Thread by @s_r_constantin

join.substack.com/p/is-this-the-… whoa this is fascinating.

Eyeblink conditioning is when an animal learns to associate a stimulus with a puff of air to the eye, and to blink when the stimulus is presented alone.

Eyeblink conditioning requires the cerebellum. Remove the cerebellum and it doesn't happen.

in fact, you can see a pause response to the stimulus in the Purkinje cells of the cerebellum that control the eyelid.

cs.cmu.edu/afs/cs/academi…

now one hypothesis of how this learning happens is that the temporal association of the air puff and the stimulus causes a synapse, or synapses, to change its "weight". This is called Long Term Depression or LTD.

The Purkinje cell is directly connected to the neuron that senses the air puff, and indirectly connected to the neuron that senses the stimulus via the parallel fibers.

Dark circles are excitation in this picture, and light circles are inhibition. You blink when the Purkinje cell *stops* firing.

On the left hand side, the air puff ("unconditioned stimulus" or "US") activates the inferior olive (IO) and inhibits the Purkinje cell. Air puff -> blink.

On the right hand side, the conditioned stimulus ("CS") travels along the mossy fibers, inhibits the granule cells, which connect to the parallel fibers, and inhibit the Purkinje cell. This is a double negative; the conditioned stimulus *activates* the Purkinje cell. No blink.

the LTD hypothesis is that when the conditioned stimulus occurs at the same time as the air puff, the synapse between the parallel fibers and the Purkinje cell becomes *weaker*, so this stimulus will activate the Purkinje cell less, prompting a blink.

The problem is, it doesn't seem to work that way. First of all, reducing excitatory input doesn't necessarily inhibit the Purkinje cell enough to cause a blink. You can block that synapse completely (with an AMPA receptor antagonist) and the Purkinje cell still fires.

Second of all, eyeblink conditioning *does not happen* if the conditioned stimulus occurs too soon before the air puff, less than about 100 ms. LTD has no theory of why this would happen; it ought to work with simultaneous association of stimuli.

Thirdly, it's not clear how LTD could learn *time* information, while conditioning does learn the expected time interval between conditioned stimulus and air puff.

Fourthly, they went and looked! They classically condition some Purkinje cells (by directly stimulating the mossy fibers and climbing fibers.) There was no LTD!

So what's actually going on? Here comes another paper! pnas.org/content/111/41…

Do some eyeblink conditioning on decerebrate ferrets. That is, you sever the cerebrum so that all you're seeing is cerebellar and brainstem function. en.wikipedia.org/wiki/Decerebra…

They see the expected gap in firing in conditioned Purkinje cells but not naive Purkinje cells. The length of the gap corresponds to the length of the trained time interval between conditioned and unconditioned stimulus.

but look! in this experiment the "conditioning" comes from *directly* stimulating the parallel cell fibers!

This means that the way the brain "knows" how long the interval is, must live inside the Purkinje neuron alone! ONE CELL!

ONE CELL must contain some mechanism that can measure TIME.

This is WILD. And pretty much disproves connectionism. Memory doesn't live in synapses alone.

ruccs.rutgers.edu/images/persona… Here's Gallister thinking about the implications of this research program.

When the brain encodes numbers, like the length of a time interval as in the ferret classical conditioning experiment, we can infer that the number needs to get *passed around* between neurons.

Neurons communicate with each other via neurotransmitter firing at synapses, so (this paper presumes) the pattern of spikes must convey the relevant information, including numbers.

the conventional neuro view is that neuron spike trains use a "rate code." That is, the firing rate -- the number of spikes in a given time interval -- is all that matters. Not the sequence of individual lengths of intervals between spikes.

A rate code is a "unary" code, like tally marks -- there is less than one bit of information per spike. A combinatorial code is like *writing* numbers in base >1. Far more information efficient.

If individual neurons can somehow encode time intervals, as the ferret experiment showed they can, then specific sequences of interspike time intervals might be possible to transmit from one neuron to another, allowing numbers to be passed around efficiently.

(Aside #1 from me: it might be possible to determine experimentally whether this is in fact happening! If some neural response that depends on a number, happens faster than a unary code could transmit it, then a more efficient coding scheme must be being used.)

