txt/2106.08858.txt

Grounding Spatio-Temporal Language with
Transformers
Tristan Karch, Laetitia Teodorescu
Inria - Flowers Team
Université de Bordeaux
[email protected] Hofmann
Microsoft Research
Cambridge, UKClément Moulin-Frier
Inria - Flowers team
Université de Bordeaux
ENSTA ParisTech
Pierre-Yves Oudeyer
Inria - Flowers team
Université de Bordeaux
ENSTA ParisTech
Abstract
Language is an interface to the outside world. In order for embodied agents to use
it, language must be grounded in other, sensorimotor modalities. While there is
an extended literature studying how machines can learn grounded language, the
topic of how to learn spatio-temporal linguistic concepts is still largely uncharted.
To make progress in this direction, we here introduce a novel spatio-temporal
language grounding task where the goal is to learn the meaning of spatio-temporal
descriptions of behavioral traces of an embodied agent. This is achieved by
training a truth function that predicts if a description matches a given history of
observations. The descriptions involve time-extended predicates in past and present
tense as well as spatio-temporal references to objects in the scene. To study the role
of architectural biases in this task, we train several models including multimodal
Transformer architectures; the latter implement different attention computations
between words and objects across space and time. We test models on two classes of
generalization: 1) generalization to randomly held-out sentences; 2) generalization
to grammar primitives. We observe that maintaining object identity in the attention
computation of our Transformers is instrumental to achieving good performance
on generalization overall, and that summarizing object traces in a single token has
little influence on performance. We then discuss how this opens new perspectives
for language-guided autonomous embodied agents. We also release our code under
open-source license as well as pretrained models and datasets to encourage the
wider community to build upon and extend our work in the future.
1 Introduction
Building autonomous agents that learn to represent and use language is a long standing-goal in
Artificial Intelligence [20,39]. In developmental robotics [ 7], language is considered a cornerstone
of development that enables embodied cognitive agents to learn more efficiently through social
interactions with humans or through cooperation with other autonomous agents. It is also considered
essential to develop complex sensorimotor skills, facilitating the representation of behaviors and
actions.
Embodied Language Grounding [50] is the field that studies how agents can align language with
their behaviors in order to extract the meaning of linguistic constructions. Early approaches in
Equal Contribution
35th Conference on Neural Information Processing Systems (NeurIPS 2021).arXiv:2106.08858v2  [cs.AI]  11 Oct 2021shake
grow
- ‘Shake red cat’
- ‘Shake thing right of lamp’
- ‘Shake thing was left of lamp ’- ‘Was grasp blue cactus’
- ‘Was grasp thing top most’
- ‘Was grasp thing was right of parrot’(a) Grow action with spatial  or
attribute reference to object(b) Shake action with  spatio-temporal  
reference to object (c) Grasp past actions  description with
 spatio-temporal reference to object
- ‘Grow blue chameleon’
- ‘Grow thing left of tv ’
- ‘Grow thing left most ’
- ‘Grasp green water ’
Traces of interactions Sampled 
descriptionsNatural
English 
version ‘You are currently growing the 
blue chameleon’‘You are currently shaking some -
thing that used to be at the left of 
the lamp’‘You previously grasped some-
thing that used to be at the right 
of the parrot’Figure 1: Visual summary of the Temporal Playground environment: At each episode (column
a, b and c), the actions of an agent (represented by a hand) unfold in the environment and generate
a trace of interactions between objects and the agent body. Given such a trace, the environment
automatically generates a set of synthetic linguistic descriptions that are true at the end of the trace.
In (a) the agent grows an object which is described with spatial (underlined) or attribute (highlighted)
reference. In (b) it shakes an object which is described with attribute, spatial or spatio-temporal
(underlined) reference. In (c) it has grasped an object (past action underlined) which is described
with attribute, spatial or spatio-temporal (highlighted) reference. The natural english version is given
for illustrative purposes.
developmental robotics studied how various machine learning techniques, ranging from neural
networks [ 40,45,24] to non-negative matrix factorization [ 32], could enable the acquisition of
grounded compositional language [ 42,41]. This line of work was recently extended using techniques
forLanguage conditioned Deep Reinforcement Learning [31]. Among these works we can distinguish
mainly three language grounding strategies. The first one consists of directly grounding language
in the behavior of agents by training goal-conditioned policies satisfying linguistic instructions
[40,45,23,22,9]. The second aims at extracting the meaning of sentences from mental simulations
(i.e. generative models) of possible sensorimotor configurations matching linguistic descriptions
[32,1,12,34]. The third strategy searches to learn the meaning of linguistic constructs in terms of
outcomes that agents can observe in the environment. This is achieved by training a truth function that
detects if descriptions provided by an expert match certain world configurations. This truth function
can be obtained via Inverse Reinforcement Learning [49,3] or by training a multi-modal binary
classifier [ 14]. Previous work [ 14,3] has shown that access to this reward is enough for sucessfully
grounding language in instruction-following agents.
While all the above-mentioned approaches consider language that describes immediate and instanta-
neous actions, we argue that it is also important for agents to grasp language expressing concepts
that are relational and that span multiple time steps. We thus propose to study the grounding of new
spatio-temporal concepts enabling agents to ground time extended predicates (Fig. 1a) with complex
spatio-temporal references to objects (Fig. 1b) and understand both present and past tenses (Fig. 1c).
To do so we choose the third strategy mentioned above, i.e. to train a truth function that predicts when
descriptions match traces of experience. This choice is motivated by two important considerations.
