UNIVERSIDAD DE SEVILLA
DOCTORAL THESIS
S udy, Design and Implemen a ion o
Neu omo phic Sys ems h ough a Spiking
Boolean Compu ing Pa adigm
Au ho :
Ál a o Ayuso Ma ínez
Supe iso s:
D . Gab iel Jiménez Mo eno and D . Juan P. Domínguez Mo ales
A hesis submi ed in ul illmen o he equi emen s
o he deg ee o Doc o o Philosophy
in he
Robo ics and Compu e Technology Lab.
Depa amen o de A qui ec u a y Tecnología de Compu ado es
Oc obe , 2024
iii
Decla a ion o Au ho ship
I, Ál a o Ayuso Ma ínez, decla e ha his hesis, en i led “S udy, Design
and Implemen a ion o Neu omo phic Sys ems h ough a Spiking Boolean
Compu ing Pa adigm”, and he wo k p esen ed in i a e my own. I con i m ha :
• This wo k was done wholly o mainly while in candida u e o a esea ch
deg ee a his Uni e si y.
• Whe e any pa o his hesis has been p e iously submi ed o a deg ee o
any o he quali ica ion a his Uni e si y o any o he ins i u ion, his has
been clea ly s a ed.
• Whe e I ha e consul ed he published wo k o o he s, his is always clea ly
a ibu ed.
• Whe e I ha e quo ed om he wo k o o he s, he sou ce is always gi en.
Wi h he excep ion o such quo a ions, his hesis is en i ely my own wo k.
• I ha e acknowledged all main sou ces o help.
• Whe e he hesis is based on wo k done by mysel join ly wi h o he s,
I ha e made i clea exac ly wha was done by o he s and wha I ha e
con ibu ed mysel .
UNIVERSIDAD DE SEVILLA
Abs ac
Escuela Técnica Supe io de Ingenie ía In o má ica
Depa amen o de A qui ec u a y Tecnología de Compu ado es
Doc o o Philosophy
S udy, Design and Implemen a ion o Neu omo phic Sys ems h ough a
Spiking Boolean Compu ing Pa adigm
by Ál a o Ayuso Ma ínez
In ecen yea s, ad ances in ansis o in eg a ion wi hin digi al compu e s
ha e enabled hem o be educed o nea -a omic scales, pushing his echnology
o i s physical and he mal limi s. This end, which has also signi ican ly
inc eased p oduc ion cos s, ein o ces he belie ha Moo e’s law is going o
become obsole e in he coming yea s. Howe e , al hough doub s may a ise abou
he possibili y o u he imp o ing he e iciency o digi al compu e s, hese
disappea when conside ing he b ain, which is he mos powe ul and e icien
sys em known. I is no based on ansis o s bu on neu ons and achie es high
pe o mance wi h minimal powe consump ion, bo h cha ac e is ics eme ging
mainly om he massi e pa allelism inhe en o he ne ous sys em. Inspi ed
by he p inciples o neu omo phic enginee ing, his wo k p oposes eplacing
ansis o s in digi al ci cui s wi h neu ons o ha ness hese bene i s. By
abs ac ing neu onal unc ion, i is possible o apply Boolean algeb a o he design
o Spiking Neu al Ne wo ks unde speci ic condi ions, in a simila way o how
i is applied o he design o digi al ci cui s. Thus, his wo k lays he ounda ion
o spiking Boolean compu a ion h ough he spiking implemen a ion o basic
logic ga es, p o iding a sys ema ic app oach o designing hese ne wo ks, which
could be aluable o esea che s in he ield. I also explo es he de elopmen o
complex spiking blocks o specialized applica ions, in which he de elopmen o
he spiking compu e is highligh ed, and p esen s an ex ensi e se o expe imen s
whose esul s demons a e hei co ec unc ionali y mainly on wo di e en
neu omo phic pla o ms, SpiNNake and Dynap-SE. The inal implemen a ions
ha e been shown o beha e as expec ed in challenging en i onmen s and unde
condi ions compa able o hose ound in biology.
ii
Acknowledgemen s
“Don’ walk behind me; I may no lead. Don’ walk in on o me; I may
no ollow. Jus walk beside me and be my iend.”
– Albe Camus
This doc o al hesis is he esul o se e al yea s o ha d wo k, du ing which
my li e has unde gone many changes and du ing which I ha e had bo h good and
di icul momen s. I would like o lea e a pe sonal e lec ion o my u u e sel :
when you ead hese wo ds, you will emembe e e y hing you ne e hough
you we e capable o doing bu managed o do, who you we e and wha you
d eam was. O e coming all he ba ie s I ha e encoun e ed du ing hese yea s
would no ha e been possible wi hou he indispensable suppo o all hose who
ha e accompanied me on his pa h, and I would like o ake ad an age o his
special momen o be hones and dedica e a ew wo ds o some o hem.
Fi s , I would like o hank my amily o he suppo hey ha e gi en me,
especially du ing he las yea and a hal , as well as emembe ing wo people
who would su ely eel e y p oud o his wo k, my g andpa en s Joaquín and
Sebas iana, who passed away du ing i s de elopmen . I will always emembe
you wi h a ec ion.
Th oughou my li e I ha e had many eache s who ha e ins illed in me
alues ha , oge he , ha e led me o be who I am oday. I would especially like
o hank one o hem, Ca men Pin o Ál a ez, o showing me music no as jus
ano he academic o p o essional ca ee , bu as a philosophy o li e. Fo all he
lo e and unde s anding you o e ed me o so many yea s, e en when I had o
say goodbye. Thank you e y much.
To my supe iso s Gab iel Jiménez Mo eno and Juan Ped o Domínguez
Mo ales: hanks o you guidance and pa ience. Gab iel, you g ea in e es
in esea ch, you as knowledge and you pe sonali y o ally ans o med me as
a s uden and made me bo n as a esea che . Juanpe, be o e I knew you, I al eady
admi ed you o being he p omise o he depa men . Inspi ed by he e o you
pu in o you wo k, which gi es i an excep ional quali y, you ha e eminded me
ha he e is no ema kable success wi hou g ea e o . Thank you o eaching
me e e y hing you lea ned and o always looking ou o he bes o me. I will
always be g a e ul o e e y hing you ha e done o me in he las ew yea s.
Finally, I also would like o hank Ángel Jiménez Fe nández, whose suppo has
also been e y impo an h oughou hese yea s, especially a he beginning, he
mos di icul momen o any PhD s uden .
Thanks also o he es o my colleagues o he Depa men o Compu e
A chi ec u e and Technology and he Robo ics and Compu e Technology Lab.,
who suppo me and ha e been pa o my daily li e since I a i ed mo e han
h ee yea s ago. Special men ion is gi en o Alejand o Lina es Ba anco o
iii
p omo ing esea ch ac i i y in he depa men and o Sa u nino Vicen e Díaz
and Fe nando Díaz del Río o hei g ea wo k as i s di ec o and sec e a y,
espec i ely.
I am deeply g a e ul o all he amazing people I ha e had he oppo uni y
o mee ou side o Se illa h ough my esea ch ac i i ies. Thanks o Tho ben
Schoepe and Hugh G ea o ex, who isi ed ou depa men in 2021 and wi h
whom I had he pleasu e o wo king o a sho pe iod o ime. Special hanks
o Fe nando Pé ez Peña o he wa m welcome a he Escuela Supe io de
Ingenie ía o he Uni e si y o Cádiz du ing my esea ch isi in 2022, e en
hough we had ne e me be o e. Thanks o e e yone I connec ed wi h a he
CapoCaccia Neu omo phic Wo kshop in 2023, including Luna Ga a, Na asa
Sama dzic, Sa ay Soldado, An ony N’d i, Thomas Tio o, Jules Lecom e and Luca
Pe es, among many o he s. Finally, I canno o ge he e o men ion some o he
people wi h whom I had he p i ilege o spending mon hs du ing my esea ch
isi o he Ins i u e o Neu oin o ma ics a he Uni e si y o Zu ich and ETH
Zu ich also in 2023: Melika Pay and, A ianna Rubino, Fa ah Ba aca , Héc o
Ramí ez, A a A abek, Ka a ina Vujic, A ianna Alonso, Josephine Loehle, Chia a
de Luca and Sap a shi Ghosh. Thank you all o you suppo and company
du ing imes when I el alone and a om home. This isi would no ha e
been possible wi hou he suppo o Giacomo Indi e i and he Neu omo phic
Cogni i e Sys ems g oup, which kindly hos ed me. Thanks also o Ka h in
Aguila , o he kindness and e o in acili a ing my isi o he ins i u e.
Now, i is he u n o e y, e y special people o me. Fi s , I would
like o men ion h ee people wi h whom I sha e a common his o y. Pablo
Sánchez Cue as, An onio Pé ez Peña and Daniel Casanue a Mo a o, hanks o
accompanying me since we s a ed s udying compu e enginee ing. We ha e
gone h ough all kinds o si ua ions, including he pandemic, a yea o ad en u es
in G anada, and he e u n o Se illa o s a a new li e. I mus also men ion
Lou des Du án López and Juan Ped o Domínguez Mo ales, my indispensable
o ice pa ne s, wi h whom I ha e sha ed an eno mous amoun o ime since I
a i ed o he depa men . Thanks o all i e o you o making my daily li e
a he uni e si y much easie , o you us and o he inc edible momen s we
expe ience e e y week.
He e is a special men ion o a e y special pe son o me, Pablo Rome o
Sánchez. Thanks o o e ing me one o he mos eal and beau i ul iendships
ha he uni e si y ga e me, ull o g ea momen s and unwa e ing loyal y e en
in he mos di icul si ua ions. You p esence in my li e has comple ely changed
i du ing hese las eigh yea s. This wo k is dedica ed o you.
To all my people om Val e de del Camino: Pablo R., I ene, Glo ia, Pablo Z.,
Guille, Ma ía, Luisa, Iuliana, Inma, Ja i, Víc o and Vik o , among many o he s,
hank you o welcoming me as one o you own o so many yea s. Val e de will
always be in my hea .
ix
I also would like o hank he amilies, old and new. To he Rome o Sánchez
and Co e Llamas amilies o gi ing me a lo e ha e y ew people ha e gi en
me h oughou my li e and o ea ing me like ano he membe o hem. To he
Rome o Ma ín and Co e Pé ez amilies... I wish you all he happiness and ha
you child en g ow up su ounded by lo e and heal h. Gael and Lia, you bi h
ep esen s an impo an momen in you pa en s’ li es and I am e y p oud o
ha e he oppo uni y o wa ch you g ow up so close.
Thank you all, hose I ha e men ioned and hose I ha e no , o being pa o
my li e o ha ing been pa o i a some poin du ing hese las h ee yea s.
This wo k has been suppo ed by Spanish g an s om he na ional esea ch
p ojec s MINDROB (PID2019-105556GB-C33) and SANEVEC (TED2021-130825B-
I00), which ha e been used o co e some publica ion cos s and also cos s
associa ed wi h he esea ch isi s.
