# Projection: A Mechanism for Human-like Reasoning in Artificial Intelligence

F. Guerin CONTACT F. Guerin. Email<EMAIL_ADDRESS>Department of
Computer Science, University of Surrey, Guildford GU2 7XH, United Kingdom.

###### Abstract

Artificial Intelligence systems cannot yet match human abilities to apply
knowledge to situations that vary from what they have been programmed for, or
trained for. In visual object recognition, methods of inference exploiting
top-down information (from a model) have been shown to be effective for
recognising entities in difficult conditions. Here a component of this type of
inference, called ‘projection’, is shown to be a key mechanism to solve the
problem of applying knowledge to varied or challenging situations, across a
range of AI domains, such as vision, robotics, or language. Finally the
relevance of projection to tackling the commonsense knowledge problem is
discussed.

###### keywords:

Reasoning, Transfer, Projection, Analogy

##  1 Introduction

There are two major problems in Artificial Intelligence: how to apply
knowledge to varied situations, and how to acquire the knowledge (learn). This
paper focuses on the first. It encompasses knowledge representation and
reasoning, with a focus here on (non-classical) reasoning (a second companion
paper will focus on representation). The focus is on the act of reasoning that
determines if some data can be seen (or interpreted) as belonging to a
particular class, not on long chains of reasoning using diverse knowledge.

A significant weakness of Artificial Intelligence (AI) systems relative to
humans is the inability to apply existing knowledge to a new problem, or to a
situation that varies from what they were programmed for or trained for (also
called transfer ability in some contexts). This causes systems to fail to
recognise objects or activities in new settings, or to fail to adapt skills to
variations (Davis and Marcus,, 2015; Ersen et al.,, 2017). The systems have
knowledge, but they are unable to apply it when the situation changes. This
problem affects AI systems during learning phases as well as in final
deployment phases. Deep learning, the currently dominant approach, is quite
good at learning from scratch, but less able to exploit prior knowledge to
learn rapidly. LeCun, (2018) gives the example of a machine learning to drive
a car by reinforcement learning (with no prior knowledge): it might need to
run off a cliff thousands of times in order to learn to avoid it, whereas most
humans learn to drive a car in about 20 hours, without crashing, which is
remarkable by AI standards. Humans must be able to apply their prior knowledge
of moving bodies, momentum, gravity, friction, etc. to make their learning
problem easier (see discussion in Sect. 5.2.1). Lake et al., (2016) give
similar examples of this stark human/AI contrast for learning to play games.
These authors point to the need for learning systems to be able to exploit
models of the world.

Whether it be for learning, or for deployed systems, there is a need to apply
knowledge across varied situations. Humans do this with ease. When training
for a new task, or tackling an unexpected situation, humans apply knowledge
of, e.g., physical interactions, or social interactions, which they learnt in
different contexts. That is why humans continue to be the only viable workers
in a wide range of industries where AI could not cope with the variation.
Applying knowledge to a situation is a problem of reasoning: It is the
recognition that this situation belongs to a category about which we have
prior knowledge or experience, which is applicable here. It is a very
fundamental cognitive act. Something very fundamental is clearly lacking from
AI. This paper is about  a mechanism called ‘projection’ which plays a crucial
role in the type of (non-classical) reasoning that could get closer to human
abilities, and the implications for representation. The essence is a top-down
process ‘projecting’ conceptual knowledge onto lower level data, and thereby
searching through alternative ways to represent that data. This requires
human-like compositional models of concepts, and also iterative inference
algorithms to find a good mapping (or interpretation) from data to model.

The word ‘projection’ is used here in a way that is not synonymous with top-
down processing. Instead it is a special case of top-down: it is a particular
type of top-down processing which uses a prior compositional model of a
concept, and can influence the interpretation of data in order to match
components required by the model (precise definition in Sec. 4). There are
other types of top-down processing that are not projection, because they do
not rely on compositional models; for example many of the examples of top-down
processing that are reviewed by Firestone and Scholl, (2016) are not
projection, e.g., wearing a heavy backpack makes hills look steeper; holding a
wide pole makes apertures look narrower; desired objects are seen as closer.

In contrast to classical AI, the projection approach does not assume that
there is a ground truth, and that the task is to find the one ‘correct’
mapping of predicates to the world state; instead it allows for various
different mappings to be forced depending on the needs of the situation. In
contrast to deep learning it does not entangle the model of a concept with the
machinery which processes the data to recognise the concept; instead it has an
explicit concept model which is separate from the processing machinery.

The idea of the mechanism of top-down ‘projection’ is nothing new to visual
perception (Epshtein et al.,, 2008), or computer vision (see Sec. 5.1.1).
However, it can be generalised to other aspects of cognition, with potential
application across areas of AI such as higher-level vision tasks, language
processing, and robotics. It is advantageous that we have already working
models of projection in vision (see Sec. 5.1), this helps us to envision
implementations for other cognitive tasks, and to assess the appropriateness
of projection for various tasks, and expected benefits. Matching this
transition from vision to other cognitive tasks, a speculative hypothesis
behind this paper is that the brain circuitry that evolved to do sophisticated
interpretation in visual perception in primates may have been copied and
employed to do other cognitive tasks in humans.

The following are key contributions:

  * •

Illustrating the wide applicability of one mechanism (projection) to solve
problems in a range of AI application domains, at a range of levels from lower
level perceptual processing to higher level abstract concepts (Secs. 5.1.2,
5.2, 5.1.3).

  * •

Explaining the relevance of projection to the long-term final solution to AI,
to achieve commonsense knowledge (Sec. 7).

  * •

Explaining the role of projection in making analogies (Sec. 5.3.1).

##  2 Projection in Humans

As a concrete example of projection, consider the description of a picture,
where a face structure (at a higher layer of description) can be described in
terms of spatial relations among the components eye, nose, mouth, brow (at a
lower layer). The projection mechanism is a top-down process whereby a set of
elements at a lower layer are grouped and interpreted as corresponding to
constituent components of a higher layer. For example in visual perception of
a human face in noisy or poorly lit conditions, every low level element might
not be clearly recognisable and identifiable on its own (Figure 1 (a)). When
an ambiguous perceived element, e.g., arising from the mouth, is given the
interpretation ‘mouth’ partly by virtue of its relationship to other face
elements, this is a result of projection. This projection idea111We adopt the
word ‘projection’ from Indurkhya, (1992); in other texts it may be referred to
as unconscious inductive inference or inference from top-down knowledge
(Gregory,, 1997). has a long history in the psychology of visual perception,
e.g. Gregory, (1997) traces it back to von Helmholtz in the Nineteenth
Century.

######  Benefit 1.

Projection can assign meaning to an ambiguous piece of data by leveraging
higher level prior knowledge and other available data.

In general projection works with hierarchical compositional knowledge
structures where higher layers (e.g. face) describe relationships among
components in lower layers (e.g. eye, nose, mouth). Projection helps to create
a mapping between elements sensed from real-world data (e.g. parts of the
mouth), and the components in an abstract knowledge structure (e.g. symbol for
mouth), where that structure defines the allowed relationships among
components. In perception projection works together (interactively) with
bottom-up processes, to recognise objects, words, or events (Epshtein et al.,,
2008; Samuel,, 1981; Indurkhya,, 2006).

kjjsdflsk kjjsdflsk

Figure 1: (a) Left: Low quality face image. (b) Middle: What looks like a face
in a cliff. (image from SnappyGoat). (c) Right: Advanced projection, the image
could represent a human consoling another.

Fig. 1 (a) is made from an actual face, so to interpret it as a face would be
considered conventional. Fig. 1 (b) is an actual cliff, but the human
projection mechanism can easily interpret it as a face; this is called novel
projection (Indurkhya,, 1992). The same mechanism can produce both
conventional and novel projections: in both cases it maps an abstract
knowledge structure to real-world elements. The difference is in society’s
consensus on what is the ground truth, or typical thing to recognise, in that
real-world data; novel projection leads to recognising something not typically
recognised. Novel projection is of interest because it is important in
creativity (ibid.). Sometimes creativity is important to recognise an instance
of a concept in data; it may require a new perspective to see something that a
cursory analysis fails to see. It is worth stressing that there is no
distinction in processing (or mechanism) between conventional and novel
projection222This point is proved by the fact that a computer system built for
conventional projection will automatically do novel projection when presented
with suitable data, as shown in Fig. 3.: something might be not typically
recognised simply because it is overlooked by many people, and the notion of
‘ground truth’ becomes more open to interpretation as one moves to more
abstract tasks. What is required in either case is a way to search among
alternative possible mappings between a knowledge structure and data from the
world. This type of flexible projection is important to the AI tasks discussed
in the following sections.

######  Benefit 2.

Projection allows for creativity through the novel application of a concept
from one domain to a different domain, or through facilitating a different
perspective using concepts within a domain.