First, prior work showed that learning truth functions was key to foster generalization [ 3], enabling
agents to efficiently self-train policies via goal imagination [ 14] and goal relabeling [ 12]. Hence the
truth function is an important and self-contained component of larger learning systems. Second, this
strategy allows to carefully control the distribution of experiences and descriptions perceived by the
agent.
2The Embodied Language Grounding problem has a relational structure. We understand the meaning of
words by analyzing the relations they state in the world [ 18]. The relationality of spatial and temporal
concepts has long been identified in the field of pragmatics [ 43,44] (see Supplementary Section C
for additional discussion). Furthermore actions themselves are relations between subjects and objects,
and can be defined in terms of affordances of the agent [ 19]. We acknowledge this and provide
the right relational inductive bias [ 5] to our architectures through the use of Transformers [ 46]. We
propose a formalism unifying three variants of a multi-modal transformer inspired by Ding et al.
[16] that implement different relational operations through the use of hierarchical attention. We
measure the generalization capabilities of these architectures along three axes 1) generalization to
new traces of experience; 2) generalization to randomly held out sentences; 3) generalization to
grammar primitives, systematically held out from the training set as in Ruis et al. [37]. We observe
that maintaining object identity in the attention computation of our Transformers is instrumental to
achieving good performance on generalization overall. We also identify specific relational operations
that are key to generalize on certain grammar primitives.
Contributions. This paper introduces:
1. A new Embodied Language Grounding task focusing on spatio-temporal language;
2.A formalism unifying different relational architectures based on Transformers expressed as
a function of mapping and aggregation operations;
3.A systematic study of the generalization capabilities of these architectures and the identifica-
tion of key components for their success on this task.
2 Methods
2.1 Problem Definition
We consider the setting of an embodied agent behaving in an environment. This agent interacts with
the surrounding objects over time, during an episode of fixed length ( T). Once this episode is over, an
oracle provides exhaustive feedback in a synthetic language about everything that has happened. This
language describes actions of the agent over the objects and includes spatial and temporal concepts.
The spatial concepts are reference to an object through its spatial relation with others (Fig. 1a), and
the temporal concepts are the past modality for the actions of the agent (Fig. 1c), past modality for
spatial relations (Fig. 1b), and actions that unfold over time intervals. The histories of states of the
agent’s body and of the objects over the episode as well as the associated sentences are recorded in
a bufferB. From this setting, and echoing previous work on training agents from descriptions, we
frame the Embodied Language Grounding problem as learning a parametrized truth function Rover
couples of observations traces and sentences, tasked with predicting whether a given sentence Wis
true of a given episode history Sor not. Formally, we aim to minimize:
E(S;W )B
L(R(S;W);r(S;W))
whereLdenotes the cross-entropy loss and rdenotes the ground truth boolean value for sentence W
about traceS.
2.2 Temporal Playground
In the absence of any dedicated dataset providing spatio-temporal descriptions from behavioral traces
of an agent, we introduce Temporal Playground (Fig. 1) an environment coupled with a templated
grammar designed to study spatio-temporal language grounding. The environment is a 2D world,
with procedurally-generated scene containing N= 3objects sampled from 32 different object types
belonging to 5 categories. Each object has a continuous 2D position, a size, a continuous color
code specified by a 3D vector in RGB space, a type specified by a one-hot vector, and a boolean
unit specifying whether it is grasped. The size of the object feature vector ( o) isjoj= 39 . The
agent’s body has its 2D position in the environment and its gripper state (grasping or non-grasping) as
features (body feature vector ( b) of sizejbj= 3). In this environment, the agent can perform various
actions over the length ( T) of an episode. Some of the objects (the animals) can move independently.
Objects can also interact: if the agent brings food or water to an animal, it will grow in size; similarly,
if water is brought to a plant, it will grow. At the end of an episode, a generative grammar generates
3sentences describing all the interactions that occurred. A complete specification of the environment
as well as the BNF of the grammar can be found in Supplementary Section A.2.
Synthetic language. To enable a controlled and systematic study of how different types of spatio-
temporal linguistic meanings can be learned, we argue it is necessary to first conduct a systematic
study with a controlled synthetic grammar. We thus consider a synthetic language with a vocabulary of
size53and sentences with a maximum length of 8. This synthetic language facilitates the generation
of descriptions matching behavioral traces of the agent. Moreover, it allows us to express four
categories of concepts associated with specific words. Thus, the generated sentences consist in four
conceptual types based on the words they involve:
•Sentences involving basic concepts. This category of sentences talk about present-time
events by referring to objects and their attributes. Sentences begin with the ’grasp’ token
combined with any object. Objects can be named after their category (eg. ’animal’, ’thing’ )
or directly by their type ( ’dog’, ’door’, ’algae’, etc. ). Finally, the color (’red’, ’blue’, ’green’ )
of objects can also be specified.
•Sentences involving spatial concepts. This category of sentences additionally involve
one-to-one spatial relations and one-to-all spatial relations to refer to objects. An object
can be ’left of’ another object (reference is made in relation to a single other object), or
can be the ’top most’ object (reference is made in relation with all other objects). Example
sentences include ’grasp thing bottom of cat’ or’grasp thing right most’ .
•Sentences involving temporal concepts . This category of sentences involves talking about
temporally-extended predicates and the past tense, without any spatial relations. The two
temporal predicates are denoted with the words ’grow’ and’shake’ . The truth value of these
predicates can only be decided by looking at the temporal evolution of the object’s size and
position respectively. A predicate is transposed at the past tense if the action it describes
was true at some point in the past and is no longer true in the present, this is indicated by
adding the modifier ’was’ before the predicate. Example sentences include ’was grasp red
chameleon’ (indicating that the agent grasped the red chameleon and then released it) and
’shake bush’ ;
•Sentences involving spatio-temporal concepts . Finally, we consider the broad class of
spatio-temporal sentences that combine spatial reference and temporal or past-tense predi-
cates. These are sentences that involve both the spatial and temporal concepts defined above.
