Democratic Population Decisions Result in Robust Policy-Gradient Learning: A Parametric Study with GPU Simulations
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Mendeley | Further Information

{"title"=>"Democratic population decisions result in robust policy-gradient learning: A parametric study with GPU simulations", "type"=>"journal", "authors"=>[{"first_name"=>"Paul", "last_name"=>"Richmond", "scopus_author_id"=>"7006528605"}, {"first_name"=>"Lars", "last_name"=>"Buesing", "scopus_author_id"=>"23003340800"}, {"first_name"=>"Michele", "last_name"=>"Giugliano", "scopus_author_id"=>"55242654700"}, {"first_name"=>"Eleni", "last_name"=>"Vasilaki", "scopus_author_id"=>"6508079959"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"79955761534", "pmid"=>"21572529", "scopus"=>"2-s2.0-79955761534", "pui"=>"361732897", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0018539"}, "id"=>"297f9aab-4fb8-3b71-8a07-f6e391860bb5", "abstract"=>"High performance computing on the Graphics Processing Unit (GPU) is an emerging field driven by the promise of high computational power at a low cost. However, GPU programming is a non-trivial task and moreover architectural limitations raise the question of whether investing effort in this direction may be worthwhile. In this work, we use GPU programming to simulate a two-layer network of Integrate-and-Fire neurons with varying degrees of recurrent connectivity and investigate its ability to learn a simplified navigation task using a policy-gradient learning rule stemming from Reinforcement Learning. The purpose of this paper is twofold. First, we want to support the use of GPUs in the field of Computational Neuroscience. Second, using GPU computing power, we investigate the conditions under which the said architecture and learning rule demonstrate best performance. Our work indicates that networks featuring strong Mexican-Hat-shaped recurrent connections in the top layer, where decision making is governed by the formation of a stable activity bump in the neural population (a \"non-democratic\" mechanism), achieve mediocre learning results at best. In absence of recurrent connections, where all neurons \"vote\" independently (\"democratic\") for a decision via population vector readout, the task is generally learned better and more robustly. Our study would have been extremely difficult on a desktop computer without the use of GPU programming. We present the routines developed for this purpose and show that a speed improvement of 5x up to 42x is provided versus optimised Python code. The higher speed is achieved when we exploit the parallelism of the GPU in the search of learning parameters. This suggests that efficient GPU programming can significantly reduce the time needed for simulating networks of spiking neurons, particularly when multiple parameter configurations are investigated.", "link"=>"http://www.mendeley.com/research/democratic-population-decisions-result-robust-policygradient-learning-parametric-study-gpu-simulatio", "reader_count"=>29, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Researcher"=>10, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>2, "Student > Master"=>2, "Student > Bachelor"=>2, "Professor"=>1, "Student > Doctoral Student"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Researcher"=>10, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>2, "Student > Master"=>2, "Student > Bachelor"=>2, "Professor"=>1, "Student > Doctoral Student"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>4, "Environmental Science"=>1, "Mathematics"=>1, "Agricultural and Biological Sciences"=>7, "Neuroscience"=>1, "Arts and Humanities"=>1, "Computer Science"=>13, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>4}, "Neuroscience"=>{"Neuroscience"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>7}, "Computer Science"=>{"Computer Science"=>13}, "Mathematics"=>{"Mathematics"=>1}, "Environmental Science"=>{"Environmental Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"Greece"=>1, "Japan"=>1, "Poland"=>1, "United Kingdom"=>4, "Switzerland"=>1}, "group_count"=>0}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/777096"], "description"=>"<p>Figure shows the effect of additive uniformly distributed synaptic\n noise on the network performance by setting\n (see\n Equation 9). Panels A and B show the network performance without and\n with lateral connections (as in previous figures) respectively. The\n plots of average reward (left column, solid line) are calculated as\n in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figures 3</a> and\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g005\" target=\"_blank\">5</a> showing\n learning curves over 9 blocks of 512 trials. The red dashed line\n shows the values without noise from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figure 3</a> (systems A and B\n correspond) for direct comparison. Similarly, the plots of average\n error (right column, solid line) are calculated as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g004\" target=\"_blank\">Figure 4</a>. The red\n dashed line shows the values without noise from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g004\" target=\"_blank\">Figure 4</a> (again, systems A and B\n respectively). We can observe that both the average reward and\n average error performance measures show that the system without\n lateral connections is far more robust to noise applied directly to\n the synaptic weight.