The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. One task that has been extensively used to test mental state attribution in a variety of clinical populations is the animations task, where participants are asked to infer mental states from short videos of interacting triangles. In this task, individuals with clinical conditions such as autism spectrum disorders typically offer fewer and less appropriate mental state descriptions than controls, however little is currently known about why they show these difficulties. Previous studies have hinted at the similarity between an observer’s and the triangles’ movements as a key factor for the successful interpretation of these animations. In this study we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database...
The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. One task that has been extensively used to test mental state attribution in a variety of clinical populations is the animations task, where participants are asked to infer mental states from short videos of interacting triangles. In this task, individuals with clinical conditions such as autism spectrum disorders typically offer fewer and less appropriate mental state descriptions than controls, however little is currently known about why they show these difficulties. Previous studies have hinted at the similarity between an observer’s and the triangles’ movements as a key factor for the successful interpretation of these animations. In this study we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database...
Proceedings of the National Academy of Sciences, 2016
Optimal control models of biological movements introduce external task factors to specify the pac... more Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called “drive,” that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.
Reaching is the simplest and the most studied type of discrete movements, i.e. movements that hav... more Reaching is the simplest and the most studied type of discrete movements, i.e. movements that have finite durations. For obvious reasons, most optimal control models of reaching were formulated in the finitehorizon framework with a pre-specified terminal time. However, we have discovered significant limitations of such formulations, and investigated the alternative, an infinite-horizon formulation.
The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. Animations tasks, in which observers watch videos of interacting triangles, have been extensively used to test mental state attribution in a variety of clinical populations. Compared to control participants, individuals with clinical conditions such as autism typically offer less appropriate mental state descriptions of such videos. Recent research suggests that stimulus kinematics and movement similarity (between the video and the observer) may contribute to mental state attribution difficulties. Here we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database, we confirmed the hypotheses that an animation’s jerk and jerk similarity between observer and animator significantly contribute to the correct ide...
The quadratic integrate-and-fire (QIF) model captures the normal form bifurcation dynamics of Typ... more The quadratic integrate-and-fire (QIF) model captures the normal form bifurcation dynamics of Type-I spiking neurons found in cortex. Remarkably, this model is known to have a dual equivalent representation in terms of phase, called the θ-model, which has advantages for numerical simulations and analysis over the QIF model. Here, I investigate the nature of the dual representation and derive the general phase model expression for all integrate-and-fire models. Moreover, I show the condition for which the phase models exhibit discontinuous onset firing rate, the hallmark of Type-II spiking neurons.
Much of studies on neural computation are based on network models of static neurons that produce ... more Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (≈ millisecond) spike-based interactions for efficient encoding of information, and a delayed-memory XOR task over extended duration (≈ second). The results show that our method indeed optimizes the spiking network dynamics on the time scale of individual spikes as well as the behavioral time scales. In conclusion, our result offers a general purpose supervised learning algorithm for spiking neural networks, thus advancing further investigations on spike-based computation.
Optimal control models of biological movements introduce external task factors to specify the pac... more Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called “drive”, that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 po... more In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis con- firmed the power law for drawing ellipses but also predicted a spec- trum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with hu- man drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accu- rately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.
We present a novel, log-radius profile representation for convex curves and define a new operatio... more We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape analysis as well as in investigating how the brain perceives and generates curved shapes and motions.
To perform nontrivial, real-time computations on a sensory input stream, biological systems must ... more To perform nontrivial, real-time computations on a sensory input stream, biological systems must retain a short-term memory trace of their recent inputs. It has been proposed that generic high-dimensional dynamical systems could retain a memory trace for past inputs in their current state. This raises important questions about the fundamental limits of such memory traces and the properties required of dynamical systems to achieve these limits. We address these issues by applying Fisher information theory to dynamical systems driven by time-dependent signals corrupted by noise. We introduce the Fisher Memory Curve (FMC) as a measure of the signal-to-noise ratio (SNR) embedded in the dynamical state relative to the input SNR. The integrated FMC indicates the total memory capacity. We apply this theory to linear neuronal networks and show that the capacity of networks with normal connectivity matrices is exactly 1 and that of any network of N neurons is, at most, N. A nonnormal network achieving this bound is subject to stringent design constraints: It must have a hidden feedforward architecture that superlinearly amplifies its input for a time of order N, and the input connectivity must optimally match this architecture. The memory capacity of networks subject to saturating nonlinearities is further limited, and cannot exceed . This limit can be realized by feedforward structures with divergent fan out that distributes the signal across neurons, thereby avoiding saturation. We illustrate the generality of the theory by showing that memory in fluid systems can be sustained by transient nonnormal amplification due to convective instability or the onset of turbulence.