Additionally, there is a case of where the spatial and the temporal aspects are entangled:
past spatial reference. This happens when an object is referred to by its previous spatial
relationship with another object. Consider the case of an animal that was at first on the
bottom of a table, then moved on top, and then is grasped. In this case we could refer to this
animal as something that was previously on the bottom of the table. We use the same ’was’
modifier as for the past tense predicates; and thus we would describe the action as ’Grasp
thing was bottom of table’ .
2.3 Architectures
In this section we describe the architectures used as well as their inputs. Let one input sample to
our model be I= (S;W), where (Si;t)i;trepresents the objects’ and body’s evolution, and (Wl)l
represents the linguistic observations. Shas a spatial (or entity) dimension indexed by i2[0::N]and
a temporal dimension indexed by t2[1::T]; for anyi,t,Si;tis a vector of observational features.
Note that by convention, the trace (S0;t)trepresents the body’s features, and the traces (Si;t)t;i> 0
represents the other objects’ features. Wis a 2-dimensional tensor indexed by the sequence l2[1::L];
for anyl,Wl2RdWis a one-hot vector defining the word in the dictionary. The output to our models
is a single scalar between 0and1representing the probability that the sentence encoded by Wis true
in the observation trace S.
Transformer Architectures. To systematically study the influence of architectural choices on
language performance and generalization in our spatio-temporal grounded language context, we
define a set of mapping and aggregation operations that allows us to succinctly describe different
models in a unified framework. We define:
4i=0
i=2i=1
i=3
‘Grasp thing left most’qObject
Encoder
Language
EncoderBody 
Encoder
Positional
Encodingq
...
reducerreduce
q ...
rreduceq
reduce
rq
reduce(c) Unstructured Transformer ( UT)
(d) Spatial-First Transformer ( SFT)
(e) Temporal-First Transformer (TFT)(a) Input Encoding
qreduce
(b) Optional Word Aggregation (-WA)
t=2 t=1 t=0
S0,2
S2,1S
WS = 
W = 
W WS
S
S WW
W
Figure 2: Visual summary of the architectures used. We show the details of UT,SFTand TFT
respectively in subfigures (c), (d), (e), as well as a schematic illustration of the preprocessing phase
(a) and the optional word-aggregation procedure (b).
•An aggregation operation based on a Transformer model, called reduce .reduce is a
parametrized function that takes 3 inputs: a tensor, a dimension tuple Dover which to
reduce and a query tensor (that has to have the size of the reduced tensor). Rlayers of a
Transformer are applied to the input-query concatenation and are then queried at the position
corresponding to the query tokens. This produces an output reduced over the dimensions D.
•A casting operation called cast .cast takes as input 2 tensors AandBand a dimension d.
Ais flattened, expanded so as to fit the tensor Bin all dimensions except d, and concatenated
along theddimension.
•A helper expand operation called expand that takes as arguments a tensor and an integer n
and repeats the tensor ntimes.
Using those operations, we define three architectures: one with no particular bias ( Unstructured
Transformer , inspired by Ding et al. [16], or UT); one with a spatial-first structural bias – objects and
words are aggregated along the spatial dimension first ( Spatial-First Transformer orSFT); and one
with a temporal-first structural bias – objects and words are aggregated along the temporal dimension
first ( Temporal-First Transformer , or TFT).
Before inputting the observations of bodies and objects Sand the language Winto any of the Trans-
former architectures, they are projected to a common dimension (see Supplementary Section B.2 for
more details). A positional encoding [ 46] is then added along the time dimension for observations and
along the sequence dimension for language; and finally a one-hot vector indicating whether the vector
is observational or linguistic is appended at the end. This produces the modified observation-language
tuple (^S;^W). We let:
UT(^S;^W) := reduce (cast(^S;^W;0);0;q)
SFT(^S;^W;q) := reduce (reduce (cast(^W;^S;0);0;expand (q;T));0;q)
TFT(^S;^W;q) := reduce (reduce (cast(^W;^S;1);1;expand (q;N+ 1));0;q)
whereTis the number of time steps, Nis the number of objects and qis a learned query token. See
Fig. 2 for an illustration of these architectures.
Note that SFTand TFTare transpose versions of each other: SFTis performing aggregation over space
first and then time, and the reverse is true for TFT. Additionally, we define a variant of each of these
architectures where the words are aggregated before being related with the observations. We name
these variants by appendding - WA(word-aggregation) to the name of the model (see Fig. 2 (b)).
^W reduce (^W;0;q)
5We examine these variants to study the effect of letting word-tokens directly interact with object-token
through the self-attention layers vs simply aggregating all language tokens in a single embedding
and letting this vector condition the processing of observations. The latter is commonly done in
the language-conditioned RL and language grounding literature [ 11,3,25,37], using the language
embedding in FiLM layers [ 36] for instance. Finding a significant effect here would encourage using
architectures which allow direct interactions between the word tokens and the objects they refer to.
LSTM Baselines. We also compare some LSTM -based baselines on this task; their architecture is
described in more detail in Supplementary Section B.3.
