Too Many Bu e flies om One Ch ysalis
Con inual Lea ning, Con inual Fo ge ing and
he Ha monic Flow o In o ma ion
Elio GRANDE a,1Luigi QUARANTIELLO, a,2
aUni e si y o Pisa
ORCiD ID: Elio G ande h ps://o cid.o g/0009-0008-2896-5900, Luigi Qua an iello
h ps://o cid.o g/0009-0005-5428-156X
Abs ac . Despi e add essing dynamic lea ning scena ios, he Con inual Lea ning
pa adigm is s ill an e ol ing field, wi h no consensus on a defini i e me hodology
among he nume ous app oaches p oposed. In his s udy, we eflec upon possible
no el pe spec i es abou he lea ning p ocess i sel , posing a ew ques ions: how
does in o ma ion ge s uc u ed in models’ pa ame e s? wha i memo y and obli -
ion we e wo aces o he same coin? he e o e, could we concei e a ne wo k ca-
pable o bo h lea ning and o ge ing con inuously? We pu o wa d ha in o ma-
ion be dis ibu ed as a ha mony, meaning ha he e should be some deg ee o con-
sonance in he da a o he con inuous lea ning p ocess o succeed. P o ided ha ,
Con inual Lea ning migh be possible, say, as a a ia ion on he heme, possibly
deeming op imiza ion as a kind o o ches a ion, e en among a ious agen s. We
encou age he enhancemen o his amewo k, whe e cu en b u e- o ce mono-
li hic models would be su passed in a o o mo e e ficien agen s, capable o e ol -
ing dynamically om hei in e ac ions.
Keywo ds. Con inual Lea ning, Con inual Fo ge ing, In o ma ion.
1. In oduc ion
«To b eed an animal wi h he igh o make p omises-is no his he pa adoxical ask
ha na u e has se i sel in he case o man? [...] Tha his p oblem has been sol ed
o a la ge ex en mus seem all he mo e ema kable o anyone who app ecia es he
s eng h o he opposing o ce, ha o o ge ulness. Fo ge ing is no me e is ine iae
as he supe ficial imagine [...].»
(F ied ich Nie zsche, Genealogy o Mo als) [1]
To b eed a ificial in elligence wi h he igh o gene alize in he long un - is no his,
pa aph asing, he pa adoxical ask ha we d eam o , making i inc emen ally acqui e
new skills and jump like a gian owa ds a ificial gene al in elligence? Un o una ely,
a cu sed phenomenon h ea ens his eage ambi ion: ca as ophic o ge ing, ha is, he
d as ic pe o mance dis up ion on p e iously lea ned i ems a e aining on a new se
1Co esponding Au ho : Elio G ande, [email p o ec ed]
2Co esponding Au ho : Luigi Qua an iello, [email p o ec ed]
HHAI 2025
D. Ped eschi e al. (Eds.)
© 2025 The Au ho s.
This a icle is published online wi h Open Access by IOS P ess and dis ibu ed unde he e ms
o he C ea i e Commons A ibu ion Non-Comme cial License 4.0 (CC BY-NC 4.0).
doi:10.3233/FAIA250656
401
o i ems [2]. No necessa ily «finding solu ions ha wo k in he eal wo ld, bu a he
finding s able algo i hms ha can lea n in he eal wo ld»[3], he Con inual Lea ning
(CL) pa adigm mainly add esses he abo emen ioned issue, longing o ca y ou ac ual
au onomous agen s, mos ly simila o li ing beings.
Mo e o mally, CL can be defined as ollows [3]:
Defini ion 1.1. Gi en D={D1,D2,...,DN}a po en ially infini e sequence o unknown
da a dis ibu ions, whe e a each ime s ep ia aining se T i={Xi,Yi}is d awn om
Di∈D, a Con inual Lea ning algo i hm ACL
iis defined as:
∀Di∈D,ACL
i:<hi−1,T i,Mi−1, i>→<hi,Mi>
whe e hiis he pa ame ic model lea ned a e seeing all he aining se s up o T i,Mi
is an ex e nal memo y ha can be used o s o e samples om p e ious aining s eps,
and iis an op ional ask label. In o he wo ds, CL hea ily ocuses on c ea ing flexible
agen s ha can adap o an infini e numbe o asks, enabling also o euse and ans-
e knowledge. This ma ks a dis inc sepa a ion om s anda d Machine Lea ning (ML)
app oaches, whe e he objec i e is o achie e op imal pe o mance on a single ask.