Control-dependent (multiplicative) noise makes it dicult to achieve optimal control because larg... more Control-dependent (multiplicative) noise makes it dicult to achieve optimal control because large control signals amplify noise. This paper considers a minimal (one-dimensional) system that includes multiplicative noise and solves the optimal control problem for arbitrary cost functions. In a limit when the control-cost approaches zero, this formulation becomes analytically solvable. The analysis reveals several important properties that are absent in traditional LQ analysis. In particular, multiplicative noise makes optimal solutions depend on the global features of cost functions.
Page 1. Two-Third power law for curved movements provides a strict constraint on optimal control ... more Page 1. Two-Third power law for curved movements provides a strict constraint on optimal control models Dongsung B Huh ([email protected]), Terrence J Sejnowski ([email protected]) One of the interesting properties of curved ...
… , 2009. ADPRL'09. IEEE Symposium on, Jan 1, 2009
Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate... more Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate real-time control of biological brain. Due to incomplete neural and anatomical data, traditional neural network training methods fail to model the sensory-motor systems. Here we introduce a novel modeling method based on stochastic optimal control framework which is well suited for this purpose. Our controller is implemented with a recurrent neural network (RNN) whose goal is approximating the optimal global control law for the given plant and cost function. We employ a risk-sensitive objective function proposed by Jacobson (1973) for robustness of controller. For maximum optimization efficiency, we introduce a step response sampling method, which minimizes complexity of the optimization problem. We use conjugate gradient descent method for optimization, and gradient is calculated via Pontryagin's maximum principle. In the end, we obtain highly stable and robust RNN controllers that can generate infinite varieties of attractor dynamics of the plant, which are proposed as building blocks of movement generation. We show two such examples, a point attractor based and a limit-cycle based dynamics.
The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. One task that has been extensively used to test mental state attribution in a variety of clinical populations is the animations task, where participants are asked to infer mental states from short videos of interacting triangles. In this task, individuals with clinical conditions such as autism spectrum disorders typically offer fewer and less appropriate mental state descriptions than controls, however little is currently known about why they show these difficulties. Previous studies have hinted at the similarity between an observer’s and the triangles’ movements as a key factor for the successful interpretation of these animations. In this study we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database...
The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. One task that has been extensively used to test mental state attribution in a variety of clinical populations is the animations task, where participants are asked to infer mental states from short videos of interacting triangles. In this task, individuals with clinical conditions such as autism spectrum disorders typically offer fewer and less appropriate mental state descriptions than controls, however little is currently known about why they show these difficulties. Previous studies have hinted at the similarity between an observer’s and the triangles’ movements as a key factor for the successful interpretation of these animations. In this study we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database...
Proceedings of the National Academy of Sciences, 2016
Optimal control models of biological movements introduce external task factors to specify the pac... more Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called “drive,” that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.
Reaching is the simplest and the most studied type of discrete movements, i.e. movements that hav... more Reaching is the simplest and the most studied type of discrete movements, i.e. movements that have finite durations. For obvious reasons, most optimal control models of reaching were formulated in the finitehorizon framework with a pre-specified terminal time. However, we have discovered significant limitations of such formulations, and investigated the alternative, an infinite-horizon formulation.
The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals... more The ability to ascribe mental states, such as beliefs or desires to oneself and other individuals forms an integral part of everyday social interaction. Animations tasks, in which observers watch videos of interacting triangles, have been extensively used to test mental state attribution in a variety of clinical populations. Compared to control participants, individuals with clinical conditions such as autism typically offer less appropriate mental state descriptions of such videos. Recent research suggests that stimulus kinematics and movement similarity (between the video and the observer) may contribute to mental state attribution difficulties. Here we present a novel adaptation of the animations task, suitable to track and compare animation generator and -observer kinematics. Using this task and a population-derived stimulus database, we confirmed the hypotheses that an animation’s jerk and jerk similarity between observer and animator significantly contribute to the correct ide...