2.4 Data Generation, Training and Testing Procedures
We use a bot to generate the episodes we train on. The data collected consists of 56837 trajectories of
T= 30 time steps. Among the traces some descriptions are less frequent than others but we make
sure to have at least 50 traces representing each of the 2672 descriptions we consider. We record
the observed episodes and sentences in a buffer, and when training a model we sample (S;W;r )
tuples with one observation coupled with either a true sentence from the buffer or another false
sentence generated from the grammar. More details about the data generation can be found in
Supplementary Section B.1.
For each of the Transformer variants (6 models) and the LSTM baselines (2 models) we perform an
hyper parameter search using 3 seeds in order to extract the best configuration. We extract the best
condition for each model by measuring the mean F1on a testing set made of uniformly sampled
descriptions from each of the categories define in section 2.2. We use the F1score because testing
sets are imbalanced (the number of traces fulfilling each description is low). We then retrain best
configurations over 10 seeds and report the mean and standard deviation (reported as solid black lines
in Fig. 3 and Fig. 4) of the averaged F1score computed on each set of sentences. When statistical
significance is reported in the text, it is systematically computed using a two-tail Welch’s t-test with
null hypothesis 1=2, at level= 0:05[13]. Details about the training procedure and the hyper
parameter search are provided in Supplementary Section B.4.
3 Experiments and Results
3.1 Generalization abilities of models on non-systematic split by categories of meaning
In this experiment, we perform a study of generalization to new sentences from known observations.
We divide our set of test sentences in four categories based on the categories of meanings listed in
Section 2.2: Basic, Spatial, Spatio-Temporal and Temporal. We remove 15% of all possible sentences
in each category from the train set and evaluate the F1 score on those sentences. The results are
provided in Fig. 3.
First, we notice that over all categories of meanings, all UTand TFTmodels, with or without word-
aggregation, perform extremely well compared to the LSTM baselines, with all these four models
achieving near-perfect test performance on the Basic sentences, with very little variability across the
10 seeds. We then notice that all SFTvariants perform poorly on all test categories, in line or worse
than the baselines. This is particularly visible on the spatio-temporal category, where the SFTmodels
perform at 0:750:020whereas the baselines perform at 0:800:019. This suggests that across
tasks, it is harmful to aggregate each scene plus the language information into a single vector. This
may be due to the fact that objects lose their identity in this process, since information about all the
objects becomes encoded in the same vector. This may make it difficult for the network to perform
computations about the truth value of predicate on a single object.
Secondly, we notice that the word-aggregation condition seems to have little effect on the performance
on all three Transformer models. We only observe a significant effect for UTmodels on spatio-
temporal concepts ( p-value = 2:38e-10). This suggests that the meaning of sentences can be
adequately summarised by a single vector; while maintaining separated representations for each
object is important for achieving good performance it seems unnecessary to do the same for linguistic
input. However we notice during our hyperparameter search that our -WA models are not very robust
to hyperparameter choice, with bigger variants more sensitive to the learning rate.
6Thirdly, we observe that for our best-performing models, the basic categories of meanings are the
easiest, with a mean score of 1:00:003across all UTand TFT models, then the spatial ones
at0:960:020, then the temporal ones at 0:960:009, and finally the spatio-temporal ones at
0:890:027. This effectively suggests, as we hypothesised, that sentences containing spatial relations
or temporal concepts are harder to ground than those who do not.
Known sentences with novel observations. We also examine the mean performance of our models
for sentences in the training set but evaluated on a set of new observations : we generate a new set
of rollouts on the environment, and only evaluate the model on sentences seen at train time (plots
are reported in Supplementary Section D ). We see the performance is slightly better in this case,
especially for the LSTM baselines ( 0:820:031versus 0:790:032), but the results are comparable
in both cases, suggesting that the main difficulty for models lies in grounding spatio-temporal
meanings and not in linguistic generalization for the type of generalization considered in this section.
Figure 3: F1scores for all the models on randomly held-out sentences. F1is measured on
separated sets representing each category of concepts defined in Section 2.2.
3.2 Systematic generalization on withheld combinations of words
In addition to the previous generalization studies, we perform an experiment in a harder linguistic
generalization setting where we systematically remove binary combinations in our train set. This is in
line with previous work on systematic generalization on deep learning models [ 29,37,26]. We create
five test sets to examine the abilities of our models to generalize on binary combinations of words
that have been systematically removed from the set of training sentences, but whose components have
been seen before in other contexts. Our splits can be described by the set of forbidden combinations
of words as:
1.Forbidden object-attribute combinations. remove from the train set all sentences contain-
ing’red cat’ ,’blue door’ and’green cactus’ . This tests the ability of models to recombine
known objects with known attributes;
2.Forbidden predicate-object combination. remove all sentences containing ’grow’ and all
objects from the ’plant’ category. This tests the model’s ability to apply a known predicate
to a known object in a new combination;
3.Forbidden one-to-one relation. remove all sentences containing ’right of’ . Since the
’right’ token is already seen as-is in the context of one-to-all relations ( ’right most’ ), and
other one-to-one relations are observed during training, this tests the abilities of models to
recombine known directions with in a known template;
4.Forbidden past spatial relation. remove all sentences containing the contiguous tokens
’was left of’ . This tests the abilities of models to transfer a known relation to the past
modality, knowing other spatial relations in the past;
5.Forbidden past predicate. remove all sentences containing the contiguous tokens ’was
grasp’ . This tests the ability of the model to transfer a known predicate to the past modality,
knowing that it has already been trained on other past-tense predicates.
7To avoid retraining all models for each split, we create one single train set with all forbidden sentences
removed and we test separately on all splits. We use the same hyperparameters for all models than in
the previous experiments. The results are reported in Fig. 4.