None heless, CL emains an e ol ing field, wi h no consensus ye es ablished on a
defini i e me hodology among he nume ous app oaches p oposed. As highligh ed in he
defini ion abo e, mos cu en s a e-o - he-a CL algo i hms ely on he use o a memo y
bu e , wi h examples om p e ious asks. In o he wo ds, o make neu al ne wo ks e ain
knowledge, hey need o be cons an ly p omp ed wi h he same in o ma ion o e and
o e . Such ehea sal app oaches [4,5], despi e being unc ional and easy o implemen ,
ep esen a simplis ic solu ion o he p oblem o o ge ing. Ra he han enabling neu al
ne wo ks o e ain knowledge e ec i ely, hese me hods essen ially equi e he sys ems
o e-lea n in o ma ion o e ime. Mo eo e , hey di e ge significan ly om he human
way o lea ning and can be compu a ionally in ensi e, posing scalabili y issues by design.
Wi h hese limi a ions, i seems ha a no el ision abou he lea ning pa adigm is
needed. Indeed, in his wo k, we wan o eflec on some ques ions conce ning he deep
na u e o con inuously lea ning om di e en da a. In he fi s place, how does in o -
ma ion ge s uc u ed in a model’s pa ame e s? Secondly, he CL communi y s ongly
assumes memo y o be an inc emen al p ocess. Wha i , ins ead, memo y and obli ion
we e wo aces o he same coin? As a consequence, could we hink o a model capable
o bo h lea ning and o ge ing con inuously?
2. To Lea n secundum na u am
Why o imi a e some hing else’s na u e when one’s own is gi en? Howe e , i no he
na u e o an animal, and pe haps mo e specifically o a mammal — owa ds which CL
seems ins ead unning — which in insic na u e is an a ificial neu al ne wo k gi en?
In The Human Use o Human Beings, No be Wiene w o e ha «cybe ne ics akes
he iew ha he s uc u e o he machine o o he o ganism is an index o he pe o -
mance ha may be expec ed om i »[6]. The an una oidably beha es igidly, ou b ain
being ins ead neo enous and plas ic. Now, i ML i sel migh be deemed as a amily o
me a-algo i hms, since op imiza ion and back-p opaga ion mean p og amming p og am-
E. G ande and L. Qua an iello / Too Many Bu e lies om One Ch ysalis402
ming3,CL con empla es in ac a so o second-o de me a-algo i hms ained, so o
say, on sequences o asks a he han o da a. Howe e , how many bu e flies can sp ou
om he same ch ysalis? Me amo phosis will be hampe ed by obli ion, a leas up un il
models’ pa ame e s — he oo p in s o co ela ions among da a — and da a i sel will
be deemed as ine objec s, li le blocks, o li le b icks. Ine ia is he main p ope y o
ha d hings, say, a he opposi e o consciousness, o en mean as a con inuous s eam.
All is no los , hough. Neu al ne wo ks do wo k — obscu ely, especially when hey
a e deep — bu hey do. Now, le us linge o a momen no so much on da a and pa am-
e e s (indeed, e e y ac i a ion o a p e ious laye migh be seen as new da a by he nex
laye wi hin a neu al ne wo k) bu mo e p ecisely on in o ma ion, i.e. some hing much
mo e unwo ldly. Reph asing an old exp ession aken om he De Con emp u Mundi
(«On Con emp o he Wo ld») by Be na d de Cluny, s a osa p is ina nume o, nume os
nudos enemus4.We can obse e pa ame e s, sa e hem, wind he aining p ocess back,
bu hey emain pa ame e s — millions o numbe s ha a e indeciphe able o he human
eye. None heless, he ma hema ical unc ion lea ned by a model has a sense, since i bo h
ep esen s a po ion o eali y and se es a pu pose.
The e o e, wo obse a ions migh be made. Fi s ly, in o ma ion flows o wa d and
backwa d wildly and i is di ficul bo h o localize "meanings" h oughou he ne wo k
and o o ecas how hey will be dis ibu ed ( his seems pa icula ly e iden in he case
o he de ac o s anda d backp opaga ion algo i hm [7], whe e all he neu ons in he ne -
wo k a e upda ed join ly, sp eading he in o ma ion associa ed o he cu en lea ning
i e a ion). Secondly, we find aces o plas ici y in a neu al ne wo k, bu as p e iously
men ioned ca as ophic o ge ing eaches us ha such kind o spon anei y is, as an oxy-
mo on, ine ial.