x i
3.22 Example o an ECG da a ile’s MLII signal while using he del a
modula o algo i hm o ex ac on and o spikes. . . . . . . . . . . 54
3.23 Example o a 2-bi spiking coun e p ocessing an inpu spike ain
buil om ECG da a using he del a modula o algo i hm. CO
indica es when he coun e o e lows, while FO indica es when
he il e ing neu on i es. . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.24 Appea ance o he applica ion de eloped o in e ac wi h he eal-
ime simula ed spiking memo y on SpiNNake . . . . . . . . . . . . 56
3.25 Robo ic pla o m used o he expe imen s ca ied ou . A) Romeo
BLE boa d. B) Ada ui HUZZAH32. C) HC-SR04 ul asonic senso . 56
3.26 Response o he sys em o he a ia ion o dis ances a which he
objec is placed om he ul asonic senso . Ou pu spikes a e
ma ked wi h ed poin s and e ical lines. . . . . . . . . . . . . . . . 57
3.27 Expe imen conduc ed on SpiNNake o s udy he sub h eshold
dynamics o a LIF neu on by injec ing inpu spike ains a
equencies o 1 Hz, 2 Hz, and 10 Hz. . . . . . . . . . . . . . . . . . . 58
3.28 Diag am o he implemen ed 3-s a e FSM. . . . . . . . . . . . . . . . 59
3.29 Spiking implemen a ion o he 3-s a e FSM. The s a es a e
ep esen ed by he SR la ches shown in g een. Blue and ed
synapses a e exci a o y and inhibi o y, espec i ely. Elemen s
ep esen ed in o ange a e ela ed o he o wa d ansi ions and
igge ed by SG1, while elemen s shown in pink a e ela ed o he
backwa d ansi ion om S3 o S1and igge ed by SG2. ...... 59
3.30 Resul s o an expe imen conduc ed on he implemen ed FSM,
ope a ing a disc e e imes. The inpu spike ains a e shown below
he do ed line. S op is used o ese he s a es, and s a o se he
s a e S1.OP con ains he spikes equi ed o ope a e, SG1indica es
o ad ance o he nex s a e and SG2indica es o e u n back o he
p e ious s a e. The spikes i ed by each o he s a es and ansi ions
a e shown abo e he do ed line. . . . . . . . . . . . . . . . . . . . . 61
x ii
Lis o Tables
3.1 O e iew o he implemen ed blocks, indica ing whe e o ind
mo e de ailed in o ma ion on each o hem. . . . . . . . . . . . . . . 24
3.2 Se o neu on pa ame e s used on SpiNNake . . . . . . . . . . . . . 26
3.3 Se o neu on and synap ic pa ame e s used on Dynap-SE. . . . . . 26
3.4 Boolean beha io o 3-inpu OR, AND, and NOR ga es. A "1"
indica es ha a spike is ansmi ed h ough he espec i e synapse
(A,B, and C) o i ed by he espec i e ou pu neu on (OR, AND,
and NOR). In he case o he NOR ga e, i will i e only i a spike is
ansmi ed h ough OP and he e is no ac i i y h ough A,Band C. 27
3.5 Resul s o he expe imen s ca ied ou on he inhibi ion-based OR
ga e o di e en numbe s o inpu s (n) and di e en ope a ing
equencies ( ) on Dynap-SE. The icks indica e ha he expec ed
beha io is ob ained in any epe i ion, while he c osses indica e
ha he SNN is no able o ope a e co ec ly. . . . . . . . . . . . . . 33
3.6 Resul s o he expe imen s ca ied ou on he inhibi ion-based
AND ga e o di e en numbe s o inpu s (n) and di e en
ope a ing equencies ( ) on Dynap-SE. The icks indica e ha he
expec ed beha io is ob ained in any epe i ion, while he c osses
indica e ha he SNN is no able o ope a e co ec ly. . . . . . . . . 34
3.7 Analysis o he esou ces used and he la ency o each o he
spiking logic ga es. n e e s o he numbe o inpu s and τ o
he ime i akes o a spike o p opaga e h ough he union o a
synapseandaneu on. .......................... 34
3.8 Abb e ia ion, desc ip ion and alue o each o he ene gy a iables. 35
3.9 Analysis o he esou ces used and he la ency o each o he
designs ela ed o he spiking memo y which we e implemen ed
on SpiNNake . n e e s o he numbe o inpu s o he decode , c
e e s o he columns o he ma ix o D la ches, i.e., he numbe o
bi s employed o each o he egis e s, and τ e e s o he ime i
akes o a spike o p opaga e h ough he union o a synapse and
aneu on................................... 43
x iii
3.10 Resul s o he expe imen s ca ied ou on spiking ipple-ca y
adde s o di e en numbe s o bi s (n) and di e en ope a ing
equencies ( ). The icks indica e ha he expec ed beha io is
ob ained, while he c osses indica e ha he SNN is no able o
ope a eco ec ly. ............................. 49
3.11 Analysis o he esou ces used and he la ency o he high-le el
designs p oposed ela ed o he implemen a ion o he spiking
ALU. n e e s o he numbe o inpu s, b o he numbe o bi s and
τ o he ime i akes o a spike o p opaga e h ough he union o
a synapse and a neu on acco ding o he pa ame e s used. . . . . . 49
3.12 Analysis o he esou ces used and he la ency o he high-le el
designs p oposed ela ed o he implemen a ion o he spiking
coun e . b e e s o he numbe o bi s and τ o he ime i akes o
a spike o p opaga e h ough he union o a synapse and a neu on
acco ding o he pa ame e s used. . . . . . . . . . . . . . . . . . . . 53
xix
Lis o Abb e ia ions
EPSP Exci a o y Pos -Synap ic Po en ial
IPSP Inhibi o y Pos -Synap ic Po en ial
STDP Spike-Timing-Dependen Plas ici y
LTP Long-Te m Po en ia ion
LTD Long-Te m Dep ession
SNN Spiking Neu al Ne wo k
ANN A i icial Neu al Ne wo k
LIF Leaky In eg a e-and-Fi e
ISI In e Spike In e al
AEIF Adap a i e-Exponen ial In eg a e-and-Fi e
SNP Spiking Neu al P
CSS Cons an Spike Sou ce
ECG Elec oCa dioG am
CPU Cen al P ocessing Uni
ALU A i hme ic Logic Uni
CU Con ol Uni
FSM Fini e-S a e Machine
1
Pa I
Thesis
3
Chap e 1
In oduc ion
“The neu ochemis y o he b ain is as onishingly busy,
he ci cui y o a machine mo e wonde ul han any
de ised by humans.”
– Ca l Sagan
O e he pas cen u y, compu e s ha e e ol ed a an exponen ial a e,
d i ing unp eceden ed echnological ad ancemen s. These sys ems ha e become
inc easingly powe ul and e icien , enabling as amoun s o ma hema ical
calcula ions o be pe o med in e e -sho e imes, he eby accele a ing p og ess
ac oss all scien i ic ields. Howe e , ecen p edic ions sugges ha his apid
p og ess could slow down conside ably as echnology app oaches physical limi s
ha may seem impossible o o e come. Howe e , na u e o e s a solu ion ha
demons a es ha al e na i e pa adigms, such as hose seen in he b ain, he mos
sophis ica ed compu ing sys em, can be used o o e come hese challenges.
This chap e explains he p inciples o b ain unc ioning and i s inhe en
p ope ies, wha neu omo phic enginee ing is, and how hese enginee s ha e
designed new echnologies inspi ed by he b ain and he ne ous sys em o b ing
he powe and e iciency o he b ain o a i icial sys ems. Finally, an analogy
is d awn be ween he undamen als o digi al ci cui s and he unc ioning o
biological neu al ne wo ks in an a emp o imp o e he unde s anding o he
unc ions hey pe o m, as well as o acili a e he design o new bioinspi ed
sys ems by using a spiking compu ing app oach, which could bene i om he
inhe en p ope ies o he b ain and whose explo a ion is he main ocus o his
wo k, hus being he main con ibu ion o his hesis.
1.1 The b ain and he ne ous sys em
Human beings, cu ious by na u e, ha e ied h oughou his o y o sol e some
o he mos di icul ques ions ega ding hei own exis ence: Who a e we?
Wha a e we? Why a e we? These ques ions a e a sample o he e olu ion
o human hough and he p eceden s o mode n science. A chaeological and
4Chap e 1. In oduc ion
an h opological indings, such as ca e pain ings, symbolic igu es, and bu ial
p ac ices, indica e ha humans al eady asked hese kinds o ques ions ens o
housands o yea s ago in p ehis o ic imes. Wi h he ad en o ancien science,
g ea e emphasis was placed on inding answe s o hese ques ions. In ancien
G eece, Hippoc a es (c. 460-370 BC) i s pos ula ed ha he b ain was he main
cause o human hough and emo ions. Mo eo e , in he Roman Empi e, Galen (c.
129-200 AD) a gued ha he b ain con olled he body h ough ne es. Al hough
A is o le (c. 384-322 BC) asse ed ha hough and emo ions we e caused by
he hea , some hing ha p e ailed un il he Renaissance, he eme gence o he
scien i ic me hod in he 15 h and 16 h cen u ies allowed science o g ea ly e ol e,
gi ing us a be e unde s anding o he b ain and i s c ucial ole in biology. Today
we know ha Hippoc a es and Galen we e igh .
The b ain is a complex o gan ha se es as he cen e o he ne ous sys em.
I is esponsible o p ocessing senso y in o ma ion, egula ing bodily unc ions,
and acili a ing hough , memo y, and emo ion. S uc u ally, he b ain is di ided
in o h ee majo pa s: he ce eb um, he ce ebellum and he b ains em. The
ce eb um, he la ges pa , is in ol ed in highe b ain unc ions such as decision
making, p oblem sol ing, and planning. I is spli in o wo hemisphe es, each
o which can be di ided in o di e en sec ions which specialize in di e en
unc ions, as shown in Figu e 1.1. The ce ebellum con ols coo dina ion and
balance, while he b ains em egula es essen ial unc ions such as hea bea and
b ea hing.
Thanks o he Spanish scien is San iago Ramón y Cajal, who is conside ed
he a he o mode n neu oscience and ecei ed he Nobel P ize in Physiology o
Medicine in 1906, we know ha neu ons, o ne e cells, a e he basic building
blocks o he b ain and he ne ous sys em (Cajal, 1906). They a e in cha ge o
ecei ing and ansmi ing in o ma ion h ough elec ical and chemical signals o
acili a e communica ion wi hin he b ain and h oughou he ne ous sys em,
and, al hough he e a e many di e en ypes o neu ons, all o hem ha e a
common s uc u e ha consis s o h ee pa s: he dend i es, he soma and he
axon, as shown in Figu e 1.2.
In addi ion, he whole neu on is su ounded by a plasma memb ane ha
sepa a es i om he ex e nal en i onmen . A es , i.e., when a neu on has
no ecei ed any signals, his sepa a ion allows i s in e nal medium o be
app oxima ely 10 imes iche in po assium (K+) han he ex e nal medium, and
he ex e nal medium o be app oxima ely 10 imes iche in sodium (Na+) han
he in e nal medium. Calcium (Ca2+)and chlo ine (Cl−)a e also p esen in bo h
mediums, bu play a mino ole in he es ing s a e (S e ens, 1979). The cons an
exchange o hese chemicals h ough po es in he neu on memb ane, i.e., ion
channels, allows an ionic cha ge balance o be eached be ween bo h mediums,
p oducing a memb ane po en ial o app oxima ely -70 mV (Ge s ne e al., 2014),
known as he es ing po en ial.
1.1. The b ain and he ne ous sys em 5
FIGURE 1.1: B ain unc ions by lobe, ex ac ed om he Shi ley Ryan
Abili yLab, 2023
The soma, o cell body, con ains he nucleus and a ious o ganelles
ha main ain cellula unc ion and mee i s me abolic needs. The dend i es
a e ee-like ex ensions o he soma ha a e sensi i e o he appea ance o
neu o ansmi e s and a e a key elemen in he up u e o he es ing s a e.
These neu o ansmi e s bind o speci ic ecep o s loca ed in he dend i es,
causing an Exci a o y Pos -Synap ic Po en ial (EPSP, posi i e) o Inhibi o y
Pos -Synap ic Po en ial (IPSP, nega i e) pe b anch, depending on he ype o
neu o ansmi e and ecep o . Then, he dend i es pe o m he in eg a ion o
hese po en ials, summing all EPSPs and IPSPs a he beginning o he axon,
which is a long, slende p ojec ion o he neu on. I he esul ing sum causes
he memb ane po en ial o each a ce ain h eshold, abou -55 mV (Ge s ne
e al., 2014), an ac ion po en ial, commonly called a "spike", is gene a ed.
Reaching his h eshold po en ial causes ol age-ga ed sodium channels o
open, allowing a apid in lux o Na+ions in o he neu on, u he inc easing
he memb ane po en ial (depola iza ion) and opening adjacen ol age-ga ed
sodium channels along he axon. In his way, he axon conduc s he esul ing
elec ical impulses away om he cell body owa d o he neu ons o muscles
in he o m o a wa e. This p opaga ion ypically occu s in only one di ec ion
due o he inac i a ion o ol age-dependen sodium channels as a consequence
o memb ane depola iza ion (Bea e al., 2020), which p e en s backwa d
12 Chap e 1. In oduc ion
p oximi y o biology in exchange o a g ea e o lesse compu a ional cos ,
espec i ely, i is usually associa ed wi h an elec ical ci cui consis ing o a
esis o and a capaci o placed in pa allel, i.e., an RC ci cui (Abbo , 1999), which
is shown in Figu e 1.6. F om his ci cui , an equa ion can be de i ed ha desc ibes
how he memb ane po en ial o LIF neu ons changes o e ime, as is shown in
Equa ion 1.1 (Ge s ne e al., 2014), whe e:
•τmis he memb ane ime cons an .
•V( )is he memb ane po en ial a ime .
•V es is he es ing po en ial.
•Rmis he memb ane esis ance.
•I( )is he inpu cu en a ime .
In his equa ion, he inpu cu en , I( ), includes he cu en s gene a ed in
esponse o he in eg a ion o inpu spikes, which con ibu e o he changes in
he memb ane po en ial. In biological neu ons, an ac ion po en ial is gene a ed
once he memb ane po en ial eaches a h eshold po en ial (V h), ollowed by
he e ac o y pe iod. Howe e , his beha io is no ep esen ed in he basic RC
ci cui model, and he e o e an addi ional mechanism should be in oduced in
he ci cui o accoun o he h eshold c ossing and subsequen ese ing o he
memb ane po en ial o i s es ing alue. This leads o Equa ion 1.2, which mus
be conside ed in he simula ion o LIF neu ons.
