CNS 2019 - Mental Models of Time - Marc Howard

past dual space future
Mental and neural representations of the
past and the future
Marc W. Howard
Center for Memory & Brain
Department of Psychological and Brain Sciences
Department of Physics
Boston University
March 25, 2019

Zoran Tiganj, Ian Bright, Nathan Cruzado, Yue Liu
Inder Singh, Karthik Shankar
Collaborators: Howard Eichenbaum, Michael Hasselmo, Earl
Miller (MIT), Miriam Meister and Beth Buffalo (Washington)
Current funding:
NIH: R01MH112169, R01EB022864, R01MH095297
NSF: IIS-1631460
ONR: N00014-16-1-2832 (Hasselmo, PI)
Private Sector: Google FRA, Facebook Reality Labs
http://sites.bu.edu/tcn/

Overview
• Compressed timeline of
the past in the brain
• Dual space for the past
(Laplace).
• Neural evidence for this
dual space.
• The future.

Compressed temporal memory
• Events are represented on a temporal axis.
• Resolution of this axis decreases as
events recede into the past.
• This compression should be logarithmic.
William James, Karl Lashley, Robert Crowder, Gordon Brown,
Randy Gallistel, Nick Chater, John Anderson . . .

Cognitive models for judging the past
Data, Singh & Howard (2017, bioRxiv))
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Recency
ResponseTime(s)
−7 −6 −5 −4 −3 −2
0.7
0.8
0.9
1.0
1.1
1.2
1.3
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Recency
ResponseTime(s)
−6 −4 −3 −2 −1
0.0
0.5
1.0
1.5
Go to Zoran’s poster (E42)!

Cognitive models for judging the past
Data, Singh & Howard (2017, bioRxiv))
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Recency
ResponseTime(s)
−7 −6 −5 −4 −3 −2
0.7
0.8
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1.0
1.1
1.2
1.3
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Recency
ResponseTime(s)
−6 −4 −3 −2 −1
0.0
0.5
1.0
1.5
Model, Zoran’s poster
-7 -6 -5 -4 -3 -2
Recency
ResponseTime
-1-2-3-4-5-6
Recency
ResponseTime
Go to Zoran’s poster (E42)!

What would a timeline look like in the brain?
0 5 10
0
2.5
5
0 5 10
0
1.5
3
0 5 10
0
5
10
Time
MacDonald, et al., 2011
• “Time cells” are compressed.
• Different stimuli trigger different
sequences.
• Hippocampus (CA1, CA3, DG), lPFC,
mPFC, striatum . . .

What would a timeline look like in the brain?
Bolkan, et al., 2017
• “Time cells” are compressed.
• Different stimuli trigger different
sequences.
• Hippocampus (CA1, CA3, DG), lPFC,
mPFC, striatum . . .

Compressed record of what happened when
Tiganj, Cromer, Roy, Miller, & Howard (2018, J Cog Neuro)
Monkey WM task; remember different stimuli during delay
Dog Cat Car/Truck
0 0.5 1 1.5
Time [s]
50
100
150
200
Cell#
0 0.5 1 1.5
Time [s]
50
100
150
200
Cell#
0 0.5 1 1.5
Time [s]
50
100
150
200
Cell#

Cognitive models of many “kinds” of memory
Howard, et al., (2015, Psych Rev)
• Quantitative description of the activity of many neurons.
• Write out solvable cognitive models of behavior.
• Modeled working memory, episodic memory, conditioning.
• Representation observed in PFC, hippocampus, striatum.

Cognitive models of many “kinds” of memory
Howard, et al., (2015, Psych Rev)
• Quantitative description of the activity of many neurons.
• Write out solvable cognitive models of behavior.
• Modeled working memory, episodic memory, conditioning.
• Representation observed in PFC, hippocampus, striatum.
Make your own cognitive models!
https://github.com/zorant/WM_demo

A dual space using the Laplace transform
F(s) =
∞
0
e−st
f(t)dt
Invertible:
F(s) ⇔ f(t)
Real-time:
dF(s)
dt
= −sF(s) + f(t)

Timelines in the Laplace domain and out
Shankar & Howard (2012, 2013)
F(s) =
t
−∞
es(t−t′)
f(t′
)dt′
• The cells F(s), with a spectrum of s values give
the Laplace transform of f(t − τ).
• A set of weights L-1
k approximate the inverse
transform (Post, 1930).
• The cells ˜f(
∗
τ), with different values of
∗
τ,
approximate the function itself.

dF(s)
dt
= −sF(s) + f(t)
• The cells F(s), with a spectrum of s values give
the Laplace transform of f(t − τ).
• A set of weights L-1
k approximate the inverse
transform (Post, 1930).
• The cells ˜f(
∗
τ), with different values of
∗
τ,
approximate the function itself.