Some disag eemen migh a ise, conce ning he missed localiza ion o in o ma ion.
In he CL li e a u e he e a e me hods ha assign each specific ask o a sepa a e g oup
o neu ons — he a chi ec u al app oaches [8]— implemen ing, a fi s glance, a clea
dis inc ion among he di e en ep esen a ions. None heless, his amily o app oaches
simply shi s he issue o wa d: in such me hods, i is no s aigh o wa d how o combine
hese se s o neu ons in o a single, au onomous ne wo k. This is confi med by he ac
ha a ask label is o en equi ed, speci ying which ne wo k o use o each sample in
inpu . Once again, his o su e ep esen s an easy solu ion, bu i does no sol e he
p oblem o eally lea ning inc emen ally.
We obse e a so o in o ma ional hos ili y o change, a somewha inco po eal ha d-
ness while he uni e sal app oxima ion heo em holds and, wi h su ficien pa ame e s
and ime, e e y con inuous unc ion defined on a closed in e al can be a bi a ily ap-
p oxima ed by a combina ion o simple unc ions [9]. Memo y, he e mean bo h as da a
and s o ed pa ame e s, seems on he o he hand o be fluid,i.e. bo h being on ologically a
flux ins ead o a bunch o hings, and bea ing ha p ope y o fluids, acco ding o which
hey dis ibu e hemsel es, e en i no wi h homogeneous densi y, all along hei con-
aine . Change he shape o he glass, and you will also eshape he wa e . I migh be ob-
jec ed ha , s ic ly speaking, he e is no con aine , o he wise said ha « he medium is he
message»[10]. Tha ’s a poin o , be e , ha ’s he poin , going way a and deeply lying
3no a ypo!
4«The o iginal and fi s ose lies in he numbe . We only possess naked numbe s». S a osa p is ina nomine,
nomina nuda enemus, was he ini ial ph ase («The o iginal and fi s ose lies in he name. We only possess
naked names»).
E. G ande and L. Qua an iello / Too Many Bu e lies om One Ch ysalis 403
in he e y concep o he en o ced ma hema ics. A e all, in o ma ion is a log-a i hm,
li e ally, a wo d becoming a numbe .
Ano he coun e a gumen migh be he sole exis ence o Con olu ional Neu al Ne -
wo ks (CNNs) [11]. S iding, padding, and epea edly fil e ing da a, CNNs su ely pu in
e idence pa icula p ope ies — like he shape o a wol ’s ail, o he colou o a beau-
i ul pai o eyes. He e, e en i no a "g andmo he cell" [12], one migh none heless a -
gue in a o o meanings’ localiza ion — wha once would ha e been called uni e salia
in e — uly o he poin ha algo i hms like G adCAM [13] o G adCAM++ [14] ex-
ac he g adien s p ecisely om he las con olu ional laye s in o de o find some local
in e p e a ion. Howe e , bewa e: in o ma ion migh s ill be in he eyes o he beholde .
Jus b inging up a e y i ial case, ake hese wo ph ases: «Today is a beau i ul
day»; «To be o no o be?». A banal e e yday sen ence migh e en equi e mo e memo y,
mo e by es han he nihilis Hamle ic doub , bu nobody could e en d eam o deeming
he Shakespe ian exp ession less significan . Wha is mean he e, is ha he only ac ha
some ea u es ge (e en wi h some p ecision) ex ac ed does no necessa ily en ail he
ex ac ion o meanings. I unp edic ably depends bo h on da a and on he model’s s uc-
u e: was i so mani es , o example, up un il he success o he a en ion mechanism,
ha a ph ase is no simply a sequence o oken?
3. Remembe me, o ge me, w i e me again
Recollec you own expe ience, aking a quie pause. How much ha e you o go en,
how much do you s ill emembe ? When you we e a child, o example, you lea ned a
specific way o walking, a echnique du co ps [15] you canno al e anymo e. Howe e ,
und essing om you own skin due o loss o bewilde men , you some imes c ossed he
ime and o go he pas . Indeed, despi e o en being li ed wi h anguish, obli ion ep e-
sen s, wi hin a ce ain ma gin, a necessa y expe ience o he p ope wo king o memo y
[16]. Why, i — le us say, na u al — memo y is no an inc emen al and cumula i e
p ocess, should i s imi a ion be so? No o men ion consciousness, ou ne ous sys em
is s uc u ally a mo e complex han a la ge a ificial neu al ne wo k, being mul ilaye
in qui e a di e en sense. Neu al ne wo ks o ge oo, bu clumsily: om memo izing
e e y hing, hey no longe emembe any hing ( ele an ). A bi o o ge ing migh mean
no ca as ophic o ge ing. Howe e , how o each hem o o ge p ope ly?