In the example of the cliff face one may be conscious of a projection
mechanism at work, e.g., on seeing eyes and nose, one may search for something
like a mouth in the appropriate location. These difficult conditions merely
make the viewer more conscious of the projection process. In everyday
cognition most projection happens subconsciously. Projection must be happening
all the time in human perception, because typical viewing conditions are
difficult, due to the many ‘defects’ in the human visual apparatus, especially
in the periphery of vision (O’Regan,, 1992). For example, blood vessels and
nerve axons obscure significant areas of the retina, and there is sparsity and
nonuniformity in the distribution of cones.

######  Benefit 3.

Projection assists in the recognition of concepts in difficult conditions.

The more advanced example of projection in Fig. 1 (c) goes beyond purely
visual concepts as it involves affective states and social interaction.
Understanding this image requires an iterative inference where bottom-up
vision detects general form, triggering the possibility that this represents
the human form; this in turn triggers a projection to imagine the human form
in a matching pose, leading to the recognition of the affective states and the
social interaction. The artist who originally created the idea of this
composition performed an analogy (Sec 5.3.1) where the relationship among
parts in the human domain is projected onto the available objects and parts in
the safety-pin domain. The higher-level relations in the human domain (e.g.
bending of the head or arm) organise lower level components in the safety-pin
domain to form the same relationship. There is no actual arm in the safety-
pin, but when the relations from the human domain are imposed on the parts of
a safety-pin then we can recognise the part in the appropriate relationship as
an ‘arm’. To perform human-like projection in machines, the machines will need
to have human-like part-based compositional models of concepts.

Projection is also required to generate images such as Fig. 1 (c). There is
currently some interest in using deep learning to generate artistic works
which showcase an artificial ‘imagination’, e.g. with Deepdream (Mordvintsev
et al.,, 2015; Miller,, 2019). There are also efforts to encourage creativity
by forcing deviation from established styles (Creative Adversarial Networks
(Elgammal et al.,, 2017)). However, current work does seem to be limited by
its lack of a crisp symbolic compositional model of concepts. Despite
significant recent work in the generation of artistic images, the state of the
art does not seem to be capable of producing something like Fig. 1 (c). When a
deep learning system is tasked with imposing the appearance of one concept on
another it tends to introduce spurious artefacts and distortions in the target
concept, which e.g., in the case of the paperclip, make it no longer look like
an actual paperclip that has been bent. Deep learning systems do learn
something about the composition of objects, but it is in a messy entangled
way, not clearly differentiating necessary from incidental features in
training examples, which leads to artefacts in generation. Visual analogies
require an understanding of objects and their parts, ideally in the form of
crisp compositional models, to be able to ‘project’ the structure of one
object onto the parts of another. Such top-down direction would seem to be
required to produce visual analogies (Schwering et al.,, 2009), such as appear
in surrealist artwork or advertising.

###  2.1 Projection beyond Visual Perception

The above examples are in visual perception (at least initially), which is a
special case of more general recognition or judgement. Consider the non-visual
example of sitting on a cushioned seat and then recognising that it is wet.
The immediate sensation of cold may trigger the wetness concept and, top-down,
an expectation of stickiness of clothing when one moves. (The human body has
no sensors specifically for wetness; this concept has a complex mapping to
sensors for touch and cold and their relation with skin movement.) In higher
level cognition, recognition can be called judgement, e.g. in reading a text
or watching a movie, and making a judgement about whether or not a character
is wealthy. The low level elements become details of behaviour or social
interactions, and the higher level concept is an elaborate model of what it
means to be wealthy. Recognition (or judgement) is  a fundamental act of
reasoning; i.e. deciding that something belongs to a class or category. Here
are further examples that span varied domains: judging if a food item (e.g.
pancake or omelette) is sufficiently similar to a cloth (with similar
‘foldable’ properties) such that a similar manipulation can be transferred;
looking out the window and deciding if the utterance ‘it is raining’ is true
(Indurkhya,, 2016); judging if a sequence of transactions in a company’s
accounts indicates that an insider fraud is taking place, or more generally,
assessing a set of facts and judging if a crime is likely to have been
committed by a person.

###  2.2 Projection in Planning

Consider the type of thinking involved in planning physical manipulation
activities, for example rearranging objects in a kitchen cupboard. There will
be a main goal state, involving desired positions of main objects, and a
series of steps will be planned. At each stage there are several potential
candidate sub activities to consider, such as temporarily placing one item on
others, or pushing one item aside. In each of these subactivities projection
is employed, e.g. to make the judgement about whether or not an object can
support another, or if the upper one will roll or fall off. The objects in
question must be modeled by some mental representations, e.g. of exemplar
concepts (cylinder, flexible bag, etc.). Objects are approximated by mental
representations, and this is a process of projection that imposes some model
on an object. Projection is also used in the selection of manipulation actions
to employ: given a need in a step (e.g. to open a gap between objects for
inserting another) the current situation can be matched to similar remembered
situations where a similar problem was solved. Projection is used to match a
stored model of a remembered situation to the current situation. Projection
can again be employed to foresee the consequences of steps: remembered
episodes (including effects) can be projected onto the current situation.
Forbus and Gentner, (1997) describe how analogy can be employed to find
similar remembered behaviours, and to use these for mental simulation. In this
way projection is a component mechanism that works as part of a larger
machinery of cognition, in order to complete physical cognition tasks.

The same ideas can also extend from physical manipulation to more abstract
domains of reasoning, for example reasoning about a criminal case. Motives can
be projected onto actors, given observed or conjectured events. Likely plans
of actors can be conjectured, with projection employed at each step, e.g. to
match the situation under consideration to familiar episodes one has reasoned
about before.

###  2.3 Summary

In all cases above the bottom-up data in the lower layer is ambiguous;
projection will assign an interpretation to a set of lower layer elements
which supports the recognition of the higher layer concept, if sufficient
evidence is deemed to be present. The mechanism of projection is precisely
what Hofstadter, (2001) calls high-level perception, and many more excellent
examples are given in Hofstadter and Sander, (2013). In summary,  projection
is an important component mechanism in human cognition at several levels and
across domains333Indurkhya’s projection (Indurkhya,, 1992, 2007) is synonymous
with Jean Piaget’s assimilation in many contexts., in the remainder we see how
it applies to AI.

##  3 Projection in Computers

Projection can be implemented in various ways, as shown in the next section.
Figure 2 illustrates the general idea, to introduce the terminology for
subsequent sections. The model is the main data structure employed, and is
structured hierarchically, with a minimum of two levels, the higher levels
describe relations among lower level elements; as in ‘face’ describing
relation among ‘mouth’, ‘eyes’, etc., in the previous section. Multiple models
are stored in long term memory, and selected as candidates for interpreting
data. The selection process is beyond our scope, but could use task context,
or other contextual factors making a particular interpretation likely.
Selected models become instantiated in a workspace for the reasoning process.
This involves an interaction of top-down and bottom-up processes for
determining how well a particular model could fit the data. The particular
assignment of elements of a model to elements of data is called a mapping or
interpretation. There may be several instances of the same model mapping to
the data in different ways, e.g. seeing a face in rock with different mappings
to elements. The reasoning process also coordinates across the various mapping
attempts by seeking the best set of mappings that could coherently explain the
data (i.e. ‘explaining away’), or enforcing a mapping that satisfies some
other goal or external pressure, e.g., if in manipulation we want to see a
particular affordance, or if we are asked to apply a particular model. Benefit
1 of projection above (disambiguating data) can be explained in other words as
follows: projection is when a low-level element of data could equally well be
interpreted as an $x$ or a $y$ based on the local data, but I decide to call
it a $y$ because that helps me to have consistent evidence for the recognition
of a higher level concept, with $y$ as a constituent part. I am forcing the
interpretation on the data, or projecting. In the case of novel projection $y$
is not a $y$ at all, and I know that, but treating it as a $y$ helps me to
complete an analogy that may have some advantage; e.g. if a robot treats the
broad base of a frying pan as like the head of a hammer and can then use it to
hammer something.

Figure 2: Conceptual overview of iterative reasoning where bottom-up processes
interact with top-down projection to find the best interpretation of data
(where an interpretation is a mapping of the elements of a model to the data).

The dominant approach in much of recent AI is a purely bottom-up process to go
from low level data to a judgement about a concept. This pathway needs to be
broken open to insert search processes in the middle which can search among
possible alternative mappings between the concept (and its subcomponents) and
the lower level data. Each possible candidate mapping that is searched entails
a different reorganisation of the low level data. Simple implementations of
projection can generate candidate mappings with a search process, and use a
trained scoring function to evaluate candidates (Ben-Yosef et al.,, 2018;
Abelha and Guerin,, 2017); here the top-down signal is implemented by the
scoring function’s selection. More complex implementations can use more
message passing between layers to ‘agree’ on a suitable mapping (George et
al.,, 2017).