Inverse is just on-center/off-surround receptive ﬁelds
Liu, Tiganj, Hasselmo, & Howard (2019)
Inverse operator L-1
k
• Requires derivatives wrt s
• A gradient of s . . .
• . . . implies
on-center/off-surround
receptive ﬁelds.
Inverse introduces error, but it’s scale-invariant.

Laplace transform of time in monkey EC
Bright, Meister, Cruzado, Tiganj, Howard and Buffalo, (submitted?)
See also Tsao, et al., (2018; Nature)

The future
Greetings, my friend. We are all
interested in the future, for that is
where you and I are going to spend
the rest of our lives. And
remember, my friend, future events
such as these will affect you in the
future.
Criswell

Beginning of the future
• Behavioral evidence for a
timeline of the future.
• Computational models for
scale-invariant future.
• Modeling is out front of the
data.

Human judgements of future events
Singh & Howard (2017, bioRxiv)
Judgment of recency (JOR)
• Rapid presentation of list.
• Choose which probe was
closer to the present.
• Scanning in STM
Judgment of imminence (JOI)
• Statistical learning
• Choose which probe was
closer to the present.
• ???

Remembering the past, predicting the future
Singh & Howard (2017, BioRxiv)
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Recency
ResponseTime(s)
−7 −6 −5 −4 −3 −2
0.7
0.8
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1.0
1.1
1.2
1.3
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Recency
ResponseTime(s)
−6 −4 −3 −2 −1
0.0
0.5
1.0
1.5

Remembering the past, predicting the future
Singh & Howard (2017, BioRxiv)
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Recency
ResponseTime(s)
−7 −6 −5 −4 −3 −2
0.7
0.8
0.9
1.0
1.1
1.2
1.3
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Recency
ResponseTime(s)
−6 −4 −3 −2 −1
0.0
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Imminence
ResponseTime(s)
3 4 5 6 7
1.0
1.2
1.4
1.6
1.8
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Imminence
ResponseTime(s)
1 2 3 4 5
0.5
1.0
1.5
2.0
Past and future both appear to be compressed timelines.

Constructing the future
Tiganj, Gershman, Sederberg & Howard (2019)
• Timeline: what and when.
• Flexible responses.
• Average over possible
futures.
0 5 10 15 20 25 30 35 40 45 50 55
Time
Scale: 5
D
R
2R
0 5 10 15 20 25 30 35 40 45 50 55
Future time
0
2
4
6
Prediction
10-5
Tim
e
0 5 10 15 20 25 30 35 40 45 50 55
Time
Scale: 20
D
R
2R
0 5 10 15 20 25 30 35 40 45 50 55
Future time
0
2
4
6
Prediction
10-6
Tim
e
*
*
See also Mommenejad & Howard (2018; BioRxiv);
Shankar, Singh & Howard (2016, Neural Comp).

Constructing the future
Tiganj, Gershman, Sederberg & Howard (2019)
• Timeline: what and when.
• Flexible responses.
• Average over possible
futures.
See also Mommenejad & Howard (2018; BioRxiv);
Shankar, Singh & Howard (2016, Neural Comp).

Take-home
• The brain computes a compressed timeline of the past.
• Computationally, we can make sense of this using a
Laplace domain dual space.
• There’s new evidence the brain computes the Laplace
transform of time.
• I think we construct a logarithmically-compressed map of
the future.

Zoran Tiganj, Nathan Cruzado, Yue Liu, Andre Luzardo
Inder Singh, Karthik Shankar
Collaborators: Howard Eichenbaum, Michael Hasselmo, Earl
Miller (MIT), Miriam Meister and Beth Buffalo (Washington)
Current funding:
NIH: R01MH112169, R01EB022864, R01MH095297
NSF: IIS-1631460
ONR: N00014-16-1-2832 (Hasselmo, PI)
Private Sector: Google FRA, Facebook Reality Labs
http://sites.bu.edu/tcn/

CNS 2019 - Mental Models of Time - Marc Howard

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CNS 2019 - Mental Models of Time - Marc Howard