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How Sensorimotor Interactions Enable Sentence Imitation

Abstract

Despite intensive debates regarding action imitation and sentence imitation, few studies have examined their relationship. In this paper, we argue that the mechanism of action imitation is necessary and in some cases sufficient to describe sentence imitation. We first develop a framework for action imitation in which key ideas of Hurley’s shared circuits model are integrated with Wolpert et al.’s motor selection mechanism and its extensions. We then explain how this action-based framework clarifies sentence imitation without a language-specific faculty. Finally, we discuss the empirical support for and philosophical significance of this perspective.

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Notes

  1. Human intention is not flat but multi-layered. According to Hurley (2001), it can be roughly divided into nonbasic intention (the goal of an actor) and basic intention (desired means to achieve that goal).

  2. Low-level controllers will generate commands needed to complete an action similar to the observed one. If the paired predictions match with actual subsequent states, then these commands represent the appropriately segmented movements of the observed action (Wolpert et al. 2003).

  3. According to Haruno et al. (2003), the higher level can learn the pattern (sequence) of movements on a probabilistic base. Please see Appendix section “Abstraction of the Sequence of Constituents”.

  4. To identify the actor’s desired states X * t , the observer’s highest level needs to issue predictive states \(\hat{X}_{t}\) that have the least mismatch with actual states \(X_{t}\). This final prediction’s paired command \(U_{t}\) can be described by Eq. (5) in Appendix “The Hierarchy of Models”.

  5. In the debate regarding what mirror neurons mirror, there are three main hypotheses (Oztop et al. 2005): mirror neurons encode (i) the detailed low-level motor parameters of the observed action; (ii) the higher-level motor plan; or (iii) the actor’s intention. In this paper, we presuppose view (iii).

  6. Hickok and Poeppel (2004) show that the brain’s speech perception is realized in two processing streams: dorsal stream maps sound into articulation-based representation and ventral stream maps sound into meaning, which are interfaced by the posterior region of the middle temporal gyrus.

  7. For simplicity, although a hearer’s visual perception of a speaker’s lip movements might affect how the speaker’s sound is perceived (e.g., the McGurk effect), we consider only auditory input, which by no means indicates that the framework is not applicable to the visual processing of written sentences.

  8. As the hearer’s perception of the number of syllables in a word is also determined by the sequential arrangement of phonemes (Mannell et al. 2014), the low level needs to check its output with sequence processing at a higher level.

  9. To describe this process computationally, the framework activates low-level controllers 1, 2, 3,…, n and generates commands \(u_{t}^{1},u_{t}^{2},u_{t}^{3}, \ldots,u_{t}^{n}\). Each efference copy of a motor command is send to its paired predictor to generate a prediction \(\hat{x}_{t + 1}^{i} = \varPhi \left({w_{t}^{i}, x_{t},u_{t}} \right)\). Each prediction is then compared with the sensory input to generate responsibility signal \(\lambda_{t}^{i} = \frac{{e^{{{{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}{{\mathop \sum \nolimits_{j = 1}^{n} e^{{{{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}\). Each signal helps a controller to revise its motor command, and the final command of the entire framework can be generated through \(u_{t} = \sum\nolimits_{i = 1}^{n} {\lambda_{t}^{i} u_{t}^{i}}\). This final motor commands is a properly segmented constituent (usually a word or free morpheme) of the utterance.

  10. Recursive processing is required for constituency and is presupposed by the framework.

  11. Following Hurley (2008), we also assume that the mechanism of an actor’s intended goal can be used to identify a speaker’s intended referent. Please see Hung (2014) for a relevant discussion.

