N
are spin-glass effects really relevant to understanding realistic
auto-associative networks?
binary  threshold-linear:
AT, J. Phys. A: Math. Gen. 24 (1991) 2645-2654.
Threshold-linear
spin glass
(SK)
Threshold-linear
neural network (Hopfield)
No. Almost.
Premio Nobel
1906
Camillo Golgi
1843-1926
Santiago
Ramón y Cajal
1852-1934
Teoria
reticolare
Teoria
cellulare
(il sincizio)
(i neuroni)
La reazione nera
1873
Arealization
and
Memory in the
Cortex
monkey
Main perspectives:
a) Content-based
b) Hierarchical
c) Statistical/modular
The statistical/modular perspective
The Braitenberg model
N pyramidal cells
√N compartments
√N cells each
A pical synapses
B asal synapses
A simple to
semantic
Reduced
updated
remove
a Pottsnetwork
model
the
(O’Kane &&glass’
Treves,
1992)
(Kropff
‘memory
Treves,
problem
2005)
(Fulvi Mari & Treves, 1998)
Cortical
modules
Potts
Structured
units
with
long-range
dilute
connectivity
connectivity
..but all cortical modules
share the same organization…
Local
attractor
S+1
“0”
state
Potts
included
statesstates (=S)
Global activity
patterns
Sparse
Sparse
Potts
globalpatterns
patterns
2 !!
 CSS?!?!
ppcc 
Cerebellar
Networks
The numbers of expansion recodingç
Each MF terminates in several hundreds rosettes
Each rosette has the dendrites of  28 GCs
Each GC receives from  4 rosettes (MFs)
There are 450 times more GCs than MFs
In humans, there are 3x1010 GCs,
each making about 300 PF synapse,
for a total 1013 storage locations
on some 5x107 Purkinje cells.
Nature 411, 189 - 193 (2001)
Scalable architecture in mammalian brains
DAMON A. CLARK*†, PARTHA P. MITRA‡ & SAMUEL S.-H. WANG*
* Department of Molecular Biology and
† Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
‡ Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974,
USA
Correspondence and requests for materials should be addressed to S.S.-H.W. (e-mail:
[email protected]).
Comparison of mammalian brain parts has often focused on differences in absolute size, revealing
only a general tendency for all parts to grow together. Attempts to find size-independent effects
using body weight as a reference variable obscure size relationships owing to independent variation
of body size and give phylogenies of questionable significance. Here we use the brain itself as a size
reference to define the cerebrotype, a species-by-species measure of brain composition. With this
measure, across many mammalian taxa the cerebellum occupies a constant fraction of the total
brain volume (0.13
0.02), arguing against the hypothesis that the cerebellum acts as a
computational engine principally serving the neocortex. Mammalian taxa can be well separated by
cerebrotype, thus allowing the use of quantitative neuroanatomical data to test evolutionary
relationships. Primate cerebrotypes have progressively shifted and neocortical volume fractions
have become successively larger in lemurs and lorises, New World monkeys, Old World monkeys,
and hominoids, lending support to the idea that primate brain architecture has been driven by
directed selection pressure. At the same time, absolute brain size can vary over 100-fold within a
taxon, while maintaining a relatively uniform cerebrotype. Brains therefore constitute a scalable
architecture.
Striatal
Networks
paleocortex
(olfactory)
archicortex
(hippocampus)
neocortex
(the rest)
Brain Behav Evol. 1997;49(4):179-213.
The telencephalon of tetrapods in evolution.
Striedter GF.
Department of Psychobiology, University of California, Irvine 92697-4550, USA.
Numerous scientists have sought a homologue of mammalian isocortex in sauropsids (reptiles and birds) and a
homologue of sauropsid dorsal ventricular ridge in mammals. Although some of the proposed theories were
enormously influential, alternative theories continued to coexist, primarily because the striking differences in pallial
organization between adult mammals, sauropsids, and amphibians enabled different authors to enlist different subsets
of similarity data in support of different hypotheses of putative homology. A phylogenetic analysis based on parsimony
cannot discriminate between such alternative hypotheses of putative homology, because sauropsids and mammals are
sister groups. One solution to this dilemma is to include embryological patterns of telencephalic organization in the
comparative analysis. Because early developmental stages in different taxa tend to resemble each other more than the
adults do, the embryological data may reveal intermediate patterns of organization that provide unambiguous support
for a single hypothesis of putative homology. The validity of this putative homology may then be supported by means
of a phylogenetic analysis based on parsimony. A comparative analysis of pallial organization that includes
embryological data suggests the following set of homologies. The lateral cortex in reptiles is homologous to the
piriform cortex in birds and mammals. The anterior dorsal ventricular ridge in reptiles is probably homologous to the
neostriatum and ventral hyperstriatum in birds and to the endopiriform nucleus in mammals. The posterior dorsal
ventricular ridge in reptiles is most likely homologous to the archistriatum in birds and to the pallial amygdala in
mammals. The pallial thickening in reptiles is probably homologous to the dorsal and intercalated portions of the
hyperstriatum in birds and to the claustrum proper in mammals. Finally, the dorsal cortex in reptiles is probably
homologous to the accessory hyperstriatum and parahippocampal area in birds and to the isocortex in mammals. These
hypotheses of homology imply relatively minor evolutionary changes in development but major changes in neuronal
connections. Most significantly, they imply the independent elaboration of thalamic sensory projections to derivatives
of the lateral and dorsal pallia in sauropsids and mammals, respectively. They also imply the independent evolution of
lamination in the pallium of birds and mammals.
Biochem Cell Biol. 1997;75(6):651-67.
The brain in evolution and involution.
Parent A.
Laboratoire de neurobiologie, Universite Laval Robert-Giffard, Beauport, QC, Canada.
This paper provides an overview of the phylogenetic evolution and structural organization of the basal
ganglia. These large subcortical structures that form the core of the cerebral hemispheres directly participate
in the control of psychomotor behavior. Neuroanatomical methods combined with transmitter localization
procedures were used to study the chemical organization of the forebrain in each major group of vertebrates.
The various components of the basal ganglia appear well developed in amniote vertebrates, but remain
rudimentary in anamniote vertebrates. For example, a typical substantia nigra composed of numerous
dopaminergic neurons that project to the striatum already exists in the brain of reptiles. Other studies in
mammals show that glutamatergic cortical inputs establish distinct functional territories within the basal
ganglia, and that neurons in each of these territories act upon other brain neuronal systems principally via a
GABAergic disinhibitory output mechanism. The functional status of the various basal ganglia
chemospecific systems was examined in animal models of neurodegenerative diseases, as well as in
postmortem material from Parkinson's and Huntington's disease patients. The neurodegenerative processes
at play in such conditions specifically target the most phylogenetically ancient components of the brain,
including the substantia nigra and the striatum, and the marked involution of these brain structures is
accompanied by severe motor and cognitive deficits. Studies of neural mechanisms involved in these
akinetic and hyperkinetic disorders have led to a complete reevaluation of the current model of the
functional organization of the basal ganglia in both health and disease.
Neocortex
Hippocampus
n
(+) +
n
(+) +
Lamination, Arealization
DG input sparsifier
CA1 feed-forward
Cerebellum
-(-)-
Expansion recoding,
Private teachers
Basal ganglia
Massive funnelling
Tonic output firing
Olfactory
bulb
++-
Who is
cutting-edge, in
cerebellar
technology?
Tectum
Spinal cord
Computational
paradigms
100’s Myrs old
that we fail
to understand