Especially ha ing o do wi h la ge, nonlinea models migh induce us o belie e ha
in o ma ion be sha ed among pa ame e s acco ding o some ha monic en i e y, a he
han o some assemblage o meanings. S angely enough, i esembles wha ancien S o-
ics called o pneûma, « he blow». P o ided ha , by «fluid memo y»we mean he eme g-
ing o (pu po edly, le alone unexpec ed pa e ns) one sense. Indeed, all in all, one is
he ne wo k whe e e e y neu on seems o find i s place. Di e en ly om meaning, sense
can be ouched, i. e. loss can be o e all educed h ough op imiza ion, bu no explic-
i ly desc ibed. Could his iewpoin help us o in e p e he phenomenon o ca as ophic
o ge ing?
Suppose you ha e a piece o polyme ic ma e . I has some chemical and physical
p ope ies, scien ifically obse able. Ye , s ic ly speaking, excep o he possibili y o
ake almos infini e shapes, i is useless. Now imagine ha , since you need o ab ica e
a hamme ou o i , you use he polyme and, while used, you gi e i you p e e ed
E. G ande and L. Qua an iello / Too Many Bu e lies om One Ch ysalis404
shape. A e wai ing o i o cool down, you finally ge a hamme . Now you g asp he
g ip o you hamme and d i e a nail. No su p isingly, you did ha by you hand and
no , say, by you oo . Now i is use ul, now i has a sense.
Un o una ely, you find ou you need also a washbowl (yes, a washbowl!). Since
no hing else is a ailable, you gi e a look a he hamme and hink: «I need o make also
a washbowl ou o ha ». So as o spa e ime and ene gy, you decide no o use you
polyme again, bu jus o wa m i up. You y no o hea up he en i e body o he ool,
o ound and hollow ou his and ha su ace... bu oday luck is no on you side and you
jus ob ain a misshapen polyme , nei he an excellen hamme no a good washbowl.
Suppose ha , a ime , you ini ialize a neu al ne wo k andomly — i. e., keeping
up wi h he me apho , a used polyme which in addi ion is pa ially capable o sel -
eshaping — and ain i in a supe ised manne on a ask a, say, he classifica ion o
pic u es po aying dogs and ca s. Random weigh s do implemen a ma hema ical unc-
ion, which in i sel does no need any adjus men and does no make any di e ence om
wha will be lea ned up o he las aining epoch. Howe e , wha is missing a he be-
ginning o he aining p ocedu e is some hing ul e io , say, he co e o supe ision: an
ambiguous mix u e o a quali a i ely significan ep esen a ion o he wo ld insc ibed in
he da a dis ibu ion, and a p ecise p ac ical goal o ealize.
A ime +1, you would like he model o expe ience a di e en da a dis ibu ion
acco ding o a ask b, say, in addi ion o ask a, dis inguish pic u es o ai planes and
ca s. You ca e ully selec he lea ning a e, choose an app op ia e op imize along wi h
i s hype pa ame e s, and employ you a o i e CL algo i hm. Ye , despi e you e o s, a
pe o mance d op ul ima ely comes up. Is no i , pe haps, ha i has been a emp ed o
iola e some a his s age well es ablished o e all and pu posi e balance? Is no i ha
you a e hoping o wo bu e flies o eme ge om a single ch ysalis?
4. Music o he neu ons
«Now he hi y-oa ed ship, in which Theseus sailed wi h he you hs, and came back
sa e, was kep by he A henians up o he ime o Deme ius Phale eus. They con-
s an ly emo ed he decayed pa o he imbe s, and enewed hem wi h sound wood,
so ha he ship became an illus a ion o philosophe s o he doc ine o g ow h and
change, as some a gued ha i emained he same, and o he s, ha i did no emain
he same.»