</p>", "links"=>[], "tags"=>["synaptic"], "article_id"=>447469, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g006", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Additive_Synaptic_Noise_/447469", "title"=>"Additive Synaptic Noise.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:36:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/776995"], "description"=>"<p>Figure shows the effect of increasing the overlap of the receptive\n fields (to ) of\n the Place Cells. Panel A shows a configuration without lateral\n connections and panel B shows a configuration with lateral\n connections (and corresponds to systems A and B from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figures 3</a> and\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g004\" target=\"_blank\">4</a>). The\n plots of the average reward (left column, solid line) are calculated\n in exactly the same way as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figure 3</a> shown over 9 blocks of\n 512 trials, rather than 5. The red dashed line shows the values from\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figure 3</a>\n over 9 blocks for direct comparison. We can observe that the system\n without lateral connections is less affected by the increase of the\n \n parameter than the system with lateral connections. The plots of the\n gradient (right column) are produced as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figures 3</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g004\" target=\"_blank\">4</a>, by plotting the\n sum of the potential weight change (calculated in the same way as in\n previous figures).</p>", "links"=>[], "tags"=>["receptive"], "article_id"=>447372, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g005", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overlapping_receptive_fields_/447372", "title"=>"Overlapping receptive fields.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:35:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/776853"], "description"=>"<p>Panels A–C (left column) show the average performance of 16\n animats calculated in the following way. Every animat completes a\n number of blocks of 512 trials (the number here varies from 0 to 5),\n with weights being updated at the end of each trial. We term these\n “blocks of learning trials”. In these figures, 0 blocks\n of learning trials means that no learning has taken place. The\n average reward is calculated independently from the blocks of\n learning trials. Following a block of learning trials, the animat\n performs of 128 independent (analysis) trials with learning being\n disabled, based on which the performance of the system is evaluated\n (mean reward over a total of 128x16 samples). The parameters for\n systems A–C are the same as in the previous figure (i.e. A: no\n lateral connections, B: lateral connections and C: very strong\n lateral connections). We note that the system without lateral\n connections achieves 70% of reward twice as fast as the\n system with lateral connections. The system with strong lateral\n connections completely fails to learn the task. We can obtain a\n better understanding of the difference between the three systems by\n plotting the gradient term for each case correspondingly (Panels\n A–C, right column). We calculate the gradient numerically by\n summing the value of the potential weight change (before learning\n where the potential change is maximal)\n over\n Place Cell index and by\n shifting the index of the\n Action Cell population so that the peak will always appear at the\n middle of the graph. To achieve a smooth graph, we average over a\n total of \n trials. We note that the gradient is larger when lateral connections\n are absent.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447226, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Analysis_of_System_Performance_/447226", "title"=>"Analysis of System Performance.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:34:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/777251"], "description"=>"<p>Figure shows the simulation process of our spiking neural network model.\n Steps shown on the left are broken down into CUDA kernels where the\n figure in brackets represents\n the total number of threads which are invoked for each kernel (for\n simplification this assumes only a single independent trial). The value\n N represents the number of Action Cell neurons (256), the value M\n represents the number of Place Cell neurons (256) and the value T\n represents the total number of number of discrete time steps, i.e.\n (which is\n when\n ). Steps\n shown on the right indicate calculations performed on the Host CPU.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447623, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g008", "stats"=>{"downloads"=>3, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_Flowchart_/447623", "title"=>"Simulation Flowchart.