##  4 Mathematical Definition

A model $M$ (corresponding to a concept) is an n-tuple of levels
$(l_{1},l_{2}\ldots l_{n})$ where each $l_{i}$ is an m-tuple
$(e_{1},e_{2}\ldots e_{m})$ of elements $e_{j}$. In level $l_{0}$ elements are
empty slots in the abstract model, and will be filled with data during
interpretation. For levels $i>1$ each element in level $l_{i}$ needs to
describe a relation among some elements in level $l_{i-1}$; this is achieved
by each element $e_{j}$ being a pair $(p,f)$ where $p$ is a tuple of specific
‘parts’, i.e. elements from the lower level, and $f$ is a scoring function
mapping parts $p$ to a real value. The scoring function $f$ assigns a value to
$p$ according to how well it captures the intended relation among parts. Since
each part can itself be composed of subparts all the way down to the lowest
level, the function $f$ has access to the full information of the hierarchy of
parts below it. Level $l_{n}$ (top of hierarchy) always has only one element,
ensuring that there can be a single overall score for an interpretation by a
model.

$D$ is a set of data points (which could be e.g. $(x,y,\mathit{colour})$
values of pixels). An interpretation or mapping of $D$ by model $M$ is a
binary relation over $D$ and $l_{1}$ where elements of $l_{1}$ are each
related to at most one (not necessarily unique) element of $D$. Some elements
of $D$ and $l_{1}$ may be unmapped (corresponding to, e.g., missing,
irrelevant or unclear data). If we populate $l_{1}$ with the data elements
mapped by the interpretation, then we can apply the scoring function of
$l_{n}$, and determine how good the interpretation is. Finding a good
interpretation can be called inference or reasoning, and can be complex. A
simple way is to run the $f$ functions of level $l_{2}$ over multiple subsets
of $D$ to find good candidates for $l_{2}$ elements, then run $l_{3}$’s $f$
functions over these candidates to find good candidates for $l_{4}$, etc. This
is roughly how current feedforward networks work. This may however miss out on
a good interpretation because the lower level scoring functions lack
information about what is needed at the top level; it may be that some data
points that produce a poor score for a certain $l_{2}$ element should
nevertheless be used because the overall model fit will be good. Therefore a
superior inference strategy uses top-down information to guide the selection
of parts in the lower levels. We call any interpretation using top-down
information ‘projection’; i.e. where the $f$ functions from a level higher
than $l_{i}$ contribute to the decision about what elements from $l_{i-1}$ to
use.

This definition of projection is quite general, such that feedforward neural
networks with skip connections can implement projection (see Sec. 6.4).
However more human-like projection requires that elements in levels are close
to what humans appear to be using (i.e. the model is more human-like), with
parts that are meaningful to humans, as in the work of Ben-Yosef et al.,
(2018) for example.

##  5 AI Applications

This section explains how projection has been applied in vision, and how it
could potentially be applied to other popular AI tasks. It also highlights the
serious difficulties for existing techniques in these tasks, and explains how
projection offers a way to overcome these.

###  5.1 Projection in Computer Vision

Sec. 5.1.1 gives concrete examples of how projection has been implemented
computationally for visual recognition tasks. Sec. 5.1.2 explains how it could
be applied in higher-level visual tasks.

####  5.1.1 Existing Implementations of Projection in Object or Character
Recognition

Ben-Yosef et al., (2018) present a two-stage process which firstly works in a
bottom-up feed-forward manner to identify one or several objects classes for
an image, and secondly projects previously learned models of those detected
classes top-down, to confirm if that object class is indeed present and give a
detailed interpretation if it is444The authors do not explicitly call it
projection, although at a key part in the Appendix, describing the mapping
from model to image, they do say “We project ground truth annotated contours
on an edge map”.. Their model of an object class (e.g. horse’s head, as in
Fig. 3) consists of primitives and relations among primitives. Primitives
consist of contours, points, and regions. Relations include, e.g. for contour-
contour relations: relative location of contour endings, smooth continuation
between contour endings, length ratio between two contours, and contour
parallelism.

Figure 3: Ben-Yosef et al.,’s (2018) full interpretation system can perform
novel projection, interpreting a man-made object as a horse’s head. Left: the
model’s contours, point and regions (rectangles) mapped to a photo of an
actual horse’s head (conventional projection/interpretation). Middle: the man-
made object. Right: The mapping of the horse contours, point and regions to
the man-made object (novel projection/interpretation). These images are
reprinted from Ben-Yosef et al., (2018) with permission from the author.

The projection occurs in the top-down process forming a detailed
interpretation for a given novel image of suspected class $a$. The relations
and primitives described in the model direct a search for primitives and
relations in the image which could match what the model requires. The only
relations tested for the primitives are the relations stored in the model of
class $a$. The result of the interpretation process is that the system has a
mapping from detected primitives in the image to known primitive parts and
relations in the model for that class, and so could potentially explain its
interpretation in a human-like way; e.g. this is the top contour of the
horse’s head, this is the bottom, this is the ear, etc. The system has a
higher accuracy at recognising small image patches than feedforward CNNs.  The
average precision (AP) for a CNN was 0.78, while the model using
interpretation had AP 0.87. More significant than this performance difference
however was the sudden drop in performance of the interpretation model when
the image patch is cropped further; this matched the type of drop in
performance for humans trying to recognise the patches, whereas the CNN model
degrades more gradually. A side-effect of this human-inspired approach is that
the models learned for objects, in terms of contours etc., can be used for
novel projection. For example, Fig. 3 shows what happened when the model
learned for horse’s head was asked to produce an interpretation for a man-made
object. (The authors worked to modify the model to reject such false
positives, but the process can easily be relaxed to encourage such visual
analogies.)

The work was subsequently extended to tackle agent-agent interactions such as
‘hugging’, ‘shaking hands’, ‘consolation’ or ‘helping’ (Ben-Yosef and Ullman,,
2018). This involves the model capturing relations between elements in the two
different agents, i.e. moving beyond the relations within a single
object/agent. The authors also note the further extension of image
understanding ideas to more abstract concepts:

> The term ‘image understanding’ as used here depends on the image
> interpretation process, but it can be more abstract, in the sense of using
> concepts which go beyond components of the physical world and relations
> between them, for example, goals, moods, judgments such as ‘dangerous’ and
> others. (Ben-Yosef and Ullman,, 2018)

A second example of projection appears in a system recognising the distorted
texts of CAPTCHAs (George et al.,, 2017). Here the models are hierarchical
compositional models of text characters; e.g. ‘A’ being composed of various
oriented line segments and angles. The reasoning employs a ‘recursive cortical
network’ (RCN) which has a hierarchical compositional structure, and performs
a forward pass (bottom-up) to generate initial hypotheses about the letters
present, followed by a backward pass (top-down, corresponding to projection)
to test the hypotheses and explain the data, performing inference by Belief
Propagation. For example, if the letters A and K are partly overlapped in an
image, a letter V could be hallucinated, and is one of the suggestions (in
addition to A, K) after the bottom-up pass. However the A and K can explain
the image without need for the V, so it can be rejected. The RCN also has
lateral connections which coordinate the choice of features grouped to form a
higher-level feature; this ensures smooth contours in letter shapes (actually
implementing some gestalt principles).

The RCN CAPTCHA recogniser of George et al., (2017) was massively more data
efficient than competing CNN approaches which required 50,000-fold larger
training sets. In addition the RCN was much more robust to variations in input
(e.g. spacing of characters, length of strings), whereas the CNN performance
degraded dramatically.

The two implementations of projection reviewed above are quite different, but
both bring significant benefits to their respective tasks, when compared with
feedforward models. Other projection examples in vision also exist (Epshtein
et al.,, 2008; Shanahan,, 2005; Leibe et al.,, 2008; Malik et al.,, 2016). It
suggests that projection is quite a general principle for recognition, so that
a variety of different implementations of the general principle can bring
advantages. Nevertheless, examples of top-down processes are in general rare
in current mainstream computer vision, which is mostly purely feedforward.

####  5.1.2 Applying Projection to Recognising Activity from Video

Firstly consider short-term, or ‘atomic’ actions: actions that are
particularly difficult in the ActivityNet Version 1.3 dataset include smoke,
grab and hug; these actions require fine-grained discrimination (Gu et al.,,
2017), because many of these actions can only be discriminated from other
similar actions by a detailed analysis of the relations among object parts
(explored in detail for still images by Ben-Yosef and Ullman, (2018)). Indeed
hug is one of the primary actions tackled by Ben-Yosef and Ullman, (2018) with
their model-based approach (using projection) on still images, which can
analyse parts of the people in detail, e.g. the hand of one person and the
back of another, and their relationship in the image. This fine-grained
analysis allows the system to discriminate between hugging and superficially
similar actions such as fighting.555Ben-Yosef and Ullman, (2018) compared
their approach against a very deep convolutional neural network model trained
on the same examples as their own approach, and showed significantly better
precision for their approach (0.80 vs. 0.69). This shows that in video
analysis we could improve recognition by applying projection to still images
within the video.