FIGURE 1.6: Rep esen a ion o he LIF model as an RC ci cui , inspi ed by
Ge s ne e al., 2014
τmdV( )
d =−(V( )−V es ) + RmI( )(1.1)
V( ) = V es , i V( )≥V h (1.2)
1.2. Neu omo phic enginee ing and Spiking Neu al Ne wo ks 13
The e a e se e al possibili ies o he implemen a ion o SNNs, which can be
classi ied in o h ee ca ego ies: so wa e o simula ion, dedica ed ha dwa e o
simula ion, and dedica ed ha dwa e o emula ion. Popula simula ion so wa e
lib a ies include PyNN (Da ison e al., 2009), NEST (Gewal ig and Diesmann,
2007), B ian (Goodman and B e e, 2008), NEURON (Hines and Ca ne ale, 1997)
and Nengo (Bekolay e al., 2014). Fo dedica ed ha dwa e simula ion pla o ms,
SpiNNake (Fu be e al., 2014), Loihi (Da ies e al., 2018) and T ueNo h
(Akopyan e al., 2015), which a e ully digi al, and B ainScaleS (Pehle e al., 2022),
which is mixed-signal, a e among he mos widely used. These so wa e lib a ies
and ha dwa e pla o ms suppo he implemen a ion o a ious neu on models
and simula e SNNs by pe o ming ma hema ical compu a ions based on he
go e ning equa ions o hese models, al hough bo h ca ego ies di e in he way
in which esou ces a e employed o pe o m hese compu a ions. While so wa e
lib a ies ely on gene al-pu pose ha dwa e, dedica ed ha dwa e pla o ms a e
speci ically designed o op imize SNN simula ion, allowing o la ge ne wo ks
and imp o ed eal- ime pe o mance. Finally, emula ion pla o ms use he
physical p ope ies o elec onic componen s o di ec ly ep oduce he neu on’s
biophysics. The Dynap-SE chip (Mo adi e al., 2017), also conside ed mixed-
signal, is an example o such an emula ion pla o m. This wo k ocuses p ima ily
on PyNN, SpiNNake and Dynap-SE, which a e u he desc ibed below. NEST
and B ian ha e also been used occasionally o e i y he esul s o speci ic
expe imen s.
• PyNN (Da ison e al., 2009) is a Py hon package designed o p o ide a
s anda dized in e ace o build and simula e SNNs in di e en simula ion
en i onmen s. I aims o make i easie o neu oscien is s and enginee s
o de elop and sha e models by allowing hem o w i e code ha can be
un on mul iple backends, such as NEST, B ian, NEURON, SpiNNake and
B ainScaleS wi hou any modi ica ions. Thus, PyNN simpli ies he p ocess
o swi ching be ween simula o s, acili a ing he compa ison and alida ion
o models and esul s ac oss di e en pla o ms.
• SpiNNake (Fu be e al., 2014), de eloped by he Uni e si y o Manches e ,
is de ined as a massi ely pa allel mul ico e compu ing sys em ha was
designed o allow modeling e y la ge SNNs in eal ime and whose
in e connec ed a chi ec u e is inspi ed by he connec i i y cha ac e is ics o
he mammalian b ain. In his wo k, he SpiNN-3 and SpiNN-5 e sions
(Rowley e al., 2019) we e used, which consis o 4 chips and 48 chips,
espec i ely, each one made up o 18 ARM968E-S co es ope a ing a 200
MHz. Mo eo e , he SpiNN-5 e sion addi ionally has 3 FPGAs, allowing i
o be connec ed o 6 o he boa ds o make up a la ge SpiNNake machine.
Rega dless o he e sion, a 100 Mbps E he ne connec ion is used as an
I/O in e ace and o send sc ip s and commands o he SpiNNake boa ds.
While he SpiNN-3 boa d allows o as e simula ions o small SNNs, he
SpiNN-5 boa d has gene ally been used o simula e SNNs ha equi ed
14 Chap e 1. In oduc ion
mo e esou ces han hose a ailable on he SpiNN-3 boa d wi h a highe
compu a ional and ime cos .
SpiNNake ini ially suppo s i e PyNN neu on models, one o which is an
Izhike ich model and he o he a e di e en a ia ions o he LIF model,
al hough i also suppo s he implemen a ion o up o 13 ex a models
and he de ini ion o new cus om models by he use (Rhodes e al., 2018;
sPyNNake , 2015).
• Dynap-SE (Mo adi e al., 2017) is a neu omo phic pla o m o eal-
ime spike p ocessing de eloped by SynSense, a echnology company
om Swi ze land specializing in neu omo phic compu ing ha closely
collabo a es wi h he Uni e si y o Zü ich and ETH Zü ich. In his
wo k, a Dynap-SE1 boa d consis ing o 4 chips was used. Each chip can
accommoda e up o 256 DPI neu ons (Indi e i e al., 2011), which a e
equi alen o Adap a i e-Exponen ial In eg a e-and-Fi e (AEIF) neu ons
(Qiao e al., 2015; B e e and Ge s ne , 2005) con igu able o beha e like LIF
neu ons. I also suppo s ou di e en ypes o synapses, which a e o ally
inspi ed by he wo majo ypes o exci a o y synapses, AMPA and NMDA,
and he wo majo ypes o inhibi o y synapses in he ne ous sys em,
GABA A and GABA B (Ge s ne e al., 2014). The di e ences be ween
hese synapses in ol e no only hei exci a o y o inhibi o y na u e bu
also he speed a which hei ion channels open in esponse o speci ic
neu o ansmi e s. Fo ins ance, AMPA synapses ha e as ion channel
speed, while NMDA channels a e slowe . Simila ly, he ion channel speed
o GABA A is much highe han ha o GABA B. Figu e 1.7 shows how, in
biology, he pos synap ic cu en s would change a e a spike a i es a a
pos synap ic neu on depending on he ype o synapse.
FIGURE 1.7: Dynamics o pos synap ic cu en s ha appea a e a single
spike a i es a he pos synap ic neu on a = 0 depending on he ype o
synapse, ex ac ed om Ge s ne e al., 2014
1.3. Spiking Boolean compu a ion 15
1.3 Spiking Boolean compu a ion
The de ini ion o wha a compu e is may gi e ise o a long philosophical
discussion; le i be de ined as a machine ha can be p og ammed o
au oma ically ca y ou sequences o a i hme ic o logical ope a ions. Al hough
a la ge numbe o ins umen s designed h oughou ou his o y be o e he
20 h cen u y could be conside ed compu e s, i seems clea ha he e was a
u ning poin in i s e olu ion: he appea ance o he mechanical compu e ,
wi h Babbage’s analy ical engine in he ea ly 19 h cen u y (B omley, 1982).
Thus, compu e s we e p ima ily analog un il he ad en o ansis o s, i.e.,
semiconduc o de ices which we e pa icula ly e ec i e a swi ching elec ical
signals, in he mid-20 h cen u y (Rio dan, 2004). Sho ly be o e, Claude Shannon
had demons a ed ha i was possible o sys ema ically apply Boolean algeb a
o elec ical ci cui s (Boole, 1847; Shannon, 1938), which allowed o he design
o elec ical ci cui s whose beha io was de ined by complex u h unc ions
based on h ee basic elemen s such as OR (conjunc ion), AND (disjunc ion) and
NOT (nega ion). Shannon’s wo k and he ad en o ansis o s, in combina ion,
led o a g ea imp o emen in logic ga es, de ices used o pe o m Boolean
unc ions which we e al eady being used in analog compu e s. Figu e 1.8 shows
an example o a ansis o -based AND ga e buil using BJTs (Bipola Junc ion
T ansis o s). These imp o ed logic ga es led o he eme gence o he digi al
compu e , which was cha ac e ized by highe accu acy and lowe e o , size and
cos han he analog compu e s ha had p eceded i .
F om his poin , he e is no doub ha digi al compu e s ha e no only
b ough abou an unp eceden ed echnological e olu ion h oughou he 20 h
cen u y, bu also ha hei impac , no only echnological bu a all le els,
has g own exponen ially up o he p esen day. This is mainly hanks o he
signi ican inc ease in he compu a ional powe o digi al compu e s o e he
las 50 yea s, d i en by he exponen ial g ow h in he numbe o ansis o s
hey con ain, which ollowed he p edic ions o Moo e’s law (Moo e e al.,
2006). Howe e , despi e being called a "law", Moo e’s law may soon no longe
apply. This is la gely due o he challenges associa ed wi h he con inued
minia u iza ion o ansis o s in elec onics. Ad ances ha e pushed ansis o s
o nea -a omic scales, hus app oaching physical and he mal limi s, esul ing
in signi ican ly highe p oduc ion cos s (Shal , 2020). Howe e , he indus y
inc easingly needs mo e powe ul compu e s wi hou signi ican ly inc easing
hei powe consump ion. How could hese limi s hen be add essed?
Science is sea ching o new al e na i es o p e en he imminen s agna ion
in he e olu ion o digi al compu e s. Cu en ly, many o hem a e being
s udied and a e he ocus o g ea esea ch e o s by enginee s, such as
he h ee-dimensional in eg a ion o ansis o s, he sea ch o new ma e ials
ha can eplace silicon and p o ide new ad an ages in he manu ac u e o
hese ansis o s, o e en he eplacemen o he ansis o s hemsel es as
16 Chap e 1. In oduc ion
FIGURE 1.8: Gene al design o an AND ga e using BJTs
he basic elemen o compu ing, as occu s in quan um compu ing o op ical
compu ing, whe e in o ma ion p ocessing is ca ied ou by qubi s and pho ons,
espec i ely. One o he mos p omising ields in his ega d is neu omo phic
enginee ing, in oduced in Sec ion 1.2, which has seen how doub s abou he
powe consump ion o digi al compu e s could disappea conside ing he main
elemen o s udy in his ield: he b ain. I only needs abou 20 wa s o ope a e
(Balasub amanian, 2021), which is much less han he powe consump ion o
oday’s compu e s, i.e., ypically be ween 30 and 500 wa s; howe e , he b ain
is clea ly mo e powe ul han any o hem when na iga ing complex p oblems
ha equi e high le els o cogni ion. On he o he hand, while he human b ain
con ains app oxima ely 86 billion neu ons (He culano-Houzel, 2009; Aze edo
e al., 2009), he numbe o ansis o s in a CPU is gene ally less han 100
billion, acco ding o Lunds om and Alam, 2022. The e o e, he numbe o basic
compu ing elemen s is simila in bo h sys ems, so... whe e does e iciency come
om?
Ca e Mead s a ed ha he main ac o ha makes he b ain much mo e
e icien han digi al compu e s is he pa allelism inhe en o he ne ous
sys em, he essence o which lies in he la ge numbe o synapses ha can
be ound in i (Mead, 1990). Taking his as inspi a ion, i can be deduced
ha a g ea inc ease in he deg ee o pa allelism o digi al sys ems could
be ano he g ea solu ion o he sea ch o educing he powe consump ion
o he ansis o s con ained in hem, which, in ac , would make i possible
o educe ope a ing ol ages and equencies wi hou losing compu a ional
powe (Kim e al., 2003). In hese sys ems, pa allelism is o en signi ican ly
imp o ed by di ec ly eplica ing ha dwa e esou ces. Fo example, in mul ico e
p ocesso s, mul iple iden ical co es a e in eg a ed in o a single chip, each
1.3. Spiking Boolean compu a ion 17
capable o execu ing ins uc ions independen ly. Simila ly, in mul ip ocesso
sys ems, en i e p ocesso s a e duplica ed, enabling mul iple p ocesso s o wo k
in pa allel. This eplica ion inc eases he numbe o elemen s ha can be used
o execu e ins uc ions simul aneously, hus imp o ing he sys em’s o e all
pa allel p ocessing capabili y. Howe e , his di e s om he ne ous sys em,
whe e i s high connec i i y allows neu ons o pa icipa e in mul iple ope a ions
simul aneously. Thus, neu ons a e no simply eplica ed, bu a e eused o engage
in di e en unc ions a he same ime. I would be simila o eusing exis ing
logic ga es in digi al sys ems o build many di e en complex ci cui s ins ead o
eplica ing hem, which would be challenging, since ansis o s a e limi ed by
hei an-in and an-ou capabili ies, i.e., he maximum numbe o inpu s and
ou pu s hey can handle, espec i ely. Neu ons, howe e , a e no so limi ed,
so... Wha i a pa adigm shi was applied o inc ease he pa allelism o cu en
sys ems?