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:37:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/776710"], "description"=>"<p>Our animat (artificial animal) “lives” on a circle and\n performs the following task. We place the animat randomly to one\n position on the circle. The animat then chooses a direction, the\n decision, . At each\n position there is one “correct” direction\n . Choices\n close to\n the correct direction receive\n some reward, according to a Gaussian reward function. This processes\n (the setting of the animat at a location, selection of a decision,\n receiving a reward and updating of the feed-forward weights) constitutes\n a single trial. After completion of a trial the animat is placed\n randomly at a new position and the task is repeated. The task will be\n fully learned if the animat chooses the correct direction at each\n position on the circle. A: Shows a schematic overview of our two layer\n model architecture consisting of Place Cells (red) and Action Cells\n (blue). Place Cells (modelled as Poisson neurons) are connected to\n Action Cells (Integrate-and-Fire neurons) using an all-to-all feed\n forward network (not all connections are shown). In addition Action\n Cells may be interconnected via lateral Mexican hat-type connections\n (not all connections are shown). The layer of Place Cells is arranged in\n a ring like topology with each neuron having a\n preferred angle, and firing with maximum probability if the location of\n the animat happens to coincide with this preferred angle. In the example\n shown the animat is placed at the location that corresponds to the\n preferred direction of neuron index . The top\n layer, also arranged in a ring topology, codes for the location the\n animat will choose. B: Shows the output spike train of the Action Cells\n demonstrating a bump formation around neuron\n () with a\n resulting decision angle matching\n the preferred angle of . In this\n example the target angle , and\n therefore the animat has made the correct decision. C: Shows the spike\n train of the input layer (Place Cells) when the animat is placed at the\n location encoded by neuron .</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447080, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g001", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_Architecture_/447080", "title"=>"Model Architecture.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:34:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/777509"], "description"=>"<p>Figure shows the performance profile of our GPU implementation with\n respect to where GPU time is spent during the simulation (shown as a\n percentage for each GPU kernel corresponding with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g008\" target=\"_blank\">figure 8</a>). The figure in brackets\n next to the vertical axis label indicates the total number of times the\n kernel function is called over single “learn step” with a\n total time simulation period of T = 128 and\n . An\n additional amount of CPU time is also required however this is\n negligible in the scale of the overall simulation. A: Represents the\n case for our model without lateral connections. B: Represents a case\n with lateral connections which is the same however it includes a kernel\n function “actionCellLateralSpikePropagation” which performs\n the lateral spike propagation simulation.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447886, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g011", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Performance_Profile_/447886", "title"=>"Performance Profile.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:38:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/777573"], "description"=>"<p>Simulation results shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g001\" target=\"_blank\">Figures 1</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g002\" target=\"_blank\"></a><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\"></a><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g004\" target=\"_blank\"></a><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g005\" target=\"_blank\"></a><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g006\" target=\"_blank\"></a><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g007\" target=\"_blank\">7</a> use the above parameters\n except where indicated otherwise. The value of\n is\n either or\n \n depending on where lateral connections are present (the later\n indicates that they are). The parameter\n is\n chosen produce an input of 180Hz. Parameters for the neuronal\n model are taken from the literature. Other parameters are found\n through parameter search.</p>", "links"=>[], "tags"=>["parameters", "producing", "simulation"], "article_id"=>447947, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.t001", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Default_model_parameters_used_for_producing_simulation_____results_/447947", "title"=>"Default model parameters used for producing simulation\n results.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 18:38:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/777446"], "description"=>"<p>Figure shows the relative performance improvement of our GPU model with\n respect to a similar Python implementation using numpy's BLAS\n implementation. Relative performance refers to the percentage increase\n in performance by considering the absolute timings of the two\n implementations over an entire simulation. The horizontal axis indicates\n <b>Ind_total</b>, that is the total number of independent\n trials which in this case represents independent animats (rather than\n animats in different configurations). A: Represents the case for our\n model without lateral connections. B: Represents a case with lateral\n connections which is the same however it includes an additional code\n execution to perform simulation of the lateral spike propagation.