Moving to temporally extended activities, one can extrapolate (although not
tried yet) to expect that applying the projection idea across temporal
sequences would boost the performance for temporally extended activities; i.e.
the primitive elements would be interactions of objects and agents at a
certain time point, and the higher order relations would be temporal relations
among primitive elements, possibly extending to further higher layers in more
abstract activities. For example, a model of loading goods into a vehicle can
begin with a person carrying something (recognisable by characteristic posture
and gait), followed by contact with the vehicle, the loading activity, and
then the unencumbered person departing. Most of the same atomic actions in a
different order would be a model of unloading. The atomic actions on their own
are ambiguous and can be given meaning by the overall activity model
projected; especially if working in noisy conditions where atomic detections
are only partially accurate. The projection here across the temporal domain
shares the characteristics that make projection appropriate in the spatial
domain for still images. Ambiguity of activity components is common in
activities that existing video classification techniques struggle with, for
example, the motion of the hand descending from the mouth could be part of
smoking or part of eating.

Disambiguating the activity in a video is similar to the segmentation problem
in CAPTCHA recognition, where it is not clear what character a certain
fragment of image belongs to; by activating several possible candidate
characters, and projecting them back down to identify what other parts of the
image could be part of that character, we can come up with a plausible
explanation for the data. The analogous situation in video is where a temporal
segment of video could be part of several longer-term activities (but not all
of those are actually happening in the video). By activating models of the
possible longer-term activities and projecting them down to the data one could
find the activities that best explain the data, and reject the possibilities
that are not required to explain the data.

Another analogy between recognising events across time and recognising CAPTCHA
characters is that events can be distorted, e.g. household activities, by
being interrupted by part of another activity, or being done in a non-standard
way with non-typical motions. Again, the top-down fitting of models can
accommodate for this by allowing for deformation of where parts of activities
occur, just like parts of characters in a CAPTCHA. Furthermore there is the
complexity of relations that needs to be computed, which suggests the need for
top-down direction to allow the system to be selective about what relations
must be computed. For example, to discriminate between difficult classes in
ActivityNet (Heilbron et al.,, 2015) such as ‘violin playing’ and ‘inspecting
a violin’ one might need to compute relative pose between human and violin.
Complex relations are also required to discriminate mixing drinks from making
a cake. All of this requires models of the activities in time, something which
can potentially be learned from data (see e.g. Dubba et al.,, 2015).

The state-of the art performance in video activity recognition is much worse
than in object recognition, hindering multiple real-world applications; hence
there is a strong need for new approaches. In a 2018 (AVA Dataset) competition
to classify human actions and localise them (in time and space in the video)
the best mean average precision666average over all videos, mean over all
classes was 21% (Ghanem et al.,, 2018). The classification turns out to be the
main difficulty in this challenge (Gu et al.,, 2017). The authors of the AVA
challenge hypothesise that better recognition will require rich models of
motion and interactions (Gu et al.,, 2017). The leading approaches did not use
top-down processing (Jiang et al.,, 2018; Girdhar et al.,, 2018).

Further insights about what makes activity recognition difficult are given in
the 2015 ActivityNet challenge (Heilbron et al.,, 2015), which is not
restricted to atomic actions. Firstly they note that activities spanning a
longer time are the hardest to classify777In recognising activity from video
there is a range of increasingly abstract tasks (and increasing difficulty),
forming a hierarchy from simpler atomic actions through to more abstract
temporally extended activities, as explained by Gu et al., (2017, citing
Barker and Wright); e.g. let us use ‘$<$’ as a symbol for ‘is a sub-element
of’ (at lower layer): ‘stepping down from the curb’$<$‘crossing
street’$<$‘walking to school’$<$‘working to pass from the third
grade’$<$‘getting an education’$<$‘climbing to the top in life’. The atomic
actions such as ‘stepping down from the curb’ require a relatively simple
analysis of objects (human, curb) and their relationship in space and time,
whereas the more abstract end of the hierarchy would require extremely
elaborate models of the concepts involved, and a video analysis spanning a
long temporal duration (e.g. in a movie)., this is not surprising given that
the typical techniques used do not employ temporally extended models of
activities. Secondly they note that similar activities cause confusion,
especially with similar objects or contexts, and similar motions; this again
is not surprising because the techniques use features derived from networks
for object recognition, with some short range temporal information, and motion
features, but no long-range temporal models. Household activities (e.g.
sorting laundry, mowing the lawn, recycling) were the hardest category of
activities. The structure in these activities is highly variable at the low
level, e.g. activities might be interrupted and resumed, and might happen in
varying orders, but there still is structure, it just requires a more
sophisticated model to account for the possible variation. This is in stark
contrast to activities in the category sports and exercise which “typically
contain a repetitive and structured temporal sequence and are usually
performed in similar scene contexts” (ibid.), existing feedforward models work
very well on these. Overall, temporal action localization (i.e. determining
when a particular action starts and ends in the video) “remains as one of the
most challenging unsolved problems in computer vision” (Ghanem et al.,, 2018).

####  5.1.3 Applying Projection to Higher-Level Vision Tasks

Higher-level tasks employ more abstract concepts; e.g. in vision: image
captioning888Current image captioning tends to perform very badly on out-of-
training-distribution images, see e.g. twitter.com/INTERESTING_JPG. Some kind
of reasoning seems necessary. (Anderson et al.,, 2018), answering questions
about images (visual question answering) (Kafle and Kanan,, 2017), and
recognising more abstract concepts in videos (Hauptmann et al.,, 2007). These
can require recognising abstract relationships among entities (e.g.
friendship), which are more challenging than object recognition due to the
variety of surface appearances (which entails the need for more training
examples for feedforward neural network training). A model-based approach
using projection can map a model to a wider variety of surface realisations
without needing to see so many examples, as demonstrated by the results of
George et al., (2017). Projection requires a model of the concept in question.
For example, for ‘friendship’ it would explicitly describe observable
relationships among people such as participating in an activity together,
eyegaze, smiling, etc. Acquiring such models is a challenge yet to be tackled.

A further vision task where projection is required is visual context. It is
surmised that there are ‘context frames’ which are structures encoding
knowledge about likely objects in a particular scene and their relationships
(Bar,, 2004); a context frame becomes activated by rapid coarse processing of
a scene, and thereafter exerts top-down influence on the perception of
elements of a scene (ibid.). For example, Torralba, (2003) has shown how the
same shape in a blurred outdoor street scene could be perceived as a car or as
a pedestrian depending on its position and orientation. This suggests that the
context frame for a street scene is a probabilistic model which allows for
buildings, streets, vehicles, and pedestrians, only at certain locations,
scales, and orientations, relative to each other. Given a blurred image with
recognisable building to the rear, and street in front, a horizontally
elongated blurred object on the ground at the far end of the street is most
likely a car, but the same blurred object rotated 90 degrees, and on the
street nearer the observer, is most likely a pedestrian. According to this
formulation the type of model for a face described in Sec. 2 may well just be
a special case of the more general class of models that could include a
context frame.

###  5.2 Projection in Robotics

A projection mechanism could help robotics to advance in applications in open
environments (e.g., everyday tasks in the home or a workplace with varied
objects or scenarios) where current performance is very far short of human
level (Ersen et al.,, 2017). While robots can be programmed for specific tasks
with specific materials, they do not generalise their behaviour well when
there are slight changes in conditions. See for example the struggles to pick
up products in the Amazon Picking Challenge (Correll et al.,, 2016). Similarly
for household tasks; while there are robots programmed to fold clothing
(Miller et al.,, 2012), that will work for certain clothing, it is quite a
leap to consider how a robot could transfer any of that knowledge to the case
of a folded pancake (Beetz et al.,, 2011), which requires specific
programming. Humans however, even young children, easily make transfers across
domains. The ability to transfer in a human-like way would go a long way to
solving robotics challenges in open environments. Such transfer is surmised to
require an element of creativity, working by creating a mapping between
scenarios (Fitzgerald et al.,, 2017). This is the mechanism of analogy, which
is hypothesised to require a top-down process that reorganises bottom-up
perceptual data (Hofstadter and FARG,, 1995; Indurkhya,, 1992). See further
discussion in Sec. 5.3.1.