The quadratic integrate-and-fire (QIF) model captures the normal form bifurcation dynamics of Typ... more The quadratic integrate-and-fire (QIF) model captures the normal form bifurcation dynamics of Type-I spiking neurons found in cortex. Remarkably, this model is known to have a dual equivalent representation in terms of phase, called the θ-model, which has advantages for numerical simulations and analysis over the QIF model. Here, I investigate the nature of the dual representation and derive the general phase model expression for all integrate-and-fire models. Moreover, I show the condition for which the phase models exhibit discontinuous onset firing rate, the hallmark of Type-II spiking neurons.
Much of studies on neural computation are based on network models of static neurons that produce ... more Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (≈ millisecond) spike-based interactions for efficient encoding of information, and a delayed-memory XOR task over extended duration (≈ second). The results show that our method indeed optimizes the spiking network dynamics on the time scale of individual spikes as well as the behavioral time scales. In conclusion, our result offers a general purpose supervised learning algorithm for spiking neural networks, thus advancing further investigations on spike-based computation.
Optimal control models of biological movements introduce external task factors to specify the pac... more Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called “drive”, that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 po... more In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis con- firmed the power law for drawing ellipses but also predicted a spec- trum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with hu- man drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accu- rately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.
We present a novel, log-radius profile representation for convex curves and define a new operatio... more We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape analysis as well as in investigating how the brain perceives and generates curved shapes and motions.
To perform nontrivial, real-time computations on a sensory input stream, biological systems must ... more To perform nontrivial, real-time computations on a sensory input stream, biological systems must retain a short-term memory trace of their recent inputs. It has been proposed that generic high-dimensional dynamical systems could retain a memory trace for past inputs in their current state. This raises important questions about the fundamental limits of such memory traces and the properties required of dynamical systems to achieve these limits. We address these issues by applying Fisher information theory to dynamical systems driven by time-dependent signals corrupted by noise. We introduce the Fisher Memory Curve (FMC) as a measure of the signal-to-noise ratio (SNR) embedded in the dynamical state relative to the input SNR. The integrated FMC indicates the total memory capacity. We apply this theory to linear neuronal networks and show that the capacity of networks with normal connectivity matrices is exactly 1 and that of any network of N neurons is, at most, N. A nonnormal network achieving this bound is subject to stringent design constraints: It must have a hidden feedforward architecture that superlinearly amplifies its input for a time of order N, and the input connectivity must optimally match this architecture. The memory capacity of networks subject to saturating nonlinearities is further limited, and cannot exceed . This limit can be realized by feedforward structures with divergent fan out that distributes the signal across neurons, thereby avoiding saturation. We illustrate the generality of the theory by showing that memory in fluid systems can be sustained by transient nonnormal amplification due to convective instability or the onset of turbulence.
Control-dependent (multiplicative) noise makes it dicult to achieve optimal control because larg... more Control-dependent (multiplicative) noise makes it dicult to achieve optimal control because large control signals amplify noise. This paper considers a minimal (one-dimensional) system that includes multiplicative noise and solves the optimal control problem for arbitrary cost functions. In a limit when the control-cost approaches zero, this formulation becomes analytically solvable. The analysis reveals several important properties that are absent in traditional LQ analysis. In particular, multiplicative noise makes optimal solutions depend on the global features of cost functions.
Page 1. Two-Third power law for curved movements provides a strict constraint on optimal control ... more Page 1. Two-Third power law for curved movements provides a strict constraint on optimal control models Dongsung B Huh ([email protected]), Terrence J Sejnowski ([email protected]) One of the interesting properties of curved ...
… , 2009. ADPRL'09. IEEE Symposium on, Jan 1, 2009
Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate... more Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate real-time control of biological brain. Due to incomplete neural and anatomical data, traditional neural network training methods fail to model the sensory-motor systems. Here we introduce a novel modeling method based on stochastic optimal control framework which is well suited for this purpose. Our controller is implemented with a recurrent neural network (RNN) whose goal is approximating the optimal global control law for the given plant and cost function. We employ a risk-sensitive objective function proposed by Jacobson (1973) for robustness of controller. For maximum optimization efficiency, we introduce a step response sampling method, which minimizes complexity of the optimization problem. We use conjugate gradient descent method for optimization, and gradient is calculated via Pontryagin's maximum principle. In the end, we obtain highly stable and robust RNN controllers that can generate infinite varieties of attractor dynamics of the plant, which are proposed as building blocks of movement generation. We show two such examples, a point attractor based and a limit-cycle based dynamics.
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Papers by Dongsung Huh