Ideally, his pa adigm shi would in ol e ede ining he undamen als o
compu ing by ansi ioning om ansis o s and logic ga es o biological neu al
ne wo ks buil o pe o m speci ic unc ions. Thus, implemen ing hese changes
would p esen wo majo challenges. Fi s , i would be necessa y o ind a
way o main ain he op imal unc ioning o neu ons ha could easily die in
inapp op ia e en i onmen s. Second, he e a e s ill many unknowns ega ding
he a chi ec u es o he neu al ne wo ks ound in he ne ous sys em and he
speci ic unc ions hey pe o m. One possible solu ion o he la e p oblem
would be no o elimina e he logic ga es, bu only o eplace he ansis o s
ha o m hem wi h neu ons. This would equi e a high-le el abs ac ion o
he unc ioning o neu ons, such ha he memb ane po en ial would no be
aken in o accoun , bu only whe he o no hey gene a e spikes. Thus, he
in o ma ion would be summa ized in he exis ence o absence o spikes ha
would p opaga e, o no , o each o he pos synap ic neu ons. This abs ac ion
would make i easible o implemen Boolean logic using neu ons, so ha any
digi al componen wi h a speci ic u h unc ion could also be implemen ed using
his new pa adigm. Taking ad an age o he an-in and an-ou capabili ies o
neu ons, hese new a chi ec u es could g ea ly op imize he numbe o esou ces
used o pe o m many di e en ope a ions, hus bene i ing om imp o ed
pa allelism. In his way, each neu on would p o ide he esul o a Boolean
ope a ion ha could be o wa ded o ano he neu on, he eby pe o ming
complex Boolean unc ions.
This wo k ocuses on he implemen a ion o hese new spiking Boolean
a chi ec u es, which a e based on SNNs o achie e close p oximi y o he
unc ioning o he ne ous sys em. The mos basic logic ga es (OR, AND and
NOT), which o m he base o Boolean algeb a, will be p esen ed i s . Following
Boolean algeb a, he combina ion o hese basic spiking logic ga es makes i
possible o build blocks ha pe o m any complex Boolean unc ion. Some o
hese complex blocks will also be p esen ed in he ollowing sec ions. Al hough
18 Chap e 1. In oduc ion
he implemen a ion o spiking logic ga es has al eady been s udied in o he
wo ks, he app oach applied in each o hem di e s om he app oach o his
wo k. Fo example, in Song e al., 2016, he implemen a ion o spiking logic ga es
based on Spiking Neu al P (SNP) sys ems is ca ied ou . Howe e , he ules hese
sys ems apply o compu e a e usually a om he complex equa ions used in he
neu on models p esen ed in Sec ion 1.1, and hus hey a e no ha close o biology
as SNNs. In o he wo ks, SNNs we e employed o implemen spiking logic
ga es bu using di e en me hods. In Reljan-Delaney and Wall, 2017, he AND
and XOR ga es we e implemen ed by assigning speci ic i ing a es o Boolean
alues one and ze o and building a ully connec ed SNN wi h synapses ha had
o be ine- uned o pe o m Boolean ope a ions. This ne wo k did no always
ope a e co ec ly, as in he case o he AND ga e. Mo eo e , since i ing a es
a e used, combining hese blocks o pe o m complex Boolean unc ions could
be challenging. The ou pu i ing a es should be p ecisely adjus ed o ma ch he
expec ed inpu a es o he subsequen blocks o ensu e he co ec ep esen a ion
o ones and ze os. Fu he mo e, ine- uning he weigh s o he synapses in he
SNNs o achie e he desi ed beha io s in oduces unce ain y and makes i mo e
di icul o unde s and he ne wo k’s unc ioning. Finally, in Mo and Wang, 2021,
he STDP lea ning mechanism was used o implemen a ully connec ed SNN ha
was ained once pe speci ic logical ope a ion and which was aken as a building
block ha could be combined o pe o m mo e complex unc ionali ies. Howe e ,
he numbe o neu ons and he numbe o synapses equi ed o implemen his
building block a e la ge, which could pose a p oblem in e ms o scalabili y, since
hese a e e y limi ed in neu omo phic so wa e and ha dwa e.
In conclusion, he app oach chosen o he de elopmen o hese ne wo ks
aims o acili a e he spiking implemen a ion o Boolean logic, especially in e ms
o de e minism and scalabili y, and also o help neu omo phic enginee s lay
a knowledge base o acili a e he unde s anding o how o op imally build
unc ion-speci ic SNNs. The de elopmen o his doc o al hesis is amed
wi hin he Robo ics and Compu e Technology esea ch g oup (RTC), o which
I belong, and which has been and is s ongly linked o he ield o neu omo phic
enginee ing hanks o i s g ea scien i ic p oduc ion, which includes a g ea
amoun o a icles published in high impac ac o jou nals, he de elopmen o
o he doc o al heses, na ional and in e na ional collabo a ions, and a se ies o
esea ch p ojec s ha ha e se ed o inance he esea ch ac i i y ha has enabled
he de elopmen o his doc o al hesis, such as:
• MINDROB: Pe cepción y cognición neu omó ica pa a ac uación obó ica
de al a elocidad (PID2019-105556GB-C33).
• SANEVEC: Un en oque basado en simulación pa a de e mina el
despliegue de una ed u bana de es aciones de eca ga de ehículos
eléc icos con bene icios medioambien ales y sociales (TED2021-130825B-
I00).
1.3. Spiking Boolean compu a ion 19
which ha e no only paid o he publica ion cos s o he published a icles,
bu also o he esea ch isi s wi hou which i would no ha e been possible o
achie e he esul s ob ained.
21
Chap e 2
Objec i es
This doc o al hesis is mainly ocused on he design and implemen a ion o SNNs
ha a e capable o pe o ming Boolean unc ions, s a ing wi h he spiking logic
ga es and, subsequen ly, implemen ing mo e complex spiking blocks ha a e
analogous o se e al digi al componen s by combining p e ious designs. In o de
o achie e his main objec i e, a se ies o asks had o be ca ied ou , which a e
de ailed below:
1. P e ious s udy o he elemen s in ol ed in he de elopmen o he wo k
(a) S udy o he biological mechanisms and beha io s exis ing in he
ne ous sys em based on neu oscien i ic knowledge.
(b) Explo a ion and compa ison o he di e en exis ing pa adigms o he
de elopmen o bioinspi ed sys ems.
(c) S udy o Spiking Neu al Ne wo ks and he di e en neu on models
ha can be used o hei implemen a ions.
(d) Explo a ion and compa ison o neu omo phic so wa e and ha dwa e
o he design and implemen a ion o Spiking Neu al Ne wo ks.
2. Design and implemen a ion o blocks capable o pe o ming Boolean
unc ions based on Spiking Neu al Ne wo ks.
(a) Design o each o he blocks using ee so wa e ools, jus i ying each
o he esou ces used.
(b) Op imiza ion o each o he designs, educing he numbe o esou ces
needed o hei implemen a ion.
(c) Implemen a ion o he blocks on SpiNNake , es ing hei unc ioning
in cons ained en i onmen s and unde ideal condi ions.
(d) Implemen a ion o he blocks on Dynap-SE, hus es ing hei
unc ioning in condi ions close o hose ound in he ne ous sys em.
(e) Analysis o esul s and e i ica ion o expec ed beha io s.
28 Chap e 3. Summa y o esul s
FIGURE 3.1: a) Design o a 3-inpu OR ga e implemen ed on SpiNNake .
b) Design o he OR ga e modi ied o i s implemen a ion on Dynap-SE.
The yellow neu on is used o add a delay in he p opaga ion o he spikes,
he ed neu on is he NOR neu on, and he g een neu ons a e he ou pu
neu ons.
p ecisely con igu e he synap ic weigh s and delays on SpiNNake o achie e his
beha io . In his way, i consis ed o only wo neu ons, whe e he i s neu on was
an OR ga e ha would i e whene e an inpu spike was ecei ed, gene a ing
an inhibi ion o weigh n−1 on he second neu on, whe e nis he numbe o
inpu synapses. These synapses also eached he ou pu neu on, bu wi h an
added delay o allow he inpu spikes o a i e a he same ime as he inhibi ion
gene a ed by he OR ga e. Thus, i would only i e i he exci a ion was g ea e
han he inhibi ion, i.e., only i nspikes we e ecei ed.
Finally, he NOT ga e consis s o a single neu on ha mus be inhibi ed when
he inpu o be nega ed ansmi s a spike, o which an inhibi o y synapse is used,
hus p e en ing he neu on om i ing. Howe e , he opposi e case implies he
gene a ion o an ou pu spike when no inpu spike is ecei ed, which gi es ise o
one o he bigges p oblems ound in he design o spiking blocks. Does i make
sense o gene a e spikes wi hou hem being ecei ed in any way? Whe e does
his ene gy come om? O iginally, o sol e his p oblem, a block called "Cons an
Spike Sou ce" (CSS) was designed, which was in cha ge o gene a ing a spike in
each simula ion ime s ep in SpiNNake . This was achie ed by ini ially injec ing
a spike using a spike gene a o in o a neu on ha was connec ed o ano he
ecu en ly so ha each caused he o he o i e. The e is biological e idence o
he p esence and unc ionali y o hese ecu en neu al ne wo ks in he human
b ain, which unde lie memo y o ma ion (Casanue a-Mo a o e al., 2022), as hey
3.2. Spiking implemen a ion o OR, AND and NOT ga es 29
FIGURE 3.2: a) Design o a 3-inpu AND ga e implemen ed on SpiNNake .
b) Design o he AND ga e modi ied o i s implemen a ion on Dynap-SE.
The blue neu on is he OR ga e, he yellow neu on is used o add a delay
in he p opaga ion o he spikes, he ed neu ons a e he NOT neu ons, and
he g een neu ons a e he ou pu neu ons.
allow ene gy o be e ained cyclically in he o m o spikes. The design o he CSS
block is p esen ed in Figu e 3.3, which also shows he usual way i was connec ed
o a NOT ga e o ob ain he desi ed beha io . This block was also exploi ed o
c ea e a new design o he AND ga e, which ope a ed as e .
These designs we e implemen ed and es ed on SpiNNake . Al hough
only a limi ed numbe o expe imen s we e conduc ed, his is jus i ied by he
expec a ion ha iden ical esul s would be ob ained unde iden ical condi ions,
since all he expe imen s we e based on a s ic simula ion o he equa ions
men ioned in Sec ion 3.1. The co ec ope a ion o hese blocks on he pla o m
was success ully e i ied. Figu e 3.4 p esen s an ex ac o a ace o an
expe imen ca ied ou on he implemen a ion o a 4-inpu AND ga e. I shows
how inpu spikes ansmi ed h ough synapses A,B,C, and Dcaused he OR
ga e o i e one ime s ep la e due o he p opaga ion delay. Whene e spikes
we e ansmi ed simul aneously h ough all inpu synapses, he AND ga e i ed
a e wo ime s eps. Simila ly, Figu e 3.5 p esen s an ex ac o a ace o an
expe imen ca ied ou on he implemen a ion o a NOT ga e connec ed o a CSS
block. In his igu e, i can be seen how bo h he CSS block and he NOT ga e i ed
a each ime s ep o he simula ion un il inpu spikes we e ansmi ed h ough
he inpu synapse A. When his occu ed, he NOT ga e was p e en ed om
i ing in he subsequen ime s ep due o he inhibi ion applied o he ou pu
neu on.
30 Chap e 3. Summa y o esul s
FIGURE 3.3: Design o a NOT ga e, p o ided wi h inpu spikes by means
o a CSS block o ope a e, whose neu ons a e ep esen ed in yellow. The
neu on wi h he SG label is a spike gene a o which only i es once. The
g een neu on is he ou pu neu on, i.e., he NOT ga e.
These aces we e gene a ed using some unc ions de ined in "sPyBlocks",
which is a Py hon package ha was de eloped o make i easie o esea che s o
wo k wi h he implemen ed spiking logic ga es and can cu en ly be ound in he
i s o he public eposi o ies men ioned abo e. This package de ines a cus om
Py hon class o each block, using PyNN unc ions o implemen he design on
objec ini ializa ion. These classes include connec ion unc ions ha elie e he
use om wo king a he neu on le el when in e connec ing blocks, and which
a e also used o building mo e complex blocks. Thus, mo e complex classes we e
c ea ed by combining he simples spiking logic ga es.
Al hough he implemen a ions beha ed as expec ed on SpiNNake , hese
spiking blocks did no wo k well a all when implemen ed on Dynap-SE, as
some limi a ions ha migh occu in a mo e ealis ic en i onmen had no been
conside ed. Fi s , i was obse ed ha , when neu ons ecei ed mo e han
one spike a he same ime om mul iple exci a o y synapses, hey s opped
i ing, which could ind i s biological coun e pa in neu onal dea h due o
o e exci a ion (Dodd, 2002). In o he cases, he implemen a ions pe o med
as expec ed. Then i was decided o look o a way o a oid he use o
mul iple exci a o y synapses o p e en o e exci a ion. In his way, new designs
we e de eloped ha we e no based p ima ily on exci a o y synapses, bu on
inhibi o y synapses, o which De Mo gan’s laws we e used o each Equa ion 3.1
and Equa ion 3.2. In hese equa ions, he nega ion o each o he logic alues
in ol ed can be achie ed by using NOT ga es.