Figure 4: F1scores of all the models on systematic generalization splits. F1is measured on
separated sets representing each of the forbidden combinations of word defined above.
First we can notice that the good test scores obtained by the UTand TFTmodels on the previous
sections are confirmed in on this experiment: they are the best performing models overall. We then
notice that the first two splits, corresponding to new attribute-object and predicate-object combinations,
are solved by the UTand TFTmodels, while the SFTmodels and the LSTM baselines struggle to
achieve high scores. For the next 3 splits, which imply new spatial and temporal combinations, the
scores overall drop significantly; we also observe much wider variability between seeds for each
model, perhaps suggesting the various strategies adopted by the models to fit the train set have very
different implications in terms of systematic generalization on spatial and temporal concepts. This
very high variability between seeds on systematic generalization scores are reminiscent of the results
obtained on the gSCAN benchmark [37].
Additionally, for split 3, which implies combining known tokens to form a new spatial relation, we
observe a significant drop in generalization for the word-aggregation ( WA) conditions, consistent
across models (on average across seeds, 0:140:093,0:150:234and0:200:061for
UT,SFTand TFTresp. with p-values <1e-04 for UTand SFT). This may be due to the fact that
recombining any one-to-one relation with the known token right seen in the context of one-to-all
relations requires a separate representation for each of the linguistic tokens. The same significant
drop in performance for the WAcondition can be observed for UTand TFTin split 4, which implies
transferring a known spatial relation to the past.
However, very surprisingly, for split 5 – which implies transposing the known predicate grasp to the
past tense – we observe a very strong effect in the opposite direction: the WAcondition seems to help
generalizing to this unknown past predicate (from close-to-zero scores for all transformer models,
theWAadds on average 0:710:186,0:450:178and0:520:183points for UT, ST and TT
resp. and p-values <1e-05). This may be due to the fact that models without WAlearn a direct and
systematic relationship between the grasp token and grasped objects, as indicated in their features;
this relation is not modulated by the addition of the wasmodifier as a prefix to the sentence. Models
do not exhibit the same behavior on split 4, which has similar structure (transfer the relation left of
to the past). This may be due to the lack of variability in instantaneous predicates (only the grasp
predicate); whereas there are several spatial relations (4 one-to-one, 4 one-to-all).
Control experiment. We evaluate previously trained models on a test set containing hard negative
examples. The aim of this experiment is to ensure that models truly identify the compositional
structure of our spatio-temporal concepts and do not simply perform unit concept recognition. We
select negative pairs (trajectory, description) so that the trajectories contain either the object or the
action described in the positive example. Results are provided in Fig. 5. We observe a slight decrease
of performances on all 5 categories (drop is less than 5%), demonstrating that the models do in fact
represent the meaning of the sentence and not simply the presence or absence of a particular object or
predicate.
8Figure 5: Control experiment: F1scores for all the models on systematic generalization splits in
the hard negative examples setting.
4 Related Work
The idea that agents should learn to represent and ground language in their experience of the world
has a long history in developmental robotics [ 50,39,40,7] and was recently extended in the context
of Language Conditioned Deep Reinforcement Learning [ 11,22,31,3]. These recent approaches
often consider navigation [ 10,9] or object manipulation [ 1,22] tasks and are always using instructive
language. Meanings typically refer to instantaneous actions and rarely consider spatial reference
to objects [ 35]. Although our environment includes object manipulations, we here tackle novel
categories of meanings involving the grounding of spatio-temporal concepts such as the past modality
or complex spatio-temporal reference to objects.
We evaluate our learning architectures on their ability to generalise to sets of descriptions that contain
systematic differences with the training data so as to assess whether they correctly model grammar
primitives. This procedure is similar to the gSCAN benchmark [ 37]. This kind of compositional
generalisation is referred as ’systematicity’ by Hupkes et al. [26]. Environmental drivers that facilitate
systematic generalization are also studied by Hill et al. [23]. Although Hupkes et al. [26] consider
relational models in their work, they do not evaluate their performance on a Language Grounding
task. Ruis et al. [37] consider an Embodied Language Grounding setup involving one form of time-
extended meanings (adverbs), but do not consider the past modality and spatio-temporal reference to
objects, and do not consider learning truth functions. Also, they do not consider learning architectures
that process sequences of sensorimotor observations. To our knowledge, no previous work has
conducted systematic generalization studies on an Embodied Language Grounding task involving
spatio-temporal language with Transformers.
The idea that relational architectures are relevant models for Language Grounding has been previously
explored in the context of Visual Reasoning . They were indeed successfully applied for spatial
reasoning in the visual question answering task CLEVR [38]. With the recent publication of the video
reasoning dataset CLEVRER [47], those models were extended and demonstrated abilities to reason
over spatio-temporal concepts, correctly answering causal, predictive and counterfactual questions
[16]. In contrast to our study, these works around CLEVRER do not aim to analyze spatio-temporal
language and therefore do not consider time-extended predicates or spatio-temporal reference to
objects in their language, and do not study properties of systematic generalization over sets of new
sentences.