  12. Based on Eq. (2) in Appendix section “A combined Forward and Inverse Model”, we may define a gradient learning rule of each controller, in which the desired command \(\left({u_{t}^{*} - u_{t}^{i}} \right)\) can be approximated by using the feedback command \(u_{fb}\):\(\Delta \alpha_{t}^{i} = \epsilon {\lambda_{t}^{i} \frac{{d\psi_{i}}}{{d\alpha_{t}^{i}}}\left({u_{t}^{*} - u_{t}^{i}} \right)} = \epsilon {\frac{{du_{t}^{i}}}{{d\alpha_{t}^{i}}}\lambda_{t}^{i} \left({u_{t}^{*} - u_{t}^{i}} \right)} \cong \epsilon {\frac{{du_{t}^{i}}}{{d\alpha_{t}^{i}}}\lambda_{t}^{i} u_{fb}}\)

  13. However, when a fluent speaker intentionally utters a sentence, not all of his or her words are necessarily consciously selected or explicitly intended. Nevertheless, this does not prevent the framework from using the mechanism to understand the speaker’s words because the words are linked to what the speaker would likely intend if she were aware of her word selection.

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Acknowledgments

This research was sponsored in part by the Ministry of Science and Technology, Taiwan under Grant No. 101-2410-H-001-100-MY2.

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Correspondence to Tzu-Wei Hung.

Appendix

Appendix

The Convertor

The convertor receives the actor’s intention d t and actual state x t at time t, and it outputs desired state x * t+1 at time t + 1. We use p t  = f (x t , d t ) and  x * t+1g(d t , p t ) to describe the parameter generated by motor control processing and a desired motor state generated by motor planning, where f and g are functions with inverse relationship \(x_{t + 1}^{*} = g\left({d_{t},f\left({x_{t},d_{t}} \right)} \right).\)

A Combined Forward and Inverse Model

Suppose each model activates multiple predictors 1, 2, 3,…, n at t, and select among their next state predictions \(\hat{x}_{t + 1}^{1},\hat{x}_{t + 1}^{2},\hat{x}_{t + 1}^{3}, \ldots,\hat{x}_{t + 1}^{n}\) through testing (see Fig. 3). Each predictor receives actual feedback x t and the efference copy of motor command u t to generate a prediction. The prediction of the i-th predictor is \(\hat{x}_{t + 1}^{i} = \varPhi \left({w_{t}^{i}, x_{t},u_{t}} \right)\), where \(w_{t}^{i}\) represents the parameters of the function approximator \(\varPhi\). This predictive next state is compared with the actual next state. If an error occurs, then the wrong prediction is sent to a responsibility estimator to generate responsibility signal \(\lambda_{t}^{i}\), which can be calculated by using the softmax activation function.

$$\lambda_{t}^{i} = \frac{{e^{{{{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}{{\mathop \sum \nolimits_{j = 1}^{n} e^{{{{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {x_{t} + - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}$$
(1)

In Eq. (1), \(x_{t}\) is the framework’s actual voice output, and \(\sigma\) is a scaling constant. The softmax activation function calculates the error signals and normalizes them into probability values between 0 and 1. Predictors with few errors receive higher responsibilities. Thus, responsibility signals can regulate predictor learning in a competitive manner. Moreover, a paired controller exists for each predictor, and it receives the desire next state x * t+1 and outputs motor commands. Suppose that the framework activates controllers 1, 2, 3,…, n and generates \(u_{t}^{1},u_{t}^{2},u_{t}^{3}, \ldots, u_{t}^{n}\). The motor command of the i-th controllers is \(u_{t}^{i} = \psi \left({\alpha_{t}^{i}, x_{t + 1}^{*}} \right)\), where \(\alpha_{t}^{i}\) is the parameter of a function approximator \(\psi\). The summation of the motor commands generated by controllers 1, 2, 3,…, n is represented by Eq. (2).

$$u_{t} = \mathop \sum \limits_{i = 1}^{n} \lambda_{t}^{i} u_{t}^{i} = \mathop \sum \limits_{i = 1}^{n} \lambda_{t}^{i} \psi \left({\alpha_{t}^{i}, x_{t + 1}^{*}} \right)$$
(2)

The Hierarchy of Models

For simplicity, we describe only a two-level hierarchy, although it is extendable to an arbitrary number of levels. Suppose that the predictor of the i-th higher-level model receives actual state X t and the efference copy of U t at t, and suppose that it outputs the approximate prediction \(\hat{X}_{t + 1}^{i}\) without activating subordinate controllers:

$$\hat{X}_{t + 1}^{i} = \varPhi \left({W_{t}^{i},X_{t},U_{t}} \right) = \left({P\left({1|W_{t}^{i},X_{t},U_{t}} \right), \ldots,P\left({n|W_{t}^{i},X_{t},U_{t}} \right)} \right)$$
(3)