3.2. Spiking implemen a ion o OR, AND and NOT ga es 31
FIGURE 3.4: Ex ac o a ace o an expe imen conduc ed on a 4-inpu
AND ga e on SpiNNake . A "1" indica es ha a spike is ansmi ed o
i ed. Spikes om he inpu exci a o y synapses a e shown in blue, hose
om he OR ga e, which inhibi he ou pu neu on, a e ep esen ed in ed,
and spikes om he ou pu neu on a e shown in g een.
FIGURE 3.5: Ex ac o a ace o an expe imen conduc ed on a NOT ga e
on SpiNNake . A "1" indica es ha a spike is ansmi ed o i ed. Spikes
om he inpu inhibi o y synapse a e shown in ed, hose om he CSS
block a e ep esen ed in blue, and spikes om he ou pu neu on a e shown
in g een.
A+B+C=A+B+C=A·B·C(3.1)
A·B·C=A·B·C=A+B+C(3.2)
A e ha , ano he obse a ion was made. By connec ing a pos synap ic
neu on o mul iple p esynap ic neu ons ia inhibi o y synapses and o ano he
p esynap ic neu on ia an exci a o y synapse, he pos synap ic neu on i ed only
when no spikes we e ansmi ed h ough he inhibi o y synapses and he e was
ac i i y h ough he exci a o y synapse. This beha io is equi alen o he NOR
ope a ion, whose u h able is included in Table 3.4. This inding was one o
he key poin s o he p og ess made while using Dynap-SE, as i imp o ed he
obus ness and bioplausibili y o he implemen a ions. Mo eo e , NOR ga es a e
an essen ial al e na i e o OR, AND and NOT ga es in Boolean logic. Since hey
could be implemen ed using only one neu on, his also highligh ed a clea e pa h
o esou ce op imiza ion.
Finally, a gene al modi ica ion was also in oduced in which he CSS block
was elimina ed, ollowing a sugges ion ecei ed in one o he e iew p ocesses
32 Chap e 3. Summa y o esul s
o he cu en ly published pape s. F om his poin on, he spiking blocks no
longe ope a ed disc e ely a a ixed equency as occu ed on SpiNNake , bu
only when expec ed o do so, which was consis en wi h he asynch onous na u e
o SNNs. This di ec ly a ec ed NOT ga es, which we e he main eason why
his CSS block was ini ially implemen ed. Thus, NOT ga es equi ed a new
sou ce o e en s ha indica ed when o ope a e, o which di e en possibili ies
would a ise depending on each design and he condi ions unde which hey had
o ope a e. This will be e lec ed especially la e on, when he cons uc ion o
complex spiking blocks is discussed in mo e de ail.
Taking in o accoun Equa ion 3.1, Equa ion 3.2 and he la e conside a ions,
inhibi ion-based designs we e de eloped o he OR and AND ga es. These
new designs, which a e shown on he igh (b) o Figu e 3.1 and Figu e 3.2,
espec i ely, also in oduced he concep o using addi ional neu ons o gene a e
delays in spike p opaga ion, which is o en used in he design o SNNs. This
app oach was used o con ol he iming o he spikes and o achie e he desi ed
beha io o each o he blocks wi hou elying on he delays o he synapses
on Dynap-SE, which, as was p e iously men ioned, a e nei he adjus able no
ixed. The implemen a ions o hese designs we e igo ously es ed h ough
an ex ensi e se ies o expe imen s o e i y he co ec beha io o bo h ga es
by a ying he numbe o inpu s and he ope a ing equency. These mainly
examined inhibi ion-based OR and AND ga es wi h 2, 3, 5, 10, 15, 20, 25, 30,
40, 50, and 60 inpu s, while ope a ing a maximum equencies o 0.5, 1, 2,
5, and 10 kHz on Dynap-SE, al hough some es s we e p e iously ca ied ou
on SpiNNake . Since such expe imen s on Dynap-SE depended on ex e nal
condi ions, unlike SpiNNake , all o hese expe imen s we e epea ed h ee imes
o ensu e ha consis en conclusions could be d awn. Figu e 3.6 shows he esul s
o an expe imen ca ied ou wi h a 5-inpu OR ga e, and Figu e 3.7 shows he
esul s o an expe imen ca ied ou wi h a 3-inpu AND ga e, bo h ope a ing a
a maximum equency o 5 KHz.
FIGURE 3.6: Tes o a 5-inpu inhibi ion-based OR ga e ope a ing a a
maximum equency o 5 KHz on Dynap-SE. δ e e s o he delay added
by neu ons and synapses while p opaga ing spikes in he ou pu pa h.
3.2. Spiking implemen a ion o OR, AND and NOT ga es 33
FIGURE 3.7: Tes o a 3-inpu inhibi ion-based AND ga e ope a ing a a
maximum equency o 5KHz on Dynap-SE. δ e e s o he delay added by
neu ons and synapses while p opaga ing spikes in he ou pu pa h.
TABLE 3.5: Resul s o he expe imen s ca ied ou on he inhibi ion-
based OR ga e o di e en numbe s o inpu s (n) and di e en ope a ing
equencies ( ) on Dynap-SE. The icks indica e ha he expec ed beha io
is ob ained in any epe i ion, while he c osses indica e ha he SNN is no
able o ope a e co ec ly.
(KHz) / n 2 3 5 10 15 20 25 30 40 50 60
0.5 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
1✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
2✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
5✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
10 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗
The esul s o all he expe imen s a e summa ized in Table 3.5 and Table 3.6.
In he case o he expe imen s pe o med wi h he inhibi ion-based OR ga e,
hei esul s demons a ed i s p ope unc ioning, excep while ope a ing a a
equency o 10 KHz. This was simila o he inhibi ion-based AND ga e, in
which one o he expe imen s pe o med wi h 3 inpu s also ailed while ope a ing
a 5 KHz. I was concluded ha his was mos likely due o he ac ha , because
he ope a ing equency was qui e high, he spikes a i ed when he neu ons
we e in he e ac o y pe iod, which p e en ed he Boolean beha io o he block.
Fu he mo e, he expe imen s indica ed how inhibi ion-based AND ga es wi h
40, 50 and 60 inpu s we e no able o ope a e co ec ly, e en when ope a ing a
equencies ha we e no conside ed high, which was due o limi a ions in he
use o spike gene a o s on Dynap-SE.
Once he implemen a ions we e pe o med and es ed, an analysis o he
esou ces used and he la encies ob ained o each o hem was ca ied ou ,
which is shown in Table 3.7. In his analysis, wo key conside a ions mus be
discussed. Fi s , i is assumed ha only one synapse is used o p o ide he spikes
ha indica e o NOT and inhibi ion-based OR and AND ga es when o ope a e.
Howe e , mul iple synapses could be employed o his pu pose depending
on he neu al ne wo k’s design equi emen s, hus inc easing he numbe o
34 Chap e 3. Summa y o esul s
TABLE 3.6: Resul s o he expe imen s ca ied ou on he inhibi ion-based
AND ga e o di e en numbe s o inpu s (n) and di e en ope a ing
equencies ( ) on Dynap-SE. The icks indica e ha he expec ed beha io
is ob ained in any epe i ion, while he c osses indica e ha he SNN is no
able o ope a e co ec ly.
(KHz) / n 2 3 5 10 15 20 25 30 40 50 60
0.5 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✗ ✗ ✗
1✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✗ ✗ ✗
2✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✗ ✗ ✗
5✓ ✗ ✓ ✓ ✓ ✓ ✓ ✓ ✗ ✗ ✗
10 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗
TABLE 3.7: Analysis o he esou ces used and he la ency o each o he
spiking logic ga es. n e e s o he numbe o inpu s and τ o he ime i
akes o a spike o p opaga e h ough he union o a synapse and a neu on.
Block Neu ons Synapses La ency
OR 1 nτ
AND 2 2n+1 2τ
NOT 1 2 τ
Inh.-based OR 3 n+4 2τ
Inh.-based AND n+2 3n+2 2τ
esou ces used. Second, he alues shown in his able apply i no op imiza ions
a e conside ed. Howe e , some blocks, pa icula ly he inhibi ion-based OR and
AND ga es, a e highly op imizable. Fo example, eusing he delay neu ons
in bo h cases, o he NOT ga es wi hin he inhibi ion-based AND ga e, could
signi ican ly educe he numbe o neu ons and synapses used.
A de ailed discussion o powe consump ion is now equi ed. Fi s ,
i is impo an o highligh exis ing d awbacks when measu ing he powe
consump ion o simula ed SNNs, whe he on gene al-pu pose sys ems o
speci ic-pu pose pla o ms, such as SpiNNake . Powe consump ion in hese
cases should be de e mined no only aking in o accoun he compu a ions
pe o med o each simula ion, bu also he s a ic powe consump ion o
he sys em on which his simula ion is unning and he powe consump ion
associa ed wi h o he ac i i ies. In his way, using a di e en sys em could
esul in a di e en measu e o powe consump ion, which makes i an un eliable
me ic when compa ing simula ed SNNs wi h o he echnologies. Howe e , he
implemen a ions on Dynap-SE a e physical and i makes mo e sense o measu e
hei powe consump ion, since i does no depend on o he ac i i ies. In Risi,
2022, Equa ion 3.3 is p o ided o measu e he dynamic powe consump ion o
SNNs implemen ed on Dynap-SE, whe e nis he i ing a e o he neu on n,
Nco es coun s he numbe o a ge co es and Ncam−ma ch is he o al numbe o
3.2. Spiking implemen a ion o OR, AND and NOT ga es 35
TABLE 3.8: Abb e ia ion, desc ip ion and alue o each o he ene gy
a iables.
Abb . Desc ip ion Value (pJ)
Espike Ene gy o gene a e one spike 883
Een Ene gy o encode one spike and append des ina ion 883
Eb Ene gy o b oadcas e en s o he same co e 6840
E Ene gy o ou e e en s o a di e en co e 360
Epulse Ene gy o he pulse ex ende ci cui 324
neu ons ha ecei e he spikes. The desc ip ions and alues o each o he ene gy
a iables ha appea in he equa ion we e p esen ed in Mo adi e al., 2017, and
a e shown in Table 3.8. Since in ou case Nco es =1, i would p obably no
make sense o conside E , al hough i was conside ed no o modi y he o iginal
equa ion, which would equi e a be e unde s anding o he ci cui s in ol ed.
This equa ion does no include he s a ic powe consump ion o he pla o m, bu
i can be use ul o p o ide an analysis o he powe consump ion o he inhibi ion-
based OR and AND ga es.
Pdyn =
N
∑
n=1
n(Espike +Een +Nco es(Eb +E ) + Ncam−ma chEpulse)(3.3)
In he inhibi ion-based OR ga e p esen ed in Figu e 3.1, a mos h ee
neu ons a e in ol ed wi hou op imiza ions. Le nou be om now on he numbe
o synapses ex ending om an ou pu neu on o o he neu ons ou side he block,
he delay neu on be neu on 1, he NOR ga e be neu on 2 and he NOT ga e be
neu on 3. Conside ing he wo s case a he ene gy le el, which is he case in
which he NOR ga e ecei es one spike h ough each inpu synapse, and also
conside ing ha each o he neu ons o he block which a e no inhibi ed i es a
he same equency ( )as a esul o he pa ame e s used, he applica ion o he
equa ions would be as ollows:
•P1= ·(883 +883 +1·(6840 +360) + 1·324)·10−12 W= ·9.290 pW
•P2=0. This neu on does no i e, since i is inhibi ed.
•P3= ·(883 +883 +1·(6840 +360) + nou ·324)·10−12 W= ·(8.966 +
nou ·0.324)pW
In his way, Pdyn =∑3
n=1Pn= ·(18.256 +nou ·0.324)pW. Conside ing
ha he ou pu neu on is only connec ed o ano he neu on and ha i ope a es
a a equency o 1 KHz, he o al dynamic powe consump ion would be 18.580
µW. Fo he case in which no inpu spikes a e p o ided o neu on 2, he powe
consump ion o his ga e would also be he la e , since he ou pu neu on would
36 Chap e 3. Summa y o esul s
no i e bu neu ons 1 and 2 would. No e ha , in his equa ion, he powe
consump ion o he spike gene a o s is no conside ed.
In he inhibi ion-based AND ga e p esen ed in Figu e 3.2, a mos i e
neu ons a e in ol ed wi hou op imiza ions. Le he delay neu on be neu on 1,
he NOT ga es be neu ons 2, 3 and 4 and he NOR ga e be neu on 5. In his case,
he wo s case a he ene gy le el would be he case in which no inpu spikes
a e p o ided o he NOT ga es, and he applica ion o he equa ions would be as
ollows:
•P1=P2=P3=P4= ·(883 +883 +1·(6840 +360) + 1·324)·10−12 W
= ·9.290 pW
•P5=0. This neu on does no i e, since i is inhibi ed.