5 Discussion and Conclusion
In this work, we have presented a first step towards learning Embodied Language Grounding of
spatio-temporal concepts, framed as the problem of learning a truth function that can predict if a
given sentence is true of temporally-extended observations of an agent interacting with a collection
of objects. We have studied the impact of architectural choices on successful grounding of our
artificial spatio-temporal language. We have modelled different possible choices for aggregation of
9observations and language as hierarchical Transformer architectures. We have demonstrated that in
our setting, it is beneficial to process temporally-extended observations and language tokens side-by-
side, as evidenced by the good score of our Unstructured Transformer variant. However, there seems
to be only minimal effect on performance in aggregating temporal observations along the temporal
dimension first – compared to processing all traces and the language in an unstructured manner – as
long as object identity is preserved. This can inform architectural design in cases where longer episode
lengths make it impossible to store all individual timesteps for each object; our experiments provide
evidence that a temporal summary can be used in these cases. Our experiments with systematic
dimensions of generalization provide mixed evidence for the influence of summarizing individual
words into a single vector, showing it can be detrimental to generalize to novel word combinations
but also can help prevent overgeneralization of a relation between a single word and a single object
without considering the surrounding linguistic context.
Limitations and further work. There are several limitations of our setup which open important
opportunities for further work. First, we have used a synthetic language that could be extended:
for instance with more spatial relations and relations that are more than binary. Another axis for
further research is using low-level observations. In our setting, we wanted to disentangle the effect
of structural biases on learning spatio-temporal language from the problem of extracting objects
from low level observations [ 6,21,17,30,8] in a consistent manner over time (object permanence
[15,48]). Further steps in this direction are needed, and it could allow us to define richer attributes
(related to material or texture) and richer temporal predicates (such as breaking, floating, etc). Finally,
we use a synthetic language which is far from the richness of the natural language used by humans,
but previous work has shown that natural language can be projected onto the subspace defined by
synthetic language using the semantic embeddings learned by large language models [ 33]: this opens
up be a fruitful avenue for further investigation.
A further interesting avenue for future work would be to use the grounding provided by this reward
function to allow autonomous language-conditioned agents to target their own goals [ 14]. In this sense,
the truth function can be seen as a goal-achievement function or reward function. While generalization
performance of our method is not perfect, the good overall f1 scores of our architectures imply that
they can be directly transferred to a more complete RL setup to provide signal for policies conditioned
on spatio-temporal language.
Broader Impact. This work provides a step in the direction of building agents that better understand
how language relates to the physical world; this can lead to personal robots that can better suit the
needs of their owners because they can be interacted with using language. If successfully implemented,
this technology can raise issues concerning automation of certain tasks resulting in loss of jobs for
less-qualified workers.
Links. The source code as well as the generated datasets can be found at https://github.com/
flowersteam/spatio-temporal-language-transformers
Acknowledgments and Disclosure of Funding
Tristan Karch is partly funded by the French Ministère des Armées - Direction Générale de
l’Armement. Laetitia Teodorescu is supported by Microsoft Research through its PhD Scholar-
ship Programme. This work was performed using HPC resources from GENCI-IDRIS (Grant
2020-A0091011996)
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13Checklist
1. For all authors...
(a)Do the main claims made in the abstract and introduction accurately reflect the paper’s
contributions and scope? [Yes] , we propose a summary of our results supporting our
contributions in Section 5.
(b) Did you describe the limitations of your work? [Yes] , in the concluding Section 5.
(c)Did you discuss any potential negative societal impacts of your work? [Yes] , in a the
Broader Impact paragraph in the Conclusion section 5.
(d)Have you read the ethics review guidelines and ensured that your paper conforms to
them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [N/A]
(b) Did you include complete proofs of all theoretical results? [N/A]
3. If you ran experiments...
(a)Did you include the code, data, and instructions needed to reproduce the main experi-
mental results (either in the supplemental material or as a URL)? [Yes] , the code is
given as supplementary material.
(b)Did you specify all the training details (e.g., data splits, hyperparameters, how they
were chosen)? [Yes] , see Sections 3.1 and 3.2.
(c)Did you report error bars (e.g., with respect to the random seed after running exper-
iments multiple times)? [Yes] , all reported scores were averaged over 10 seeds and
std is reported in all plots (Fig. 3, Fig. 4 of Section 3) and in the main text. We also
performed statistical tests to measure significance.
(d)Did you include the total amount of compute and the type of resources used (e.g.,
type of GPUs, internal cluster, or cloud provider)? [Yes] , details are given in
Supplementary Section D.2.
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(a) If your work uses existing assets, did you cite the creators? [N/A]
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(d)Did you discuss whether and how consent was obtained from people whose data you’re
using/curating? [N/A]
(e)Did you discuss whether the data you are using/curating contains personally identifiable
information or offensive content? [N/A]
5. If you used crowdsourcing or conducted research with human subjects...
(a)Did you include the full text of instructions given to participants and screenshots, if
applicable? [N/A]
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Board (IRB) approvals, if applicable? [N/A]
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spent on participant compensation? [N/A]
14SUPPLEMENTARY MATERIAL
A Supplementary: Temporal Playground Specifications
A.1 Environment
Temporal Playground is a procedurally generated environment consisting of 3 objects and an agent’s
body. There are 32 types of objects, listed in Fig. 6 along with 5 object categories. Each object has a
continuous 2D position, a size, a continuous color code specified by a 3D vector in RGB space, a type
specified by a one-hot vector, and a boolean unit specifying whether it is grasped. Note that categories
are not encoded in the objects’ features. The agent’s body has its 2D position in the environment and
its gripper state (grasping or non-grasping) as features. The size of the body feature vector is 3 while
the object feature vector has a size of 39. This environment is a spatio-temporal extension of the one
used in this work [14].