The remainder of this section speculates on how projection could be applied in
robotics, where models are robot skills combining perception and action (i.e.
where the motions involved are parameterised by values returned from
perception; see e.g. Gajewski et al., (2019)). Projection can allow a skill to
be transferred across varied situations. Ideally a robot should be able to act
similarly to a human toddler who learns a new manipulation skill and then is
eager to apply it to every situation that affords the opportunity (much like
the saying that “If all you have is a hammer, everything looks like a nail.”).
Consider for example a “peg in hole” skill which includes perception routines
to detect a hole, and its orientation, and to recognise the shape and major
axis of the (cylindrical) peg. Assume the robot has been coded with a skill
that consists of a first phase where the end of the peg is pressed to the
aperture, but not in the correct orientation for insertion, followed by a
second phase where the peg is kept in contact with the inner edges of the hole
(using force feedback) while being rotated into the correct orientation,
followed by a final phase where it is pushed into the hole. Each of the phases
of motion will be parameterised according to the keypoints (e.g. nearest edge
of aperture) and orientations extracted by perception for a particular
scenario. To enable projection the perception routines need to use a
hierarchical compositional model: the aperture of the hole must be modeled as
consisting of relationships among neighbouring edge segments, surrounding a
space (similar to how George et al., (2017), described above, would model the
letter ‘o’). The inner walls of the hole must be likewise modeled as a
composition of wall segments. This model can then be projected on varied
scenes to identify approximate holes, for example in a crate packed with
groceries where there is a gap creating an approximate hole; here the items
surrounding the gap have enough edge components in a suitable configuration to
approximate an aperture. When the aperture and hole orientation are identified
the motor skill can be applied to insert e.g. a bottle. The skill can likewise
be generalised to an open jar of food for inserting a cooking utensil. To deal
with complex varied shapes we could first approximate shapes with a coarse
mesh, before searching for elements of an aperture.

In this projection the perceptual process is driven top-down. Starting with a
need to achieve a task, this triggers likely skills, and then the perceptual
elements that are prerequisites of those skills are selected for. E.g., to
attempt to see possible holes, even if only approximate matches. Perceptual
grouping processes (e.g. seeing separated edges or surfaces as one long edge
or surface) and perceptual approximations (e.g. ignoring fine grained detail,
or approximately fitting geometric shapes) can be influenced by top-down
pressure. This top-down direction overcomes the problem of too many potential
approximate matches for perceptual abstractions if they were all triggered
bottom-up from the environment. When the task exerts a top-down pressure in
this way we can say that the perception or the representation is ‘task-driven’
(Guerin and Ferreira,, 2019; Zhu et al.,, 2020). A disposable representation
can be created as needed at a specific time, and a different representation
can later be created for the same scene, if the task is different. This also
exposes the forcing aspect of projection: in mapping a model to a situation it
can create similarity rather than simply record an existing similarity
(Kittay,, 1982).

A second example shows how the perceptual elements matched do not need to all
belong to one feature such as an aperture, but can be different parts
referenced in the skill. Consider a group of rectangular cereal boxes in a
shelf, tightly packed like books in a bookcase, so that the smaller side
surface of each box is facing the robot, and each box is wedged between
others. Assume the robot has a skill for removing a box by first exerting
pressure on the top surface and pulling back towards itself, causing a
rotation of the box, and exposing the left and right sides for a subsequent
grasp. Let us call this the skill “pull surface to rotate”. The key
environmental elements in this model (skill description) are the top surface
which will be pushed, the surface of the shelf on which the box stands, which
resists the push, and the direction of the pull, where there must be free
space. When the robot wants to transfer the skill to a different scenario it
needs to make a mapping between the key model elements and entities in the new
scenario. This is effectively assigning an interpretation to the elements of
the new scenario as parts of the skill description (similarly to how contours
in an image could be assigned an interpretation as parts of a face or horse’s
head above). For example: a pizza box lies flat in a freezer. The robot needs
to carry out a search through possible mappings from its skill elements to the
scenario elements. In this it searches through the available surfaces of the
new target object, and the directions in which the motion could be applied,
and simulates the effects of these, eventually choosing to push on a side
surface and rotate the box upwards. This search process requires an
interaction between bottom-up information from what the environment affords,
and the top-down needs of the task dictating the elements to search for,
together with simulation to try out potential mappings of the skill to
environmental elements. An implementation of this does not exist. The general
idea is discussed further in Sec. 6.2.

######  Benefit 4.

Projection can allow skills to be transferred to novel scenarios.

From the perspective of the projection process this is really no different
than what has been called Benefit 2 or 3 above, but for robotic skills some
new processes need to be added to check the physical plausibility of a
proposed mapping from a scenario to a skill (which were not required in e.g.
recognising a face in a cliff). The use of projection to transfer skills can
be thought of like the toddler applying a new skill to everything; one should
be able to attempt a mapping from a skill to any scenario, e.g. to push on a
surface and pull to rotate an object. In many scenarios the result is poor,
much like one can try to see a face in any cliff, or in a pattern of clouds.
This is also the idea behind doing ‘the same thing’ in ‘Tabletop’ (Hofstadter
and FARG,, 1995). In the other direction one could fix the scenario and apply
all skills in the library to see what is produced. This is a productive aspect
to projection: an agent can generate multiple different possibly novel
representations of a scene by applying its skills. Some of these may lead to
interesting creative solutions to a manipulation problem. It is also worth
appreciating the creativity in mundane everyday manipulations. Everyday
activities in unstructured environments involve the interpretation of
scenarios that were never encountered in exactly the same configuration
before. Also the skills applied are typically unique (in their details) to the
agent that has learned them. That is why the act of projection can be seen as
one “through which a cognitive agent asserts its creative spirit onto the
environment” (Indurkhya,, 2006).

The above description of the pull-to-rotate skill omits the steps involved in
progressing from learning a skill (e.g. from demonstration (Burke et al.,,
2019; Zhang et al.,, 2018)) in a given scenario to generalising that skill
(see e.g. Huang et al., (2019)) by understanding the essential elements and
their relations. There are many elements of surfaces, edges, objects in any
learning scenario, and the robot will not initially know which are important
to the success of the skill. The progression to a generalised skill could
involve trial and error while applying to new scenarios, or the application of
causal models to explain what happens in a scenario. Here I am only focusing
on the projection mechanism that takes an existing model (of the skill here)
and applies it to varied scenarios. The application constitutes a sort of
reasoning or judgement: if the robot finds a mapping of elements and is
confident that it should work, then the robot has made the judgement that this
scenario is one belonging to the class where the skill can apply.

####  5.2.1 Transferring Physics Knowledge

Sec. 1 gave the example of transferring prior knowledge of moving bodies,
e.g., momentum and friction, to a novel scenario (learning to drive). In a
human this may happen through early development. Pushing objects on surfaces
gives an idea of different frictions, and the experience of overcoming static
friction. The beginnings of momentum may be learned by swinging a heavy
object, for example a bucket of water, and discovering the difficulty of
stopping it, and its destructive power to move other objects in a collision.
The combination of friction and momentum ideas can be experienced with
knowledge of running and stopping, leading to sliding on a gravelly surface,
or other surface with lower friction. These are just some example
interactions; a human is likely to experience many during development, and may
generalise over similar experiences by self-supervised learning (e.g. for
prediction, see LeCun and Misra,, 2021), producing a generalised ‘schema’ for
momentum and another for friction.999Any newly experienced episode should
spawn a schema based on this example of one, and should later become more
generalised as further similar experiences are gathered. The schema is a model
at an abstract level, e.g. for momentum, representing a generic heavy object
and a motion path, and the expectation of difficulty to slow it, or its
ability to crash through an obstacle. It is only one step more abstract than
actual experienced episodes; it is not modern textbook physics knowledge, but
would be common to ancient peoples also. It suffices for the knowledge to be
implicit and tied to certain experienced contexts, not necessarily generalised
to universal rules. Such a model can then apply by projection to a new
scenario with a moving object, to create an appropriate expectation when
elements are instantiated (mapped) to that scenario; e.g. to create the
expectation in a learner driver of the possibility of sliding on gravel and
continuing straight when attempting to make a turn at speed. Transferring
these ideas to robotics requires a similar training regime with diverse
experiences, and self-supervised learning to generalise models. Each model or
schema of a physical interaction (like that for momentum above) captures a
fragment of physics. A large set of models would approximate human intuitive
notions of physics.

###  5.3 Projection for High Level Understanding

Recognising more abstract concepts in videos or text is required for advanced
applications in video retrieval, or text understanding (e.g. summarisation).
E.g., consider the concepts of betrayal, or falling in love, which might not
be explicitly mentioned in the medium at all. Recognising such concepts from
video or text involve the same reasoning process if both become translated
into some abstract representation of scenes and activities happening along a
timeline, and higher-level concepts are relations among entities in this
abstract description. Understanding text requires the reader to fit concepts
to an ongoing simulation of an unfolding story, entertaining alternatives
(where multiple interpretations are possible) and then dismissing alternatives
when simulations are inconsistent (Allen,, 1995); understanding video requires
the same. E.g. imagine that the task is to identify the scene where the first
act of betrayal is depicted, and the scene where the betrayal becomes apparent
to the betrayed. We would need a model of betrayal which includes a trust
relationship established between two characters at some time, and some
discretionary actions taken by one party against the interests of the other at
another time, especially when such actions form part of a plan to achieve some
goal. Many actions may be ambiguous in isolation, but as plans and goals are
gradually recognised those actions take on more definite meanings. This may
mean that scenes from an earlier part of the story take on a new
interpretation in light of later revelations (i.e. under top-down pressure
(projection) from the concept that has been hypothesised to be present).
Another example is the concept ‘fraud’. With a sophisticated model of insider
fraud in a company, one could develop an AI application that would detect
fraud from company accounts by projecting this model. As with the betrayal
example, many transactions would be difficult to interpret at first, but with
further analysis some of them may fit a model of preparatory behaviour for a
fraud attempt. Again we can see the subjective role of the observer in making
a judgement about betrayal or fraud, and recall the discussion in Sec. 5.2
which noted that projection is is an act “through which a cognitive agent
asserts its creative spirit onto the environment” (Indurkhya,, 2006).