In Eq. (3), \(\varPhi\) refers to a vector-valued and nonlinear function approximator; \(W_{t}^{i}\) is the synaptic weight of the higher-level j-th pair; X t is the current state (posterior probability); U t is the higher-level command; and \(P\left({j|W_{t}^{i},X_{t},U_{t}} \right)\) refers to the posterior probability in which the j-th pair is selected under \(W_{t}^{i},X_{t},{\text{and}}\;U_{t}\). Likewise, the i-th higher-level prediction \(\hat{X}_{t + 1}^{i}\) is compared with actual state X t from the subordinate level to generate higher-level responsibility (i.e., prior probability) \(\lambda_{i}^{H} \left(t \right)\) via the estimator

$$\lambda_{i}^{H} \left(t \right) = \frac{{\hat{\lambda}_{i}^{H} \left(t \right)e^{{- {{\left| {x_{t} - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{\left| {x_{t} - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}{{\mathop \sum \nolimits_{j = 1}^{N} \hat{\lambda}_{i}^{H} \left(t \right)e^{{- {{\left| {x_{t} - \hat{x}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{\left| {x_{t} - \hat{x}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}$$
(4)

\(\lambda_{i}^{H} \left(t \right)\) can regulate the subordinate level in a competitive manner. Moreover, each higher-v predictor has a paired controller that receives the desired next state X * t+1 and current state X t from the subordinate level as input. X * t+1 is an abstract representation that determines the selection and activation order of subordinate controllers. Each higher-level controller generates commands to the subordinate level, and the command of the i-th higher-level controller is \(U_{t}^{i} = \varPsi \left({\varLambda_{t}^{i}, X_{t + 1}^{*},X_{t}} \right)\), where \(\varLambda_{t}^{i}\) is the parameter of a function approximator \(\varPsi\). Then, \(U_{t}\), the summation of (prior probability) commands for the lowest pairs, is weighted by \(\lambda_{i}^{H} \left(t \right)\):

$$U_{t} = \left({\hat{\lambda}_{1}^{L} \left(t \right), \ldots,\hat{\lambda}_{n}^{L} \left(t \right)} \right) = \mathop \sum \limits_{i = 1}^{N} \lambda_{i}^{H} \left(t \right)U_{t}^{i} = \mathop \sum \limits_{i = 1}^{N} \lambda_{t}^{H} \left(t \right)\varPsi \left({\varLambda_{t}^{i}, X_{t + 1}^{*},X_{t}} \right)$$
(5)

Abstraction of the Sequence of Constituents

Suppose that the k-th higher-level model receives a sequence of actual input [\(x_{0},x_{1}, \ldots,x_{t}\)] (represented by X t ) and generates a prediction regarding a sequence of output [\(\hat{x}_{1}^{\text{k}}, \ldots,\hat{x}_{t}^{\text{k}}\)] (represented by \(\hat{X}_{t + 1}^{\text{k}}\)). The task of this higher level is to determine the prediction that has the least mismatch with the next actual sequence of input. The comparison result can be represented as Eq. (4). The responsibility signal can be used to revise higher-level commands (see Eq. (5)), which determines the behavior of the subordinate level. The efference copy of the commands can also be used for further prediction (and revision). We also use a recurrent network to describe the higher-level prediction of sequence \(\hat{X}_{t + 1}^{\text{k}} = f\left({W_{t}^{k}, X_{t}} \right)\), in which f is a nonlinear function that can use weights \(W_{t}^{k}\) to predict a vector of posterior probabilities. The network dynamics can be described as:

$$\tau \frac{d}{{d_{t}}}a_{i} \left(t \right) = - a_{i} \left(t \right) + \mathop \sum \limits_{j = 1} W_{ij}^{K} b_{j} \left(t \right)$$
$$b_{i} \left(t \right) = \left\{{\begin{array}{*{20}l} {g\left({a_{i} \left(t \right)} \right)} \hfill & {\left({\text{output}} \right)} \hfill \\ {X_{t}^{i}} \hfill & {\left({\text{input}} \right)} \hfill \\ \end{array}} \right.$$

In the above differential equation, g(X) is the sigmoid function with derivative g(X)(1 − g(X)), \(a_{i}\) is the activation, and \(b_{i}\) is the output at the i-th node. In Haruno et al.’s (2003) simulation, their models successfully learned two sequences and determined the one that should be reproduced under a given context, even when 5 % noise was added.