All positions are constrained within [1;1]2. The initial position of the agent is (0;0)while the
initial object positions are randomized so that they are not in contact (d(obj1;obj 2)>0:3). Object
sizes are sampled uniformly in [0:2;0:3], the size of the agent is 0:05. Objects can be grasped
when the agent has nothing in hand, when it is close enough to the object center (d(agent;obj)<
(size(agent) +size(obj))=2)and the gripper is closed ( 1,1when open). When a supply is on an
animal or water is on a plant (contact define as distance between object being equal to the mean size
of the two objects d= (size(obj1) +size(obj2))=2), the object will grow over time with a constant
growth rate until it reaches the maximum size allowed for objects or until contact is lost.
Category
Object
Typefurniture animal
 plantliving thing
supply
dog
cat
chameleon
human
flycactus
carnivorous
flower
tree
bushgrass
algae
tea
rose
bonsaiparrot
mouse
lion
pig
cowcupboard
sink
window
sofa
carpetdoor
chair
desk
lamp
tablewater
food
Can move independently, 
can be grown with food 
or waterCan be grown with water
Figure 6: Representation of possible objects types and categories . Information about the possible
interactions between objects are also given.
15A.2 Language
Grammar. The synthetic language we use can be decomposed into two components: the instanta-
neous grammar and the temporal logic. Both are specified through the BNF given in Figure 7.
Instantaneous grammar:
<S>             ::= <pred> <thing_A>
<pred>          ::= grow | grasp | shake
<thing_A>       ::= <thing_B> | <attr> <thing_B> | thing <localizer> | 
                    thing <localizer_all>
<localizer>     ::= left of <thing_B> | right of <thing_B> |
                    bottom of <thing_B> | top of <thing_B>
<localizer_all> ::= left most | right most | bottom most | top most
<thing_B>       ::= dog | cat | … | thing
<attr>          ::= blue | green | red
Temporal aspect:
<S>             ::= was <pred> <thing_A>
<thing_A>       ::= thing was <localizer> | thing was <localizer_all>
Figure 7: BNF of the grammar used in Temporal Playground . The instantaneous grammar allows
generating true sentences about predicates, spatial relations (one-to-one and one to all). These
sentences are then processed by the temporal logic to produce the linguistic descriptions of our
observations; this step is illustrated in the Temporal Aspect rules. See the main text for information
on how these sentences are generated.
Concept Definition. We split the set of all possible descriptions output by our grammar into four
conceptual categories according to the rules given in Table 1.
Concept BNF Size
1. Basic<S> ::= <pred> <thing_A>
152 <pred> ::= grasp
<thing_A> ::= <thing_B> | <attr> <thing_B
2. Spatial<S> ::= <pred> <thing_A>
156 <pred> ::= grasp
<thing_A> ::= < thing <localizer> | thing <localizer_all>
3. Temporal<S> ::= <pred_A> <thing_A> | was <pred_B> <thing_A>
648<pred_A> ::= grow |shake
<pred_B> ::= grasp |grow |shake
<thing_A> ::= <thing_B> | <attr> <thing_B>
4. Spatio-
Temporal<S> ::= <pred_A> <thing_A> | was <pred_B> <thing_A>
1716<pred_C> <thing_C >
<pred_A> ::= grow |shake
<pred_B> ::= grasp |grow |shake
<pred_C> ::= grasp
<thing_A> ::= thing <localizer> | thing <localizer_all> |
thing was <localizer> |
thing was <localizer_all> |
<thing_C> ::= thing was <localizer> |
thing was <localizer_all>
Table 1: Concept categories with their associated BNF. <thing_B> ,<attr> ,<localizer> and
<localizer_all> are given in Fig. 7
16B Supplementary Methods
B.1 Data Generation
Scripted bot. To generate the traces matching the descriptions of our grammar we define a set of
scenarii that correspond to sequences of actions required to fulfill the predicates of our grammar,
namely grasp ,grow andshake . Those scenarii are then conditioned on a boolean that modulates them
to obtain a mix of predicates in the present and the past tenses. For instance, if a grasp scenario is
sampled, there will be a 50% chance that the scenario will end with the object being grasped, leading
to a present-tense description; and a 50% chance that the agent releases the object, yielding a past
tense description.
Description generation from behavioral traces of the agent. For each time step, the instanta-
neous grammar generates the set of all true instantaneous sentences using a set of filtering operations
similar to the one used in CLEVR [ 27], without the past predicates and past spatial relations. Then
the temporal logic component uses these linguistic traces in the following way: if a given sentence
for a predicate is true in a past time step and false in the present time step, the prefix token ’was’ is
prepended to the sentence; similarly, if a given spatial relation is observed in a previous time step and
unobserved in the present, the prefix token ’was’ is prepended to the spatial relation.
B.2 Input Encoding
We present the input processing in Fig. 8. At each time step t, the body feature vector btand the
object features vector oi;t,i= 1;2;3are encoded using two single-layer neural networks whose
output are of size h. Similarly, each of the words of the sentence describing the trace (represented
as one-hot vectors) is encoded and projected in the dimension of size h. We concatenate to the
vector obtained a modality token mthat defines if the output belongs to the scene (1;0)or to the
description (0;1). We then feed the resulting vectors to a positional encoding that modulates the
vectors according to the time step in the trace for btandoi;t,i= 1;2;3and according to the position
of the word in the description for wl.
We call the encoded body features ^btand it corresponds to ^S0;tof the input tensor of our model (see
Fig. 2 in the Main document). Similarly, ^oi;t,i= 1;2;3are the encoded object features corresponding
to^Si;t,i= 1;2;3. Finally ^wlare the encoded words and the components of tensor ^W.
We callhthe hidden size of our models and recall that j^btj=j^oi;tj=j^wlj=h+ 2. This parameter
is varied during the hyper-parameter search.