The e o e, Pdyn =∑5
n=1Pn= ·37.160 pW, which ansla es in o a o al
dynamic powe consump ion o 37.160 µW o he inhibi ion-based AND ga e
ope a ing a 1 KHz. I is impo an o no e ha all scena ios in his ga e can be
gene alized in o wo main cases: 1) a ying he numbe o inhibi ed NOT ga es
wi hou inhibi ing all o hem, and 2) inhibi ing all NOT ga es. In he i s case,
he o al dynamic powe consump ion would be ·(nNOT +1)·9.290 pW, whe e
nNOT is he numbe o NOT ga es ha i e. In he second case, he o al dynamic
powe consump ion would be ·(18.256 +nou ·0.324)pW. The la e scena io is
simila o he one desc ibed o he inhibi ion-based OR ga e.
In Chap e 1, i was men ioned ha some wo ks in he s a e o he a
had al eady implemen ed spiking logic ga es using di e en app oaches. In
Song e al., 2016, SN P sys ems we e used o his pu pose. These sys ems
a e pu ely heo e ical compu a ional models and no physically implemen able,
since, unlike LIF neu ons, o example, which can be ep esen ed by elec ical
ci cui s o physical implemen a ion, hey lack a clea physical implemen a ion
and he e o e can only be simula ed. This is p obably why no men ions ha e
been ound in e ms o powe consump ion. In e ms o la ency, he de eloped
SN P sys ems equi e a simila numbe o ime s eps o hese designs, excep
o he OR ga e, o which hei design equi es one mo e ime s ep han ha
o he inhibi ion-based OR ga e. Howe e , hei compu a ions would p obably
be much as e due o he simplici y o he ules in ol ed, wi h smalle ime
s eps. SN P sys ems would also be be e in e ms o scalabili y, since he
compu a ions pe o med on hese ules a e simple han hose equi ed o sol e
di e en ial equa ions, and hus i would be possible o simula e a la ge numbe
o elemen s. Ne e heless, i mus be aken in o accoun ha he main eason why
neu omo phic enginee s use SNNs is hei bioplausibili y, an aspec in which hey
clea ly ou pe o m SN P sys ems.
In Reljan-Delaney and Wall, 2017, he implemen a ion o AND ga es
based on i ing a es using SNNs is pe o med on Ma Lab. Howe e , his
implemen a ion was no o ally de e minis ic, and he e o e i could ha dly be
3.3. Applica ions 37
used o he cons uc ion o complex Boolean blocks, as any sys em dependen
on a non-de e minis ic componen would beha e chao ically. In ac , he au ho s
admi ed ha hei AND ga e was no p ope ly ope a ing in all cases.
In Mo and Wang, 2021, unc ional OR and AND ga es we e implemen ed
using a ained ully-connec ed SNN. Rega ding la ency, each ime one o hese
blocks is placed in se ies, i akes wo addi ional ime s eps (2τ) o compu e he
esul s. In con as , Table 3.7 includes some blocks wi h a la ency o τ. Mo eo e ,
a ious op imiza ions could be applied o hese designs while implemen ing
complex blocks o educe no only he numbe o esou ces used bu also he
la ency o he esul ing blocks, an app oach ha does no appea o be easible
wi h hese ained blocks. In e ms o scalabili y, hey also equi e mo e neu ons
han any o he designs lis ed in Table 3.7. As a esul , any complex design c ea ed
by combining hem would equi e a la ge numbe o esou ces han any complex
design buil om he combina ion o he designs p esen ed in his sec ion.
3.3 Applica ions
Once he spiking OR, AND, and NOT ga es we e implemen ed, hei
combina ion allowed implemen ing spiking blocks ha pe o m any complex
Boolean unc ion, i.e., i was possible o implemen any spiking combina ional
logic, enabling an in ini e ange o applica ions o hese logic ga es and making
i c ucial o de e mine which o hem could mos signi ican ly ad ance scien i ic
knowledge. In his doc o al hesis, h ee di e en applica ions a e p oposed ha
could ep esen h ee di e en scien i ic ields. These a e he ollowing:
• Design and implemen a ion o he main componen s o he spiking
compu e (Neu omo phic compu ing and elec onics).
• Fil e ing QRS complexes in elec oca diog ams using a spiking coun e
(Biomedical enginee ing).
• De elopmen o an obs acle de ec ion sys em based on SNNs (Au onomous
obo ics).
This sec ion discusses he p og ess made in he de elopmen o he i s wo
applica ions, he esul s o which a e cu en ly published. The p og ess made on
he las o he h ee applica ions is discussed in Sec ion 3.4.3.
3.3.1 Main componen s o he spiking compu e
Digi al compu e s a e complex sys ems capable o pe o ming compu a ions and
a e composed o bo h so wa e and ha dwa e elemen s. A he ha dwa e le el,
he e a e wo main ypes o digi al elemen s: hose ha execu e ope a ions and
hose ha s o e in o ma ion. The g ea es exponen o he o me is he p ocesso ,
o Cen al P ocessing Uni (CPU), while he g ea es exponen o he la e is he
44 Chap e 3. Summa y o esul s
may seem he mos logical, bu i also u ned ou o be a much mo e expensi e OR
ga e in e ms o esou ces. This al e na i e OR ga e was designed by assigning
a sepa a e neu on o each inpu ha needed o be in eg a ed, wi h each inpu
synapse connec ing o a di e en neu on. To ensu e ha only one neu on could
i e a a ime, some simple ules we e in oduced o make hem i e wi h p io i y.
Le nbe he numbe o inpu s o he decode , ibe he index o an inpu neu on,
and OPibe he inpu synapse associa ed wi h neu on i. Ini ially, se i=n−1.
These ules a e he ollowing:
• I OPi ansmi s a spike, neu on i i es, and all neu ons jwi h 0 ≤j<ia e
inhibi ed.
• O he wise, dec emen iby 1 and epea he p ocess o he nex neu on un il
i=0.
These p io i y ules allowed hese neu ons o be connec ed o an ou pu
spiking block wi hou causing o e exci a ion. Howe e , i was also obse ed ha
he numbe o esou ces used was nneu ons and (n2+n)/2 synapses. Mos o
hese synapses a e inhibi o y o high alues o n. This esul s in an exponen ial
inc ease in he numbe o synapses equi ed o his implemen a ion, which is
he eason why his OR implemen a ion was only used o his pu pose. This
implemen a ion o he decode sol ed he p oblem encoun e ed in i s o iginal
implemen a ion wi h espec o case "00" by elimina ing he CSS block, which
was esponsible o p oducing he cons an igge ing o he co esponding AND
ga e. In his implemen a ion, his case does no e en ha e a place, since i is he
no-ope a ion case, which is o ally in line wi h he spiking philosophy. Finally,
aking in o accoun his al e na i e OR ga e, he inhibi ion-based AND ga es
and he in oduc ion o delay neu ons, he implemen a ion o he decode was
achie ed ollowing he design shown in Figu e 3.13.
Wi h espec o each o he ope a ions pe o med by his ALU, i is necessa y
o del e in o he implemen a ion o he blocks ha enable wo o hem: he XOR
and ADD ope a ions. The XOR ga e was also implemen ed in Ayuso-Ma inez
e al., 2022 (Appendix A) oge he wi h he o iginal implemen a ion o OR, AND
and NOT ga es, and i s design has emained he same since hen. This ne wo k
consis s o a ully-connec ed SNN wi h wo laye s o neu ons, in which each
neu on in he inpu laye is connec ed one- o-one wi h a co esponding neu on in
he ou pu laye h ough exci a o y synapses and also connec ed o he es o he
neu ons o his laye h ough inhibi o y synapses. In his way, only one neu on
i es i he es a e inhibi ed. To co ec ly in oduce he XOR ope a ion in o he
spiking ALU, a sligh modi ica ion was equi ed, which consis ed o eplacing
each neu on o he inpu laye wi h a NOT ga e.
To allow ADD ope a ions, i was necessa y o implemen a new componen :
he adde . The e a e se e al a ian s o digi al adde s; howe e , o he sake o
simplici y, in his wo k, he ipple-ca y adde was used, e en hough i is no
he mos op imal o hem all. In hese adde s, hal adde s and ull adde s a e
3.3. Applica ions 45
FIGURE 3.13: Design o he implemen ed simple ALU o pe o ming
logical and a i hme ic ope a ions wi h wo 3-bi numbe s. A and B ha e
a delay o 3τ, indica ed as +3 in he scheme.
digi al ci cui s used o add wo bi s. A hal adde pe o ms he addi ion ope a ion
wi hou accoun ing o a ca y-in, while a ull adde includes a ca y-in o mo e
complex addi ion. The digi al ci cui o a ull adde is shown in Figu e 3.14, which
also includes a hal adde . Each o he ga es wi hin bo h ci cui s is ansla ed in o
i s spiking o m using he blocks p esen ed in his doc o al hesis, inally eaching
he spiking implemen a ion o he ipple-ca y adde , whose design is shown
in Figu e 3.15. In his design, some pu ple neu ons ha e wo inpu exci a o y
synapses, which could aise conce ns abou po en ial o e exci a ion. Howe e ,
due o he beha io o he neu ons in he ne wo k, o e exci a ion should no
be possible, as a spike will ne e be ecei ed simul aneously h ough bo h
inpu synapses. This op imiza ion allowed using o iginal OR ga es ins ead o
inhibi ion-based OR ga es, which would sligh ly inc ease he numbe o esou ces
used.
46 Chap e 3. Summa y o esul s
FIGURE 3.14: Digi al ci cui o a ull adde based on AND, OR and XOR
ga es. The a ea ep esen ed in g een co esponds o he digi al ci cui o a
hal adde , which does no ake in o accoun he alue Cin.SHA and CHA
ep esen he sum and ca y ou pu s o he hal adde , espec i ely, while
SFA and CFA deno e he sum and ca y ou pu s o he ull adde .
As also occu ed wi h he es o expe imen s conduc ed on Dynap-SE o
p e ious blocks, an ex ensi e se ies o expe imen s we e pe o med o alida e
he spiking implemen a ions o , i s , he ipple-ca y adde , and second, he
ALU. In he case o he ipple-ca y adde , each expe imen consis ed in he
addi ion o wo numbe s o 2, 3, 4, 5 o 6 bi s pe o med a ope a ing equencies
o 0.5, 1, 2, 5 o 10 KHz. The e we e wo di e en se s o expe imen s depending
on whe he andom numbe s o speci ic numbe s we e used o he addi ion
ope a ions. In he la e case, hese numbe s we e A=3 and B=2n+1−1,
whe e nis he numbe o bi s conside ed in each expe imen . This se o
expe imen s enabled he e i ica ion o he co ec p opaga ion o pa ial esul s.
To co ec ly in e p e he esul s o hese expe imen s, i was essen ial o conside
he delay in oduced by neu ons and synapses in he p opaga ion o he spikes,
which caused each neu on Si o i e a e he neu on Si−1 o i≥1, leading
o o e laps be ween he ou pu spikes co esponding o di e en ope a ions
a high equencies. Thus, he spikes i ed by hese neu ons had o be ead
diagonally, whe e he slope o he esul ing line was p opo ional o he alue
o τ. Figu e 3.16 shows he esul s o a es in which wo 5-bi andom numbe s
we e added a an ope a ing equency o 2 KHz.
The esul s o he expe imen s ca ied ou on he spiking ipple-ca y adde
a e summa ized in Table 3.10. Simila o he inhibi ion-based ga es, some
expe imen s ailed when ope a ing a high equencies, as he neu ons we e
unable o main ain he expec ed Boolean beha io . A inal expe imen was
pe o med o alida e he co ec ope a ion o he spiking ALU. This consis ed
in using a pa e n o nine pai s o numbe s, which we e used o pe o m each
o he allowed ope a ions nine imes. The esul s a e shown in Figu e 3.17.
Finally, an analysis was pe o med o quan i y he numbe o esou ces used
and he la ency o each o he blocks designed o he implemen a ion o he
3.3. Applica ions 47
FIGURE 3.15: Design o a 3-bi , 2-inpu spiking adde using SNNs and inspi ed by he digi al ipple-ca y adde ci cui .
The g een a eas inside he ull adde s ep esen a SNN equi alen o a hal adde ci cui . The pu ple neu ons ep esen
whe e pa ial o o al esul s can be ob ained in he addi ion ope a ion, hus Siand Ci ep esen one digi o he inal
esul and a pa ial ca y o he nex digi , espec i ely. C2 ep esen s he inal ca y, indica ing whe he he e is o e low
du ing he coun . The ed neu ons pe o m NOT o NOR ope a ions. Delays a e ep esen ed as (+n), whe e nis he
alue o he co esponding added delay.