When animals need to perceive numbers/quantities, they need to do so over many-orders-of-magnitude ranges.

Probabilities, for instance; light intensities; cognitive maps of familiar terrain, ranging from centimeters to kilometers. 6 orders of magnitude is plausible.

It's hard to believe that we encode over a million different numbers with a unary code.

And perhaps we don't! Perhaps we use something more like scientific notation. An exponent and a significand, as in "3.09 x 10^16".

A suggestive reason why is found in Weber's Law. en.wikipedia.org/wiki/Weber%E2%…

Weber's law is the first major finding of psychophysics, discovered in 1860. It says that the smallest increment of change in a sensation that an animal can distinguish is proportional to the intensity of that sensation.

Integrate both sides, and all this means is that the *perceived* intensity of a sensation is proportional to the *log* of the "real" intensity.

For instance, the perceived brightness of a light is proportional to the logarithm of the energy hitting the retina from photons.

Weber's law holds experimentally for perceived weight of an object held in the hand, perceived pitch of an auditory tone, perceived line length, and other perceptual quantities.

This smells like scientific notation. You're transmitting a logarithmic "what scale are we at" quantity along with a relative "compared to this scale, how big is it" quantity.

mindblowingly, this can be shown to happen within a single neuron.

There's a single blowfly neuron that detects horizontal motion across the visual field. When the blowfly changes its flight behavior, the dynamic range changes. sci-hub.do/10.1016/S0896-…

The firing rates of this neuron are invariant to scaling up or down in the variance of the sensory inputs (low-variance as when flying straight, or high-variance as when chasing in a zig-zag pattern.)

moreover, the *spike train itself*, not just the rate-coded signals, has invariant statistical properties under changes in input variance.

What is the "engram", the physical object that encodes memory?

It must be long-lasting (that's the whole point of memory) and it must be able to encode numbers/quantities.

DNA? well, it can encode numbers, but it's in the nucleus and hard to change and at least according to Central Dogma information isn't supposed to be written to it.

RNA? In the cytoplasm? Well, that's not obviously impossible.

Could be other things, could be proteins, something with methylation or isomerization, We Just Don't Know.
(This is Gallistel's speculation, not mine. I shudder at the sheer variety of things inside cells and would not try to guess.)

Meanwhile, how far can we generalize the fact that individual Purkinje neurons can encode numbers in eye-blink conditioning experiments?

A lot, thinks Gallistel.

Here are some spooky facts about the cerebellum: it contains 80-90% of the neurons in the brain, and has evolved faster than the neocortex in humans and apes.

Like the cerebral cortex, the cerebellum is pretty structurally uniform; it has the same types of cells and the same circuit structure all the way through. It's not unreasonable to hypothesize that *all* Purkinje neurons can encode numbers.

en.wikipedia.org/wiki/Purkinje_… Purkinje cells are HUGE and highly branched.

If you just went through the brain with a microscope, knowing nothing else, you would point at them and say those are the Special Neurons.

We normally think of the cerebellum as "just" handling balance and motor control -- cerebellar disorders are generally ataxias -- but I wonder if "higher" cognition of some kind also happens in the cerebellum.

en.wikipedia.org/wiki/Cerebella… Schahmann's Syndrome is a disorder confined to the cerebellum, observed in human adults and children, which is *not* primarily defined by motor symptoms.

Schmahmann's Syndrome, sorry.

People with Schmahmann's Syndrome have deficits in spatial cognition, executive function, working memory, language, abstract thinking, and affect. Therefore the cerebellum does *something* with "higher" functions.

Here's Schmahmann's original paper: neuro.psychiatryonline.org/doi/pdf/10.117…

People with spinal cerebellar ataxias (SCA's, a group of degenerative genetic disorders affecting the cerebellum) have cognitive as well as motor symptoms: problems with short-term memory, executive function, and emotional instability and impulsivity.