In these examples the reasoning process involves interaction between bottom-up
interpretations and top-down projection from plausible models. This presumes
complex models of plans and concepts such as betrayal. The variety of surface
appearances and difficulty of amassing training data make this type of problem
more suited to a model projection approach. It takes time for humans to learn
such models, and a child watching a complex movie will not interpret the
scenes as an adult would, and similarly for a novice inspecting company
accounts. Even for concepts that children understand, projection is important
for them to be able to be recognised in a wide variety of situations.

Full understanding of natural language may require projection using models
learnt outside of language processing, e.g. from sensorimotor interaction. To
model a physical situation described in text, and to understand the
consequences of various actions or events, one would need at least a partial
simulation of the physical situation (see further comments on projection’s
role in simulation at the end of Sect. 7). Beyond physical situations, many
concepts in language borrow from sensorimotor experiences or other concrete
experiences by analogy (Lakoff and Johnson,, 1980), e.g. the idea of time
‘running out’ as though it were a container of liquid or particles; human-
level understanding of such language may require a link to the physical model,
to understand consequences, by analogy, in the same way as a human.

> Language does not stand alone. The understanding system in the brain
> connects language to representations of objects and situations and enhances
> language understanding by exploiting the full range of our multisensory
> experience of the world, our representations of our motor actions, and our
> memory of previous situations. (McClelland et al.,, 2020)

####  5.3.1 Projection’s Role in Novel Analogy

The difference between the projection described in the previous subsections
and making novel analogies is that above the model being projected is commonly
applied to the domain it is projected on, whereas in a novel analogy the model
comes from a domain not usually applied to this data. In analogy there is a
source and destination, e.g., in the sentence “The speaker was meandering.”
the source is a river taking a slow twisting path in a valley or floodplain,
eroding and depositing sediments; the target is a speaker making a speech.
Novel analogies require search processes in addition to projection. In the
meander example: it is necessary to search through aspects of the target
‘speech’ (e.g. the physical movement of the speaker, the pronunciation of
words, the choice of topics, etc.) that could potentially serve as elements to
be mapped to a model of the source, and it is necessary to search through
aspects of the source (e.g. is it the speed, the changing direction, the
erosion?) that could be modelled and mapped to the target.101010We are
assuming here that the person hearing the sentence is encountering this
analogy for the first time. When it becomes familiar no such search is
required. This is a parallel search process with interaction between
preliminary results in the two searches. Projection is the top-down forcing
element in this interaction, because it imposes the structure of the source on
the target (the similarity creating aspect noted by Kittay, (1982)). Balancing
this in the bottom-up direction is the resistance of the target to having any
arbitrary structure imposed on it. In the meander metaphor the final result
may vary for different people: some may focus on changing direction applied to
topics in the speech, while others may focus on the slow speed and lack of
clear purpose.

With metaphorical language a common approach in AI is to paraphrase it into a
more common expression which the computer can process with standard techniques
(Mao et al.,, 2018), using dictionary resources which code alternative
meanings for common metaphors. This approach loses some nuance of the original
meaning. Analogical machinery could help to achieve human-level understanding:
the concept in the metaphor would be applied to the elements of the novel
domain by projection to create a representation of the analogy in the
computer. In general, language processing requires the fitting of possible
candidate concept representations to the ongoing story in a top-down process
sharing similarities with model fitting in vision or finding mappings for
transfer in robotics. There needs to be considerable flexibility in how
concepts can be applied. Consider for example ‘This can contain the water.’
and ‘We need to contain the fallout from this scandal.’ There is a need for a
knowledge representation (concept representation) for ‘contain’ or ‘container’
which could give extreme flexibility in application. Even the simplest words
seem to require the same kind of projection machinery:

> To check whether a plate is on a table we can look at the space above the
> table, but to find out whether a picture is on a wall or a person is on a
> train, the equivalent check would fail. A single on function operating in
> the same way on all input domains could not explain these entirely divergent
> outcomes of function evaluation. On the other hand, it seems implausible
> that our cognitive system encodes the knowledge underpinning these
> apparently distinct applications of the on relation in entirely independent
> representations. The findings of this work argue instead for a different
> perspective; that a single concept of on is indeed exploited in each of the
> three cases, but that its meaning and representation is sufficiently
> abstract to permit flexible interaction with, and context-dependent
> adaptation to, each particular domain of application. (Hill et al.,, 2019)

This analogy mechanism can also be applied in robotics to transfer skills
across different domains. In the language of mapping a ‘source’ and a
‘target’, the source is the skill from our repertoire that we want to apply,
and the typical situation it has operated in, the target is the new scenario
in a different domain that we are attempting to adapt the skill to. Sec. 5.2
assumed that the key elements of the source are known, and only a search of
ways to represent the target is required to map components. In a full novel
analogy a search of possible ways to represent the source is also required.
The effect of this type of analogical machinery is that scenes are open to
multiple perspectives (as stated in Sec. 5.2), but also that each skill can be
very general (across domains) as soon as it is learned (although the early
applications may not be very successful when the consequences of cross-domain
transfer are not yet understood). This may get closer to how humans learn a
skill in a context first, and then can quickly generalise that to other
contexts.

##  6 The Current Status and Prevalence of Projection in AI

Despite the advantages that human-like projection could bring to robotics or
advanced vision tasks like video analysis, it is mostly not being researched
in these areas; instead the vast majority of work uses feedforward neural
networks (FFNNs). A number of likely reasons include: it is not fashionable at
present (many researchers simply follow the dominant trend); people find it
easier to improve and extend existing (e.g. FFNN) techniques rather than build
a new approach; the examples of projection in Sec. 5.1.1 show that
considerable effort is needed in designing new models and annotated datasets
to capture human-like compositional models (Ben-Yosef et al.,, 2018), as well
as iterative inference algorithms (George et al.,, 2017). This section
considers the status of projection, and related work.

###  6.1 Compositional Models

The need for compositional models has been discussed extensively elsewhere
(Lake et al.,, 2016). A compositional model with relations among parts can
accommodate examples that combine parts in ways not seen in training data, and
this is a way to overcome the explosion of training data needed for simpler
pattern recognition approaches (See Yuille and Liu, (2018) Sec. 7 and Chollet,
(2017) Chap. 9). For a complex concept, compositional models allow it to to be
recognised in quite different manifestations, and examples of this were
discussed in Sec. 5.3. Generative models that capture underlying structure
allow ‘analysis by synthesis’ or ‘generative inference’ (van Bergen and
Kriegeskorte,, 2020). However, although the need for compositional models has
been recognised by the prominent researchers cited above111111These are not
necessarily widely accepted opinions however, the authors are analysing the
limits of the currently popular approaches which are not based on
compositional models., most current work does not use compositional models.

Deep learning models learn the manifold of the training distribution, and this
limits them to the manifestations in the training distribution, with some
interpolations between being successful. If a deep learning model is used to
generate samples it can generate unrealistic samples when pushed to generate
in regions of the space without training examples, and the way in which its
latent space does not capture reality becomes apparent. For example, in GANs
generating images conditioned on pose, human legs can be broken in pieces when
an out of distribution pose is forced (Ma et al.,, 2017). Efforts to lengthen
the sleeve on a T-shirt can lead to the arm taking on an intermediate colour
between skin and clothing. The model does not capture the underlying structure
of the real world. Humans in contrast can use their background knowledge of
underlying real-world structure to go beyond the manifestations they have
seen. For example, a human can understand the pose of a ballet dancer even
when the body appears in a configuration they have never seen before and are
incapable of producing themselves (e.g. with legs making a 180∘ angle while
the body stands upright with one leg pointing up and one down). To generalise
to articulations that are possible but not seen in training examples, it is
necessary to model the underlying skeletal structure and the constraints on
the joints. It is difficult to see how current methods could learn this from
surface appearance without some strong inductive biases.