48 Chap e 3. Summa y o esul s
FIGURE 3.16: Tes o adding wo 5-bi andom numbe s a an ope a ing equency o 2 KHz wi h he implemen ed
spiking ipple-ca y adde . SOP is shown in blue, he spike ains ela ed o A and B a e ep esen ed in yellow and
ed, espec i ely, and he ou pu spike ain is shown in g een. The spikes colo ed pu ple a e ela ed o he inal ca y,
indica ing whe he he addi ion ope a ion o e lows. All spikes con ained be ween wo ed lines ep esen a single
addi ion ope a ion.
3.3. Applica ions 49
TABLE 3.10: Resul s o he expe imen s ca ied ou on spiking ipple-ca y
adde s o di e en numbe s o bi s (n) and di e en ope a ing equencies
( ). The icks indica e ha he expec ed beha io is ob ained, while he
c osses indica e ha he SNN is no able o ope a e co ec ly.
(KHz) / n 2 3 4 5 6
0.5 ✓ ✓ ✓ ✓ ✓
1✓ ✓ ✓ ✓ ✓
2✓ ✓ ✓ ✗ ✓
5✓ ✓ ✓ ✗ ✗
10 ✗✗✗✗✗
TABLE 3.11: Analysis o he esou ces used and he la ency o he high-
le el designs p oposed ela ed o he implemen a ion o he spiking ALU.
n e e s o he numbe o inpu s, b o he numbe o bi s and τ o he ime i
akes o a spike o p opaga e h ough he union o a synapse and a neu on
acco ding o he pa ame e s used.
Block To al neu ons To al synapses La ency
Al e na i e OR n(n2+n)/2 τ
Decode 2n+4n(n+1)·2n+3/2 ·n2+7/2 ·n−1 3τ
Ripple-ca y adde 5b2+12b−11 5b2+28b−20 ...
ALU 5b2+23b+12 5b2+48b+29 ...
spiking ALU, which is shown in Table 3.11. The la ency o he ipple-ca y adde
depends on he neu on Siand can be calcula ed using he ollowing o mula:
(5i+2)·τ,∀i∈ {1, 2, . . . , b−1}, whe e iis he bi index and bis he o al numbe
o bi s. Fo S0, he la ency is equal o 3τ. Thus, he la ency o he ALU depends
on he ope a ion o be pe o med, since each block in cha ge o pe o ming each
ope a ion has i s own la ency. Fo example, in he case o pe o ming he addi ion
ope a ion, his la ency also depends on he numbe o bi s, as occu s wi h he
ipple-ca y adde .
3.3.2 Fil e ing QRS complexes in elec oca diog ams using a
spiking coun e
An implemen a ion o a spiking coun e was p esen ed (Appendix D), aiming
no only o le e age he inhe en ad an ages o SNNs bu also o se e as a
aluable componen o p ocessing spiking in o ma ion based on spike ains.
A compa ison was hen made be ween LIF neu ons, which gene ally ac as high-
pass il e s by equi ing a minimum equency o he inpu spike ain o gene a e
an ou pu spike ain, and his spiking coun e , whose coun ac ion was no
a ec ed by he equency wi h which i was pe o med. In his way, spiking
coun e s can no be conside ed il e s, al hough hey a e also use ul o gene a e
an ou pu spike ain wi h a equency lowe han ha o he inpu spike ain.
50 Chap e 3. Summa y o esul s
FIGURE 3.17: Tes o he implemen ed spiking ALU ope a ing a 1 KHz. The spike ains i ed by he decode , OPOR,
OPXOR,OPAND and OPADD a e ep esen ed in blue. The spike ains ela ed o A and B, which we e delayed by 3τ o
ma ch he decode ou pu , a e shown in yellow and ed, espec i ely. The ou pu spike ains i ed by each o he OR,
XOR, AND o adde blocks inside he ALU a e ep esen ed in g een. No e ha each ype o ope a ion is pe o med only
when he co esponding spike ain OP con ains spikes.
3.3. Applica ions 51
This is due o he ac ha , unlike in he case o a LIF neu on, whose equency
di ision elies on complex a iables and di e en ial equa ions, he equency
di ision caused by he use o his spiking coun e depends solely on he numbe
o bi s i con ains and he pa ame e s used. As a esul , he beha io o he
spiking coun e is independen o he sub h eshold dynamics o he neu ons ha
compose i , making i easie o unde s and and mo e p edic able.
To implemen his spiking coun e , i was i s necessa y o design a spiking
egis e . To his end, double-neu on SR la ches we e used, wi h an addi ional
neu on added o each la ch o p e en spikes om being in oduced i i was
al eady in he ac i e s a e, he eby a oiding he o e exci a ion o he neu ons. In
his way, his new design o he SR la ch could be implemen ed on Dynap-SE,
which would no be he case o he o iginal design p esen ed in Sec ion 3.3.1.1.
An addi ional neu on was in oduced o allow he ese o all he la ches
simul aneously, esul ing in he design shown in Figu e 3.18.
FIGURE 3.18: Design o a spiking egis e o 4 bi s. Biindica es he
synapses which a e used o se each o he SR la ches, independen ly. Rese
is used o pe o m he ese o all o hem.
Finally, he design o he spiking coun e , shown in Figu e 3.19, was
mainly based on his spiking egis e . While he egis e was used o s o e he
coun , a coun signal was used o indica e when o inc ease his coun by one.
Consequen ly, each o he la ches was no expec ed o be se o ese h ough
ex e nal spike ains, bu h ough he spike ains gene a ed by an in e media e
combina ional logic based on he use o NOT ga es, which made i possible o
pe o m he bina y combina ions necessa y o ep esen he numbe o spikes
52 Chap e 3. Summa y o esul s
ha had been ecei ed h ough he synapse ep esen ing he coun signal. This
combina ional logic allowed SR la ches o beha e as swi ches, changing hei
s a e e e y ime a spike was i ed om he NOT ga e o which hey we e
connec ed. An analysis o he esou ces used and he pe o mance o he block is
shown in Table 3.12.
FIGURE 3.19: Design o a spiking coun e o 4 bi s. Coun is he inpu
synapse h ough which spikes inc ease he coun by one.
Al hough i was heo e ically possible o implemen his design on Dynap-
SE, SpiNNake was chosen o accele a e he expe imen s due o ime cons ain s.
Ini ially, a heo e ical s udy o he expec ed esul s was conduc ed using a spike
ain wi h a i ing a e o 1 KHz as he coun signal o a 4-bi spiking coun e ,
which inc eased he coun alue by one e e y 1 ms, as shown in Figu e 3.20.
Subsequen ly, his coun e was implemen ed on SpiNNake . In his second
expe imen , he expec ed beha io o he block was alida ed. I s esul s a e
p esen ed in Figu e 3.21, showing wo main di e ences wi h espec o he
heo e ical s udy. Fi s , he neu ons in he double-neu on la ches i ed al e na ely.
In addi ion, synap ic delays we e e lec ed in he iming o he spikes.
FIGURE 3.20: Ideal beha io o a 4-bi spiking up-coun e when ecei ing
an inpu spike ain wi h a cons an equency o 1 KHz.
3.3. Applica ions 53
TABLE 3.12: Analysis o he esou ces used and he la ency o he high-
le el designs p oposed ela ed o he implemen a ion o he spiking
coun e . b e e s o he numbe o bi s and τ o he ime i akes o a spike
o p opaga e h ough he union o a synapse and a neu on acco ding o he
pa ame e s used.
Block To al neu ons To al synapses La ency
Imp o ed SR la ch 3 9 τ
Regis e 3b+1 9b+1τ
Coun e 6b−6 17b−8τ
FIGURE 3.21: Real beha io o he p oposed implemen a ion o a 4-bi
spiking up-coun e when ecei ing an inpu spike ain wi h a cons an
equency o 1 KHz.
Once implemen ed, i was p oposed o use he spiking coun e in he
de elopmen o a spiking sys em o il e QRS complexes. SNNs a e especially
use ul o wo king wi h ime-dependen pa e ns, especially when he e is
plas ici y. The aim was o ind ou whe he a s a ic s uc u e, in which no
plas ici y exis ed, could somehow wo k eliably wi h mo e ealis ic spike ains.
Thus, expe imen ing wi h he elec ical signals gene a ed by he hea was he
pe ec case, as hey con ain a cha ac e is ic pa e n o a ia ions which, al hough
may be sligh ly di e en o each indi idual, is well de ined. The QRS complex
is one o he essen ial componen s o his pa e n, as i s du a ion and ampli ude
a e pa icula ly use ul o he de ec ion o ca diac abno mali ies (Ch is o , 2004;
Co adi e al., 2019).
An expe imen was designed o show ha a spiking coun e can be used as
a equency di ide o p ep ocess a spike ain and hen il e QRS complexes
using a LIF neu on. Fo his pu pose, he PhysioNe A hy hmia Da abase om
he Massachuse s Ins i u e o Technology and Be h Is ael Hospi al (MIT-BIH)1
was used. Fi s , i was essen ial o encode he elec ical signals con ained in a
da a ile in o spikes, o which he del a modula o algo i hm (Co adi e al.,
2019) was used, in which he spikes ep esen a change in he po en ial o he
signal ha exceeds a ce ain h eshold, posi i ely o nega i ely (on and o spikes,
espec i ely). In his wo k, only MLII (Modi ied Limb Lead II) signals we e
1h ps://www.physione .o g/con en /mi db/1.0.0/
60 Chap e 3. Summa y o esul s
This implemen a ion was es ed h ough an ex ensi e se ies o expe imen s,
which mainly a ied he ope a ing equency in a way simila o he expe imen s
conduc ed o he inhibi ion-based OR and AND ga es. These expe imen s
p o ed ha he FSM beha ed as expec ed while ope a ing a 0.5 KHz, 1 KHz
and 2 KHz, bu hey did no o ally wo k as expec ed when wo king a 5 KHz.
I should be s udied o wha ex en he imp o ed SR la ches, which ha e an
addi ional neu on o a oid o e exci a ion in he la ches, could ha e imp o ed
he esul s ob ained. Figu e 3.30 shows he esul s o an expe imen in which
he FSM was es ed wi h disc e e ope a ion spikes. No e ha , when OP and SG1
ansmi ed a spike simul aneously, he FSM always mo ed o he nex s a e, bu
when OP and SG2coincided, i only e u ned o he p e ious s a e i s a e S3was
ac i e a ha ime. Ano he impo an de ail is ha , i SG1o SG2 ansmi ed
a spike bu OP did no , he la ches did no change hei s a e, as none o he
ansi ions was ac i a ed.
3.4. Wo k pending publica ion 61
FIGURE 3.30: Resul s o an expe imen conduc ed on he implemen ed FSM, ope a ing a disc e e imes. The inpu spike
ains a e shown below he do ed line. S op is used o ese he s a es, and s a o se he s a e S1.OP con ains he spikes
equi ed o ope a e, SG1indica es o ad ance o he nex s a e and SG2indica es o e u n back o he p e ious s a e. The
spikes i ed by each o he s a es and ansi ions a e shown abo e he do ed line.
63
Chap e 4
Discussion
This chap e discusses some gene al aspec s o he pa adigm in oduced o he
implemen a ion o spiking blocks ha ha e no ye been explo ed in de ail, and
i also desc ibes some possible lines o u u e wo k which a ise om he wo k
p esen ed in his doc o al hesis.
In Sec ion 3.1, i was men ioned ha he i ing imes o he spike gene a o s
in Dynap-SE may a y sligh ly om he expec ed alues. In ac , his a iance can
occu no only in he spike gene a o s bu also in he neu ons o an implemen ed
SNN, as hey sha e a common analog na u e, which could lead o unexpec ed
beha io s o hese neu ons. Suppose he scena io in which he pa ame e s o a
single LIF neu on ha e been adjus ed so ha he accumula ed cu en induced
by wo spikes which a i e simul aneously is su icien o b ing he memb ane
po en ial o he h eshold po en ial, hus causing he neu on o i e. Conside ing
ha one o he wo spikes could a i e ea lie and aking in o accoun ha LIF
neu ons end o b ing hei memb ane po en ial o hei es ing po en ial, i is
clea ha a d op in i s memb ane po en ial would occu be ween he a i al o
bo h spikes. In his way, he impac o his d op on he neu on’s beha io would
depend on i s speci ic pa ame e s. I he d op is la ge enough, his would cause
he neu on no o each he h eshold po en ial a e he a i al o bo h spikes,
hus p e en ing he expec ed beha io om being achie ed.