Patients with focal cerebellar lesions have language problems including agrammatism en.wikipedia.org/wiki/Agrammati…, which involves grammatical errors. Problems with tense, number, gender, inflection, complex sentences, "wh"-questions, and conjunctions.

this is suggestive!

agrammatism seems to be a problem with *structure*. moving clauses around, using "functional" words and morphemes that change the meaning or context. the parts of language that go beyond association/clustering. And it's happening in the cerebellum!

Children born with incompletely developed cerebellums have motor delays, language problems, and spatial reasoning problems.

On the behavioral-emotional side, they have tactile defensiveness, trouble reading social cues, and stereotypies/stims.

watermark.silverchair.com/1210561.pdf?to… Adults with cerebellar lesions can't copy a drawing (19/20) and often have trouble with mental arithmetic (14/20).

Affective disinhibition takes the form of "overfamiliarity,
flamboyant and impulsive actions, and humorous but
inappropriate and flippant comments."

"baby talk" in a high pitched voice; "whining,
undressing in the corridors, and talking with her mouth full of food"; pulling covers over her head during the mental examination.

"simultanagnosia; e.g. when shown an advertisement in a
magazine she failed to grasp the meaning of the scene, but recognized the elements within the scene."

"Foresight and planning were extremely poor, with
performance on a maze task falling at an 8-year-old level" (in a 22yo woman with a cerebellar lesion due to a tumor.)

"marked disinhibition, with frequent swearing, and attempts to kiss the examiner" (in a 65yo man with cerebellar damage due to stroke)

"since the stroke she stated that she was unable to
follow the stream of logic [in classic literature] as swiftly as normal, and she had difficulty keeping track of the train of the thoughts in the narrative."

Unlike dementia and other "confusional states", arousal/alertness are not affected; unlike cortical brain damage, there aren't phenomena like aphasia, apraxia, and agnosia.

"On the Porteus Mazes, patients did not have difficulty drawing the lines, but rather their errors resulted from poor planning, often going into blocked paths, and requiring several attempts to find the correct solution."

Schmahmann hypothesizes a "dysmetria of thought" associated with cerebellar disorders: sci-hub.do/10.1016/S1364-…

The "where pathway" of visual cortex, referring to spatial location, projects down to the cerebellum; the "what pathway" for feature recognition does not.

The peripheral visual field projects down to the cerebellum; the central visual field does not.

this suggests spatial reasoning, navigation, etc. are cerebellar, while object recognition is not.

motor learning is impaired in cerebellar damage, tasks involving shifting attention between modalities are impaired, Tower of Hanoi tasks (so, planning/sequencing) are impaired.

"Posterior fossa syndrome" happens in children who've had tumors removed from their cerebellum. They become mute, and lie curled up in bed whining inconsolably without forming intelligible words.

Over time, they recover speech, but in a high-pitched, odd voice, and continue to have motor and cognitive deficits.

Dysmetria as a motor disorder means "overshoot" and "undershoot" of intended movements, which is a feature of cerebellar lesions. The person cannot estimate how far to go.

"Dysmetria of thought" is a somewhat analogous cognitive phenomenon where a person with cerebellar damage misjudges and "overshoots" or "undershoots" how much thought a task calls for.

Here is one cerebellar patient's response to a standard cognitive task. Asked to give a one-sentence response, he wrote eight. Asked to draw a clock face with numbers, he drew these highly detailed sketches.

This is a kind of "cognitive overshoot" as a result of cerebellar dysfunction.

the overall pattern of what the cerebellum does, seems to revolve around "relationship" or "measurement."

How far, how hard, where, or when to move; where things are; how to plan and sequence tasks; numbers and grammatical structure.

Is this related to the ability of the Purkinje neurons to encode numbers? It's a very tempting thought.

Also weird and suggestive: the absolute and relative size of the cerebellum *accelerated* in growth between Cro-Magnons and contemporary humans. That's only 50,000 years ago! ncbi.nlm.nih.gov/pmc/articles/P…

Pleistocene humans -- Cro-Magnons and Neanderthals -- already had art, stone tools, burial, and fire. Pretty fancy!

What innovations do you get between the Cro-Magnons and today? Stuff like this:
en.wikipedia.org/wiki/Upper_Pal…, where you get the first use of (wild) cereals, the domestication of the dog, bows and arrows, and the first weaving and pottery.