###  6.2 Mapping Models to Data: Inference System

George et al., (2017) show that iterative inference with a model is relatively
complex, even for simple concepts. Lake et al., (2016, Sec. 4.3.1) also
discussed the computational challenges of inference with models. Both of those
examples relate to written characters of text. Ben-Yosef et al., (2018) do
inference with models of small parts of objects. There is a need to move up to
higher level concepts, e.g. human activities, and models of physical and
social interactions. We see the outline of the required inference algorithm in
George et al., (2017), and also the iterative inference sketched by van Bergen
and Kriegeskorte, (2020): iterations of message passing between higher and
lower layers to converge on an interpretation of the data. This paper has
focussed on the top down information in ‘projection’ but this is just part of
the more general idea of complex iterative inference in which messages may
pass between components at various levels of abstraction. In general we can
expect to have specialised modules to handle parts of interpretation, such
tasks as (e.g. for video) object recognition, tracking, atomic actions,
assignment of intentions to agents, etc. but no such module should be expected
to complete in one pass from input to output, instead they should negotiate
with each other to agree an interpretation. This may require a blackboard or
workspace where candidate interpretations are constructed and compete to be
the winning interpretation. The workspace would also need to link to world
knowledge and simulation to impose plausibility constraints. While the effort
to build an inference algorithm for complex concepts is daunting, an exciting
aspect is that this may be a ‘master algorithm’ that is used across a wide
variety of sensorimotor and cognitive tasks.

###  6.3 Models: Representation, Inference, and Learning

Projection relies on hierarchical compositional models. These structures may
be hand-designed or learned. In the case that the structures are hand-
designed, this is still not like classical AI which suffered brittleness when
outside scenarios the designer envisaged (Brooks,, 1991). Classical AI assumed
a one-to-one mapping between its symbols and entities in the world; the world
was to be interpreted in only one way: the ‘ground truth’ interpretation
envisaged by the designer. A system with projection is different because
interpretation is not fixed by the designer: the system itself can search for
different ways to map symbols to real-world entities, and can change its
interpretation at any time, and can come up with interpretations the designer
might not have envisaged. This means that projection makes the knowledge
structures extremely transferable, to distort the system’s perspective on
reality and apply to a wide variety of situations (which may entail making
mistakes); which is very different to classical AI.

One barrier to implementing projection is the perceived need to learn the
models first. It is not clear how this learning should be done in general, for
complex concepts, and it is probably difficult. The preference for learning
rather than hand-crafting models may stem from the fear of repeating the
mistakes of classical AI with its hand-crated representations that proved
brittle when connected to the real world, and also the limited complexity of
hand-crafted models. However, if work could progress in parallel on the three
major AI problems, they might help each other: 1. Representation
(Understanding what models should look like); 2. Inference (Mapping models to
data); 3. Learning models. If we knew more about the types of models that
bring classification closer to human level (which Ben-Yosef et al., (2018),
e.g., clearly have done), and allow efficient inference, then that would help
us to understand how to design learning algorithms that could learn those
types of models. The current dominance of learning in AI acts as a barrier to
progress in representation and inference.

###  6.4 Related Work in Deep Neural Networks

If projection and compositional models are important in human cognition then
why are purely feedforward neural networks (FFNNs) fairly successful on some
of those tasks that humans can do? van Bergen and Kriegeskorte, (2020) explain
how a recurrent neural network (RNN, i.e. with feedback or top-down
connections) can be unrolled to a larger FFNN which emulates the RNN, where
the recurrent connections become skip (or residual) connections. This is an
important insight: although we normally think of projection as top-down, the
same effect could be achieved in a FFNN. Concretely: if a few FFNN layers give
us a guess ‘this might be a horse’s head’, then we might want to look again at
the contours to check if the top of the horses head is indeed there with the
shape we expect, hence we can have the result of that lower contour layer
passed in to the next FFNN layer again (via skip connection). However, the
FFNN version of an RNN is less efficient, and some RNNs would lead to
infeasible FFNNs if unrolled (ibid.). van Bergen and Kriegeskorte, argue for
generative models and iterative algorithms for inference, especially to enable
“robustness to variations in the input”. FFNNs need to see examples of
variations in training, while generative models can ‘imagine’ combinations not
in the training distribution.

Some recent works do bring an element of iterative inference within a neural
network framework. Goyal et al., 2021b  introduce a workspace to which
selected specialist modules can contribute information. The contents of the
workspace are then broadcast to all modules. Key-query-value attention is used
both to decide who gets to write to the space as well as what information
modules read from the space afterwards. In an alternative approach Goyal et
al., 2021a  use a working memory to store information about entities and use
neural ‘production rules’ to manipulate it. If a rule matches some entities in
memory then it is triggered and a computation is performed to update the
working memory. The computation is implemented by a multi-layer perceptron.
Mittal et al., (2020) describe experiments with deep recurrent neural net
architectures in which bottom-up and top-down signals are combined; they use
key-query-value attention to be selective about which information is combined.
They applied the system to various tasks and provided insightful analysis of
how the top-down information was used. Firstly the top-down information is
used very sparingly, e.g. in one experiment only 2.86% of the total attention
was to top-down information. Secondly when noise is added to data there is
increased attention to top-down information; “the model learns to rely more
heavily on expectations and prior knowledge when the input sequence is less
reliable.” (ibid.) Thirdly top-down information is relied on more when objects
in vision are occluded or partially occluded. Iterative inference is also a
feature of the recent GLOM (Hinton,, 2021) which aims to represent part-whole
hierarchies in visual scenes.

In these works there is a trend towards more iterative inference, which is
moving closer to human-like reasoning; i.e. the trend starting with skip
connections, and progressing to attention models which maintain, and iterate
with, higher-level hidden states, and then the recent Perceiver (Jaegle et
al.,, 2021) where latent units can have multiple interactions with each other
and the input data. There is an evolution towards the type of inference which
van Bergen and Kriegeskorte, (2020) describe. The following are some major
gaps between the above approaches and what needs to be tackled to achieve
human-like reasoning:

  * •

The tasks tackled and the concepts are fairly low level, e.g. predicting
future frames in a video of MNIST digits moving and bouncing off the frame’s
edges (Mittal et al.,, 2020). Mittal et al., explicitly state that in contrast
to other work on higher level entities “the current work focuses more on micro
modules.” It is impossible to know if the current approaches are adequate to
tackle more advanced concepts until it is attempted, but it seems likely that
new approaches would need to be introduced.

  * •

Representations of concepts need to be composed of parts that are similar to
the parts humans use, if human-like reasoning is to be emulated. It is not
clear if this is necessary in order to have a competent AI system, but large
differences in internal representation are likely to lead to different
reasoning outcomes in certain situations, e.g. current object recognition
systems focus less on contours and more on textures than humans and as a
result generalise quite differently to humans (Geirhos et al.,, 2019). How to
discover human-like parts in the case of vision has been addressed by Ben-
Yosef et al., (2018), but less is known about how to determine parts of more
abstract concepts.

  * •

Iterative inference will need to get more complex than e.g. a single
bidirectional interaction with a workspace (Goyal et al., 2021b, ). As
described by van Bergen and Kriegeskorte, (2020), it may be necessary to move
away from the idea of setting the goal as mapping inputs to outputs, but
rather to target the network’s dynamics; then rather than a fixed number of
iterations, the number of interactions could vary, according to the network
dynamics, as appropriate to the difficulty of the particular reasoning
problem.

  * •

There needs to be a way to incorporate background knowledge (all the systems
above are trained from scratch). Humans have background conceptual knowledge
that can be applied across varied reasoning tasks. Background knowledge seems
to be the only way to deal with high level tasks without needing infeasibly
large amounts of training data.

It is difficult to encourage research on more human-like model-based
approaches if the performance benefit is not dramatic relative to FFNN
approaches. Moving to higher level tasks can be expected to bring a bigger
performance difference, where the FFNN unrolled approach may be infeasible,
and where there are more possible diverse manifestations of the same concept,
meaning the required training set and training time for an FFNN becomes
infeasible.

###  6.5 Characteristics of Tasks Suited to Projection

Projection is not important for every task, this section looks at
characteristics of suitable tasks. Firstly if there are not many examples to
train from then the learner will not be able to see the many different ways in
which parts can be arranged, and interpolation between examples will be
insufficient. This is exacerbated in situations where the concepts appear in
many varied configurations in the data, e.g. the distorted text in CAPTCHAs,
or the many ways a betrayal could be depicted in a movie. Projecting a model
overcomes this, as described in Sec. 6.3. George et al.,’s system boasts much
higher accuracy and data efficiency (lower sample complexity) than FFNN
approaches. Secondly if there is high ambiguity in data and the concepts that
one is trying to recognise have complex relationships with the data, then
there are three problems:

  1. 1)

A bottom-up process can see sufficient evidence for many things in the data,
but perhaps only one is correct. This relates to the difficulty of segmenting
the characters in recognising CAPTCHAs; a local piece of data could plausibly
be a part of a few different concepts (or in understanding movies the piece of
data could be a particular event in a movie).