This e ec has no been obse ed in he implemen a ions on Dynap-SE o
he spiking blocks designed in his doc o al hesis, p obably because hese d ops
we e insu icien o cause unexpec ed beha io s in SNNs wi h ew laye s o
neu ons using he pa ame e s p esen ed in Chap e 3. Howe e , in SNNs wi h
many laye s o neu ons, he cumula i e e ec o hese empo al a ia ions could
e en ually become signi ican enough o a ec hei unc ionali y. The e o e,
an in-dep h s udy o his aspec would be equi ed du ing he implemen a ion
o SNNs o much g ea e complexi y han hose p esen ed. In App. Band
App. C, wo solu ions we e p oposed o sol e his possible p oblem in he
u u e while main aining he spiking Boolean pa adigm. The i s o hese wo
solu ions, which would equi e he leas e o , would consis in adjus ing he
neu on pa ame e s o minimize he d op in memb ane po en ial, which could be
64 Chap e 4. Discussion
done by ex ending he ime i akes o his po en ial o decay. Howe e , his
could signi ican ly limi he maximum ope a ing equency o he implemen ed
blocks, as o e lapping ope a ions may occu . The second solu ion would
be he ideal solu ion, bu also he mos complex o achie e, since i would
consis in implemen ing a mechanism o he synch oniza ion o spikes coming
om di e en synapses. The e is biological e idence o he exis ence o spike
synch oniza ion mechanisms in he ne ous sys em (MacLeod e al., 1998; Riehle
e al., 1997).
A po en ial synch oniza ion mechanism could le e age he la ches used o
implemen he spiking coun e . This would in ol e using a SR la ch o each
inpu synapse, which would be ac i a ed upon he a i al o he i s spike a
he co esponding synapse. An AND ga e would hen gene a e an ou pu spike
only when all SR la ches we e ac i e, a which poin he la ches would also be
ese . The ou pu synapse would ha e a weigh equal o he sum o he weigh s
o all inpu synapses, mimicking he e ec o spike in eg a ion on a pos synap ic
neu on. This mechanism would in oduce a delay equal o he delay o he las
inpu spike. Al hough his would inc ease he la ency o he implemen ed blocks,
i would ensu e hei co ec ope a ion. Howe e , in cases whe e inpu spike
ains ha e high i ing a es, his mechanism could p oduce ewe ou pu spikes
han expec ed.
In Chap e 3, many expe imen s we e p esen ed ha aimed o es he
beha io o he spiking blocks implemen ed on Dynap-SE unde se e al
ope a ing equencies. Howe e , i has been men ioned ha hey may ail when
hese equencies a e pa icula ly high, which could be associa ed wi h he apid
a i al o spikes o neu ons ha a e s ill wi hin hei e ac o y pe iod, hus
p e en ing hei Boolean beha io . Wha should be he ope a ing equency hen?
The esul s showed ha , ope a ing a 1 KHz, he beha io o all he implemen ed
blocks was as expec ed in all cases. The e o e, i is p oposed o make hese blocks
ope a e a ha equency whene e possible o a oid unexpec ed beha io s.
Reducing he e ac o y pe iod o he neu ons inside he blocks would help hei
maximum ope a ing equencies o inc ease.
In e ms o powe consump ion, an analysis o he consump ion o
inhibi ion-based OR and AND ga es on Dynap-SE was ca ied ou oge he wi h
a compa ison wi h o he wo ks o he s a e o he a in Sec ion 3.2. Howe e , a
compa ison should also be made be ween hese dynamic powe consump ions
and he dynamic powe consump ion o ansis o s, e.g., CMOS ansis o s,
which can be calcula ed using he o mula p esen ed in Equa ion 4.1, ex ac ed
om Beloglazo e al., 2011, whe e ais he swi ching ac i i y, Cis he physical
capaci ance, Vis he supply ol age and is he clock equency. No e ha his
clock equency is equi alen o a cons an ope a ing equency in he spiking
designs p esen ed.
Chap e 4. Discussion 65
Pdyn =aCV2 (4.1)
To ensu e a ai compa ison, i mus be conside ed ha in he dynamic powe
consump ion s udies p esen ed in his doc o al hesis he neu ons i ed one spike
e e y 1 ms, co esponding o a equency o 1 KHz, hus ha ing a=1 and =1
KHz, meaning ha he ansis o swi ches a e e y clock cycle (1 ms). The supply
ol age, as epo ed in Mo adi e al., 2017, was V=1.3 V. Assuming a capaci ance
o C=0.5 F, which is a qui e small bu ypical alue o cu en ansis o s, he
dynamic powe consump ion o a CMOS ansis o can be calcula ed as shown
in Equa ion 4.2.
Pdyn =1·0.5 ·10−15 ·1.32·103=0.845 pW (4.2)
The calcula ed alue is signi ican ly lowe han he 9.29 µWob ained o a
single neu on in he spiking designs, assuming a i ing a e o 1 KHz and a single
ou pu synapse. I should also be aken in o accoun ha he pa ame e s used in
Equa ion 4.2 co espond o ansis o s wi h dimensions o only a ew nanome e s,
whe eas, in Dynap-SE, a 0.18 µm echnology is used. Howe e , as discussed in
Mo adi e al., 2017, he eal eason why he SNNs implemen ed on his pla o m
could bene i om e y low powe consump ion would be, as is he case o
he ne ous sys em and he b ain, he abili y o hese ne wo ks o implemen
massi ely pa allel a chi ec u es, hus educing he amoun o esou ces used and
he e o e hei o e all powe consump ion. This could be demons a ed in he
u u e by implemen ing designs ha euse a la ge numbe o neu ons o ca y
ou he di e en pa ial ope a ions needed o pe o m speci ic unc ions.
Finally, he e is ano he aspec ha also needs o be aken in o accoun . The
elec ical ci cui s used in Dynap-SE o implemen DPI neu ons a e made up o
many o hese ansis o s, so compa ing he powe consump ion o a CMOS
ansis o e sus he powe consump ion o many o hem oge he would be
i ial i pa allelism we e no conside ed. Howe e , since he designs p esen ed
in his hesis a e biologically plausible, hey could be physically implemen ed
using no only elec ical ci cui s bu also eal neu ons, in a hypo he ical u u e
whe e neu ons could be manipula ed and in e connec ed a will. Expe imen s
would hen be ca ied ou o e i y whe he i would be possible o main ain he
Boolean beha io o he neu ons e en in he mos complex possible en i onmen .
This, on he o he hand, could also se e o disco e whe he he e a e
s uc u es simila o he designs o he mos basic combina ional blocks in he
ne ous sys em, which could implici ly sugges he exis ence o Boolean unc ion
calcula ions in biology.
67
Chap e 5
Summa y and conclusions
This chap e p esen s a summa y o he main conclusions ha can be d awn om
he wo k desc ibed in his documen , highligh ing he key poin s co e ed in he
p e ious sec ions:
• An in-dep h s udy o he biological ounda ions o he ne ous sys em and
he b ain was ca ied ou , desc ibing he ea u es ha biological neu al
ne wo ks exploi o make he b ain he mos e icien compu e cu en ly
in exis ence.
• This wo k is closely ela ed o he ield o neu omo phic enginee ing, whose
aims and ad ances a e de ailed in his hesis, as well as one o he main
wo king ools o hese enginee s, he Spiking Neu al Ne wo ks (SNNs).
Thus, he unc ioning o hese bioinspi ed ne wo ks, he main neu on
models and he neu omo phic al e na i es used o hei implemen a ion
we e explo ed in dep h.
• Based on he use o SNNs, his wo k ini ially p oposed o adop a
spiking Boolean compu ing pa adigm ha would allow implemen ing
combina ional blocks exhibi ing he main ad an ages o SNNs, which a e
low-powe consump ion and high eal- ime capaci y, bo h ela ed o hei
massi e capaci y o pa allelism. In addi ion, his pa adigm would allow
neu omo phic enginee s o implemen any spiking combina ional logic in
a sys ema ic way, which could be e y use ul in hei esea ch.
• This hesis demons a es he abili y o SNNs o exhibi Boolean beha io s
unde a pa icula se o neu on pa ame e s h ough he spiking
implemen a ion o he mos basic blocks, i.e., he logic ga es, om which
any o he combina ional block can also be implemen ed.
• These new spiking a chi ec u es we e alida ed in bo h digi al and
analog en i onmen s using he SpiNNake and Dynap-SE neu omo phic
pla o ms and unde an ex ensi e se ies o expe imen s, which
demons a ed hei bioplausibili y by o e coming ce ain di icul ies ha
68 Chap e 5. Summa y and conclusions
a biological neu al ne wo k could also be subjec o, such as o e exci a ion
o spike synch oniza ion.
• Du ing he design o inhibi ion-based OR and AND ga es, i was possible
o implemen NOR ga es using only one neu on. Since NOR ga es a e also
uni e sal ga es, i.e., any Boolean unc ion can be cons uc ed om hem,
blocks implemen ed using such ga es could be qui e op imal.
• The pe o mance and scalabili y o he implemen ed blocks on SpiNNake
and Dynap-SE we e analyzed. Fo inhibi ion-based OR and AND ga es, an
analysis o dynamic powe consump ion was also ca ied ou . This analysis
was used o make a compa ison wi h he wo ks ound in he s a e o he a ,
hus ob aining be e esul s han o he implemen a ions based on SNNs
and he use o di e en pa adigms.
• No compa able spiking implemen a ions we e ound o many o he
p esen ed blocks, which highligh s hei no el y and he po en ial o he
p oposed pa adigm o building spiking implemen a ions. As a esul , i
was no possible o include di ec compa isons in e ms o pe o mance,
scalabili y o powe consump ion.
• A se ies o applica ions we e ca ied ou ha seek o demons a e he
use ulness o he spiking Boolean compu ing pa adigm and hus exploi
he main ad an ages o SNNs when pe o ming known asks encompassed
wi hin di e en b anches o science. Among hem, he ad ances made in
he implemen a ion o a spiking compu e s and ou due o he complexi y
o he SNNs in ol ed, whose beha io s we e also alida ed h ough an
ex ensi e se ies o expe imen s.
• Finally, some issues o be aken in o accoun in he u u e we e discussed,
such as he possibili y o p oblems a ising om di e ences in he a i al
imes o spikes o he neu ons o a ne wo k and some possible solu ions
ha could be a emp ed o be applied i his occu s in ne wo ks o much
g ea e complexi y han hose p esen ed in his hesis.
Thus, all he objec i es p oposed in Chap e 2we e me .
69
Chap e 6
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77
Pa II
Se o pape s
79
Appendix A
Spike-based building blocks o pe o ming
logic ope a ions using Spiking Neu al
Ne wo ks on SpiNNake
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Accep ed and published
Type: Con e ence Pape
Con e ence Name 2022 In e na ional Join Con e ence on Neu al Ne wo ks
(IJCNN)
Place: Pado a, I aly.
Da e: July 2022
Publishe : IEEE
Numbe o pages: 9
ISSN: 2161-4407. ISBN: 978-1-7281-8671-9
DOI: h ps://doi.o g/10.1109/IJCNN55064.2022.9892479
89
Appendix B
Cons uc ion o a spike-based memo y using
neu al-like logic ga es based on Spiking
Neu al Ne wo ks on SpiNNake
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Accep ed and published
Type: Regula Pape
Jou nal Name: IEEE T ansac ions on Eme ging Topics in Compu ing
Publishe : IEEE
Da e: June 2023
Numbe o pages: 13
ISSN: 2168-6750
DOI: h ps://doi.o g/10.1109/TETC.2023.3281063
103
Appendix C
Analog Implemen a ion o a Spiking Sys em
o Pe o ming A i hme ic Logic Ope a ions
on Mixed-Signal Neu omo phic P ocesso s
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Giacomo Indi e i
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Accep ed o publica ion
Type: Regula Pape
Jou nal Name: Ad anced In elligen Sys ems
Publishe : Wiley
Numbe o pages: 20
ISSN: 2640-4567
125
Appendix D
A SNN-Based Implemen a ion o a Spiking
Coun e o Fil e ing and P ocessing Spike
T ains in Real Time
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Accep ed and published
Type: Book Chap e
Book Name: Recen Ad ances and Eme ging Challenges in STEM
Publishe : Sp inge
Da e: Augus 2024
Numbe o pages: 11
ISSN: 2662-3161. ISBN: 978-3-031-64105-3
DOI: h ps://doi.o g/10.1007/978-3-031-64106-0_38
137
Appendix E
Li e Demons a ion: Cons uc ion o a
spike-based memo y using neu al-like logic
ga es based on Spiking Neu al Ne wo ks on
SpiNNake
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Published on a Xi
Type: Con e ence Pape
Numbe o pages: 1
DOI: ...
139
Appendix F
A Low-Cos Real-Time Spiking Sys em o
Obs acle De ec ion based on Ul asonic
Senso s and Ra e Coding
Au ho s
• Al a o Ayuso-Ma inez
• Daniel Casanue a-Mo a o
• Juan P. Dominguez-Mo ales
• Angel Jimenez-Fe nandez
• Gab iel Jimenez-Mo eno
Publica ion
S a e: Published on a Xi
Type: Jou nal Pape
Numbe o pages: 22
DOI: h ps://doi.o g/10.48550/a Xi .2409.02680