Object
EncoderLanguage
EncoderBody 
Encoder
............bt
bt
oi,t
oi,twl
Positional
EncodingPositional
EncodingPositional
Encoding
wlm
mm
Figure 8: Input encoding. Body, words and objects are all projected in the same dimension.
17B.3 Details on LSTM models
To provide baseline models on our tasks we consider two LSTM variants. They are interesting
baselines because they do not perform any relational computation except for relations between inputs
at successive time steps. We consider the inputs as they were defined in Section 2.3 of the main paper.
We consider two LSTM variants:
1.LSTM -FLAT : This variant has two internal LSTM : one that processes the language and one
that processes the scenes as concatenations of all the body and object features. This produces
two vectors that are concatenated into one, which is then run through an MLP and a final
softmax to produce the final output.
2.LSTM -FACTORED : This variant independently processes the different body and object
traces, which have previously been projected to the same dimension using a separate linear
projection for the object and for the body. The language is processed by a separate LSTM .
These body, object and language vectors are finally concatenated and fed to a final MLP and
a softmax to produce the output.
B.4 Details on Training Schedule
Implementation Details. The architectures are trained via backpropagation using the Adam
Optimizer[ 28]. The data is fed to the model in batches of 512 examples for 150 000 steps. We use a
modular buffer to sample an important variety of different descriptions in each batch and to impose a
ratio of positive samples of 0.1 for each description in each batch.
Model implementations. We used the standard implementations of TransformerEncoderLayer and
TransformerEncoder from pytorch version 1.7.1, as well as the default LSTM implementation. For
initialization, we also use pytorch defaults.
Hyper-parameter search. To pick the best set of parameters for each of our eight models, we
train them on 18 conditions and select the best models. Note that each condition is run for 3 seeds
and best models are selected according to their averaged F1score on randomly held-out descriptions
(15% of the sentences in each category given in Table 1).
Best models. Best models obtained thanks to the parameter search are given in Table 2.
Model Learning rate Model hyperparams
hidden size layer count head count param count
UT 1e-4 256 4 8 1 :3M
UT-WA 1e-5 512 4 8 14 :0M
TFT 1e-4 256 4 4 3 :5M
TFT-WA 1e-5 512 4 8 20 :3M
SFT 1e-4 256 4 4 3 :5M
SFT-WA 1e-4 256 2 8 2 :7M
LSTM -FLAT 1e-4 512 4 N/A 15:6M
LSTM -FACTORED 1e-4 512 4 N/A 17:6M
Table 2: Hyperparameters. (for all models)
Robustness to hyperparameters For some models, we have observed a lack of robustness to
hyperparameters during our search. This translated to models learning to predict all observation-
sentence tuples as false since the dataset is imbalanced (the proportion of true samples is 0.1). This
behavior was systematically observed with a series of models whose hyperparameters are listed in
Table 3. This happens with the biggest models with high learning rates, especially with the -WA
variants.
18Model Learning rate Model hyperparams
hidden size layer count head count
UT-WA 1e-4 512 4 4
UT-WA 1e-4 512 4 8
SFT 1e-4 512 4 4
SFT-WA 1e-4 512 4 8
SFT-WA 1e-4 512 2 4
SFT-WA 1e-4 512 4 4
TFT 1e-4 512 4 4
TFT-WA 1e-4 512 4 8
TFT-WA 1e-4 512 2 4
TFT-WA 1e-4 512 4 4
Table 3: Unstable models. Models and hyperparameters collapsing into uniform false prediction.
C Supplementary Discussion: Formal descriptions of spatio-temporal
meanings
The study of spatial and temporal aspects of language has a long history in Artificial Intelligence and
linguistics, where researchers have tried to define formally the semantics of such uses of language.
For instance, work in temporal logic [ 2] has tried to create rigorous definitions of various temporal
aspects of action reflected in the English language, such as logical operations on time intervals (an
action fulfilling itself simultaneously with another, before, or after), non-action events (standing
still for one hour), and event causality. These formal approaches have been complemented by work
in pragmatics trying to define language user’s semantics as relates to spatial and temporal aspects
of language. For instance, Tenbrink [43] examines the possible analogies to be made between
relationships between objects in the spatial domain and relationships between events in a temporal
domain, and concludes empirically that these aspects of language are not isomorphic and have their
own specific rules. Within the same perspective, a formal ontology of space is developed in [ 4],
whose complete system can be used to achieve contextualized interpretations of language users’
spatial language. Spatial relations in everyday language use are also specified by the perspective
used by the speaker; a formal account of this system is given in [ 44], where the transferability of
these representations to temporal relations between events is also studied. These lines of work are of
great relevance to our approach, especially the ones involving spatial relationships. We circumvent
the problem of reference frames by placing ourselves in an absolute reference system where the x-y
directions unambiguously define the concepts of left,right ,top,bottom ; nevertheless these studies
would be very useful in a context where the speaker would also be embodied and speak from a
different perspective. As for the temporal aspect, these lines of work focus on temporal relations
between separate events, which is not the object of our study here; we are concerned about single
actions (as opposed to several events) unfolding, in the past or present, over several time steps.
19D Supplementary Results
D.1 Generalization to new observations from known sentences
Figure 9: Generalization to new traces of observations. F1 scores of all models on the train
sentences with new observations. UTand TFToutperform other models on all four categories of
meanings.
D.2 Computing Resources
This work was performed using HPC resources from GENCI-IDRIS (Grant 2020-A0091011996).
We used 22k GPU-hours on nvidia-V100 GPUs for the development phase, hyperparameter search,
and the main experiments.
20