  2. 2)

It is difficult to learn the complex relationships from scratch, from data.
When the relationship is only approximated then the model can be fooled by
examples which present some strong evidence but not in quite the right
configuration.

  3. 3)

If there are multiple possible concepts, each requiring different relations,
then a FFNN implementation would need to compute all of these in parallel
which could be infeasible.

In contrast the projection approach can solve problem 1) by a top-down and
bottom-up interaction: a first bottom-up pass gives preliminary hypotheses
about concepts present (only a subset are really present), and a rendering of
those hypotheses through top-down generation can find the minimum number of
concepts to explain what part of the data could belong to explained by each
concept (George et al.,, 2017). This is a type of imagination, and more
generally projection should be helpful in cognitive tasks requiring
imagination. Concepts for which all the required evidence is present can still
be ruled out if there is a simpler explanation for the data as a whole.
Compositional models can solve problem 2) by first learning sub-concepts, and
then learning higher concepts as relations among sub-concepts. Existing FFNNs
do this to an extent, but they have not succeeded in learning human-like
compositional models, as shown by Ben-Yosef et al., (2018) and Ben-Yosef and
Ullman, (2018); FFNNs tend to pay more attention to textures and would need
some additional biases, and perhaps curriculum learning, to force them to
learn more human-like compositional models. Problem 3) is solved by only
computing relations required by concepts that are likely after a first bottom-
up pass (Ben-Yosef et al.,, 2018).

Many tasks currently successfully tackled by FFNNs do have these
characteristics to a degree. Projection becomes more relevant for tasks that
have the characteristics more strongly, such as the higher-level tasks
outlined in Sect. 5.3. For recognition from still images the following tasks
challenge current techniques and projection would be promising for them:
abstract recognition121212meaning that the general form of the object is
present, but the local features do not resemble those of the real object, for
example in recognising a shape resembling an object in clouds. or Fig 1 (b)
and (c). (Dickinson,, 2009), when using context is required to help
recognition, when objects occur with heavy occlusion, or a collage of multiple
images (Russakovsky et al.,, 2014) (which is similar to abstract recognition),
and also when a small patch needs to be recognised (Ullman et al.,, 2016)
(which is similar to occlusion).

Finally, projection has a role for general purpose AI: Most existing AI
systems focus on a single task, or fixed set of tasks, such as a robot picking
and placing orders, or a system captioning images, or translating language. In
the future AI systems will be expected to perform more diverse tasks, until
they are expected to have the diversity of humans. Projection then becomes
more important, to incorporate top-down input and to create a representation
appropriate to the task at hand. In robotics a system would be overloaded if
it had to consider every possible manipulation it could potentially do on
entering a workshop; instead the robot needs to be directed by its task, and
attend to the objects and features that could be used for the task (this is
called task-driven representation in Sec. 5.2). In vision a human looking at a
street scene and identifying every object that could be there, and every
concept that could be inferred, would likewise be overloaded. Typical computer
vision tasks of identifying objects in images or captioning images are quite
artificial compared to what humans normally do while carrying out real-world
tasks. Humans rarely have the task of identifying everything in an image, or
creating a caption for no particular purpose; humans normally approach a scene
with a very specific task of finding something they are looking for (not
necessarily an object, but perhaps an action or event), this uses top-down
direction.

Conversely, there are also tasks where employing projection will not be
beneficial. For example, projection will not be beneficial where ample
training data is available to cover all the distribution of cases that will
arise at deployment-time. Also in narrow task specific systems, such as the
areas where automation is already very successful, projection will not be
beneficial.

##  7 Implications for Representation (Concepts, Common Sense, and Situations)

Projection provides a way to connect models of knowledge to lower level data,
and can bridge the symbolic and sub-symbolic, so it has implications for
concepts and commonsense knowledge. Connecting commonsense knowledge bases to
the world is a major challenge for AI. There have been numerous efforts at
creating knowledge bases designed for commonsense reasoning, however a recent
survey of work on benchmarks for commonsense reasoning found that: “Despite
the availability of common and commonsense knowledge resources discussed in
Section 3 [their paper], none of them are actually applied to achieve state-
of-the-art performance on the benchmark tasks, and only a few of them are
applied in any recent approaches” (Storks et al.,, 2019, Sec. 4.4); instead
they found that people train deep learning models with various datasets, and
the knowledge is implicit in the learned model and pre-trained word
embeddings.

AI has for decades attempted to code commonsense concepts, e.g. in knowledge
bases, but struggled to generalise the coded concepts to all the situations a
human would naturally generalise them to, and struggled to understand the
natural and obvious consequences of what it has been told. This led to brittle
systems that did not cope well with situations beyond what their designers
envisaged. John McCarthy (1968) said “a program has common sense if it
automatically deduces for itself a sufficiently wide class of immediate
consequences of anything it is told and what it already knows”; that is a
problem that has still not been solved. Marvin Minsky (1998) estimated that
“Common sense is knowing maybe 30 or 50 million things about the world and
having them represented so that when something happens, you can make analogies
with others.” Minsky presciently noted that common sense would require the
capability to make analogical matches between knowledge and events in the
world, and furthermore that a special representation of knowledge would be
required to facilitate those analogies. We can see the importance of analogies
for common sense in the way that basic concepts are borrowed, e.g. the tail of
an animal, or the tail of a capital ‘Q’, or the tail-end of a temporally
extended event (see also examples of ‘contain’, ‘on’, in Sec. 5.3.1). More
than this, for known facts, such as “a string can pull but not push an
object”, an AI system needs to automatically deduce (by analogy) that a cloth,
sheet, or ribbon, can behave analogously to the string. For the fact “a stone
can break a window”, the system must deduce that any similarly heavy and hard
object is likely to break any similarly fragile material. Using the language
of Sec. 5.2.1, each of these known facts needs to be treated as a
schema131313Similar facts will be assigned the same schema, which generalises
over them., and then applied by analogy to new cases.

Projection is a mechanism that can find analogies (see Sec. 5.3.1) and hence
could bridge the gap between models of commonsense concepts (i.e. not the
entangled knowledge in word embeddings learnt from language corpora) and text
or visual or sensorimotor input. To facilitate this, concepts should be
represented by hierarchical compositional models, with higher levels
describing relations among elements in the lower level components (for reasons
discussed in Sec. 6.1). There needs to be an explicit symbolic handle on these
subcomponents; i.e. they can not be entangled in a complex network. For visual
object recognition a concept can simply be a set of spatial relations among
component features, but higher concepts require a complex model involving
multiple types of relations, partial physics theories, and causality. Secs.
5.2 and 5.3 give a hint of what these concepts may look like, but a full
example requires a further paper.

Moving beyond the recognition of individual concepts, a complete cognitive
system needs to represent and simulate what is happening in a situation, based
on some input, e.g., text, visual. This means instantiating concepts in some
workspace to flesh out relevant details of a scenario. Sometimes very little
data is available for some part of a scenario, and it must be imagined. For
example suppose some machine in a wooden casing moves smoothly across a
surface, but the viewer cannot see what mechanism is on the underside, the
viewer may conjecture it rolls on wheels, and if it gets stuck one may imagine
a wheel hitting a small stone. This type of imagination is another projection:
assuming a prior model of a wheeled vehicle is available, then the parts of
this can be projected to positions in the simulation (parts unseen in the
actual scenario). Similarly for a wheel hitting a stone: a schema abstracted
from a previously experienced episode of such an occurrence can serve as a
model. Simulation and projection must work together to imagine scenarios,
because an unfolding simulation may trigger new projections. If the simulation
is of something happening in the present, then sensor data can enter to
constrain the possibilities for the simulation.

##  8 Conclusion

Projection appears to be a core mechanism working together with other
mechanisms to solve tasks in perception and cognition in humans. Computational
implementations of projection in vision have shown promising results. It
remains to be seen how much benefit the mechanism can bring to other higher-
level vision tasks (such as video understanding), and other AI areas such as
robotics and language processing. However, as argued above, there are reasons
to believe it will be very important in all of these areas. Finally it may be
a key component for solving the longstanding commonsense knowledge problem,
because of its ability to map models of knowledge to varied situations, using
analogical machinery. Very little current work in AI attempts to use
projection. Deep learning without iterative inference and without using human-
like compositional models of concepts is more popular. I hope this paper might
encourage more work on projection.

## Acknowledgements

This paper owes most to Bipin Indurkhya’s ideas on projection in human
psychology and is essentially exploring their ramifications for AI. Early
drafts benefited from extensive comments (and/or discussion, suggested papers)
from Yaji Sripada, Chenghua Lin, Ranko Lazic, Lilian Tang, Andrew Gilbert,
Quoc Vuong. The idea of using “fraud” as an example concept came from Yaji
Sripada. Thanks to Guy Ben-Yosef and Shimon Ullman for further explanation of
their top-down process, and for permission for image use. Thanks to the
anonymous reviewers for useful comments and references.

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