(Plu a ch, Pa allel Li es) [17]
By lea ning and o ge ing simul aneously, we ha e come ac oss he ancien enigma o
" he ship o Theseus": is i always he same model which we a e dealing wi h, when pe -
o ming con inuous lea ning? Despi e us being ca as ophically pushed o eply: «nei-
he i is, no i should be», his holds only as long as he componen s o such an en i y
— be i he Theseus’ ship o a neu al ne wo k filled wi h memo ies — we e s ic ly con-
side ed a collec ion, pa adoxically coun e ing he b illian idea o eusabili y. We migh
indeed find clues o he opposi e di ec ion: among o he s, he wonde — s ill s udied and
om someone conside ed illuso y [18] — o eme gen abili ies [19]. Res ing he eyes
on in-con ex lea ning, a ascina ing hypo hesis o implici ly lea ned me a-g adien s has
been pu o wa d [20], while some a en ion has been placed on he seman ic ex u e o
da a [21].
E. G ande and L. Qua an iello / Too Many Bu e lies om One Ch ysalis 405
F om he poin o iew o a model ha is accus omed o aking pho og aphs o da a
acco ding o a uni o m eali y called «g ound u h», CL will esemble beholding he
landscape om a mo ing ain. Time will go by b inging wi h i i sel a sequence o
expe iences shi ing in he da a dis ibu ion bu suddenly, con inuously unning away,
lea ing jus a halo. No only, hen, would i be ha d o i o accumula e memo ies,
bu i also will no s ic ly manage sequences o ames, e en wi h b u ally changing
dis ibu ions. Tasks being simila o no es in a melody, a musical analogy appea s o
a ise. Wha i CL we e mean as a a ia ion on a heme and op imiza ion alluded o a
consonan blend o cho ds and oices?
The e y di ficul y lies in op imizing models elegan ly se ing a fluc ua ing pu pose,
i. e., nei he simply jux aposing memo ies no o ien ing lea ning in an uni ocal way.
Such a dynamic and "pe manen ly unbalanced" AI, in insically mul i ocal, whe e ain-
ing and in e ence phases would be supe imposed, would pe haps be e en in he long un
a chime a — o , mo e simply, a b ain. Ye , un il hen, an al e na i e solu ion should be
ound o b u e- o ce algo i hms which de ou ons o da a. Say, besides eeding o wa d
and back-p opaga ing, he e should be also space o mo ing le and igh .
A simila easoning is exp essed as he collec ionless p inciple [22]. As he name
sugges s, i ep esen s an al e na i e poin o iew on subsymbolic AI, which in essence
e ol es a ound he idea o dis ega ding la ge da a collec ions — he ones needed by
e e y cu en ML algo i hm — and le ins ead he agen s p ocess he en i onmen al
s imuli and lea n om hem in a uly online ashion.
Now, his p ope ly desc ibes a possible way o gi e a ificial agen s he ins abili y we
men ioned be o e, he one hey in insically equi e o lea n dynamically. In a scena io
wi h s ong ela ions, bo h human- o-agen and agen - o-agen , one way o ge ou o he
iddle migh lie in he accu a e choice o he da a wi h which o eed he model, so as
no o go "o - heme". I would be possible o " une" he models — ei he me apho ically
and no — p o iding he adequa e da a poin s o each ins an in ime.
Fu he mo e, i we aim a dis inguishing — s ill, no igidly localizing — he sub-
unc ions ha compose a laby in hine global unc ion jus like we disce n umpe and
piano h oughou a hapsody, op imiza ion should be mean as a so o o ches a ion.
As a esul , we imagine ha his kind o collec ionless agen s could easily communica e
and coope a e o e ime, benefi ing om he unique expe iences he o he en i ies had,
o e coming he single monoli hic models sup emacy.
5. Conclusion
Wha can Con inual Lea ning become? In his wo k, we ad oca e he de elopmen o a
new ML pa adigm, ha could e ec i ely suppo he con inuous adap a ion o an in elli-
gen agen in a dynamic en i onmen . We imagine an ne o endless in e ac ions among
agen s and humans, all ha monized on he same heme. A he same ime, we hope o
su pass he need o gigan ic and cen alized models, he ones ha , besides a supe ficial
sma beha io , a e indeed a g ea example o ine ficiency and s upidi y.
Being p omp ed wi h he same da a o e and o e and o e , p ac ically ha ing he
en i e human knowledge a disposal, o finally say some hing easonable; is his in elli-
gence?
E. G ande and L. Qua an iello / Too Many Bu e lies om One Ch ysalis406
6. Ack o ledgmen s
Wo k suppo ed by PNRR - M4C2 - In es imen o 1.3, Pa ena ia o Es eso PE00000013 -
"FAIR - Fu u e A ificial In elligence Resea ch" - Spoke 1 "Human-cen e ed AI", unded
by he Eu opean Commission unde he Nex Gene a ion EU p og amme.
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