Control Variable Processing for Estimated Intention

Suppose that the highest models generate predictive control parameters \(\hat{p}_{t}^{1},\hat{p}_{t}^{2},\hat{p}_{t}^{3}, \ldots, \hat{p}_{t}^{n}\) at time t. Each predictive parameter will be compared with actually observed parameter p t from the control variable encoding (Fig. 4). The comparison result is represented by the responsibility signal:

Fig. 4
figure 4

Control variable processing in action comprehension mode

$$\lambda_{t}^{i} = \frac{{e^{{{{- \left| {p_{t} + - \hat{p}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {p_{t} + - \hat{p}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}{{\mathop \sum \nolimits_{j = 1}^{n} e^{{{{- \left| {p_{t} + - \hat{p}_{t}^{i}} \right|^{2}} \mathord{\left/{\vphantom {{- \left| {p_{t} + - \hat{p}_{t}^{i}} \right|^{2}} {\sigma^{2}}}} \right. \kern-0pt} {\sigma^{2}}}}}}}$$
(6)

The mechanism of intention/parameter matching in control variable processing generates simulated intention \(\hat{d}_{t}^{1},\hat{d}_{t}^{2},\hat{d}_{t}^{3}, \ldots, \hat{d}_{t}^{n}\). The final estimated intention is represented by:

$$d_{\text{t}} = \mathop \sum \limits_{i = 1}^{n} \lambda_{t}^{i} d_{t}^{i}$$
(7)

Searching for Meaning

Here, we use Oztop et al.’s (2005) algorithm of mental state search to infer the meaning that the speaker intends to convey. To initialize the algorithm, we also set T k and S k to an empty sequence (T k  = S k  = []). T k and S k represent sequences of observed and mentally simulated vectors of control variables extracted under the mental state k. Next, repeat steps (1)–(5) from speech onset to speech end.

  1. 1.

    Pick next possible mental state (j) (which can be thought of as an index for the possible referent to which the speaker is referring).

  2. 2.

    Observe: Extract the relevant control variables based on the hypothesized mental state (j), \(x_{j}^{i}\), and add them to T j (T j  = [T j , \(x_{j}^{i}\)]). Here, i indicates that the collected data were placed in ith position in the visual control variable sequence.

  3. 3.

    Simulate: Mentally simulate speech with mental state j while storing the simulated control variables x j in S j (S j  = [\(x_{j}^{0}, x_{j}^{1}, \ldots, x_{j}^{N}\)], where N is the number of control variables collected during observation).

  4. 4.

    Compare: Compute the discounted difference between T j and S j , where N is the length of T j and S j . \(D_{N} = \frac{{\left({1 - \gamma} \right)}}{{\left({1 = \gamma^{N + 1}} \right)}}\mathop \sum \limits_{i = 0}^{N} \left({x_{\text{sim}}^{i} - x^{0}} \right)^{T} {\mathbf{W}}\left({x_{\text{sim}}^{i} - x^{i}} \right)\gamma^{N - i}\), where \(x_{\text{sim}}^{i}\) ∈ Sj and \(x^{i}\) ∈ Tj and W is a diagonal matrix normalizing components of \(x^{i}\) and γ is the discount factor.

  5. 5.

    If DN is smallest so far, set j min = j.

Return: j min (the observer infers that j min is the actor’s intended meaning).

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Hung, TW. How Sensorimotor Interactions Enable Sentence Imitation. Minds & Machines 25, 321–338 (2015). https://doi.org/10.1007/s11023-015-9384-8

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Keywords

  • Sensorimotor interactions
  • Action imitation
  • Sentence imitation
  • Word-referent mapping
  • Syntactic abstraction