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447818, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g010", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_Performance_Speedup_/447818", "title"=>"Relative Performance Speedup.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:38:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/777359"], "description"=>"<p>This figure shows the CUDA kernel used to perform the update of a\n spiking Action Cell neuron. Conceptually the kernel is relatively\n simple, using linear algebra style computation to update the neurons\n membrane potential (d_u_out) using the previous potential (d_u). The\n kernel also saves to the GPU Device memory the probability of firing\n (d_YProb) and the actual spike contribution (d_Y) of the neuron\n without requiring any localised caching of data. The variable index\n is calculated using a thread (tx) and block of thread identifiers\n (blockIdx.x) and represents the neuron index position within a large\n list of all neurons being simulated by the kernel. The value\n blockIdx.y indicates the independent trial number for each neuron\n this used to calculate the offset variables of N_offset and\n NT_offset which are used to ensure unique values for each neuron in\n each independent trial are accessed. The variable\n configuration_offset is similarly used to represent an index in\n which to look up one of the independent parameter configuration\n values. The corresponding function pow2mod uses bit shift operations\n to perform an efficient integer modulus operation where the divisor\n is a power of 2. The kernel function arguments are all prefixed with\n “d_” to indicate memory on the GPU device rather than\n the GPU host. The argument “seeds” is also an area of\n memory on the GPU device which is used to hold seeds for the\n parallel random number generation.</p>", "links"=>[], "tags"=>["simulation"], "article_id"=>447735, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g009", "stats"=>{"downloads"=>1, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spiking_Simulation_Kernel_/447735", "title"=>"Spiking Simulation Kernel.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:37:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/777163"], "description"=>"<p>To obtain a better understanding of the difference between the\n performance of the two systems from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g006\" target=\"_blank\">Figure 6</a> (A: no lateral\n connections, B: with lateral connections) we plotting the\n eligibility trace for each case with and without an additive noise\n term . This\n corresponds to from\n Equation 9 for and and\n allows us to look at the gradient information without taking into\n account the shape of reward. We calculate the eligibility trace\n ()\n numerically by summing the value of the potential eligibility trace\n (before learning, where the potential change is maximal) over Place\n Cell index and by\n shifting the index of the\n Action Cell population so that the maximum will be at the middle of\n the graph. To obtain smooth curves, we calculate this value over a\n total of \n trials. The left column panels show the eligibility trace without\n noise. The right column panels show the the eligibility trace,\n including noise ( as in\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g006\" target=\"_blank\">Figure 6</a>).\n In both cases the same random seeds are used when generating spikes\n and target angles to ensure both systems are presented with the same\n information. The resulting right column figures therefore give an\n indication of the effect of the noise. We note that the eligibility\n trace of system without lateral connections is relatively unchanged\n by the effect of noise, where as the system with lateral connections\n results in an eligibility trace drastically reduced in\n magnitude.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447539, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g007", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Noise_Analysis_/447539", "title"=>"Noise Analysis.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:36:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/776799"], "description"=>"<p>Figure shows the effect of varying the lateral connection strength\n parameter on the\n spiking activity of the Action Cells over a period of\n \n (before learning has taken place). For clarity, the figures show a\n decision angle of value of \n suggesting a centralised high activity around Place Cell index\n (as in\n <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g001\" target=\"_blank\">Figure 1</a>).\n A: Shows a system without lateral connections where\n . B:\n Shows a system with lateral connections where\n . C:\n Shows a system with very strong lateral connections where\n .</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447172, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Lateral_Connection_Strength_/447172", "title"=>"Lateral Connection Strength.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:34:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/776918"], "description"=>"<p>We investigate the effect of the reward function shape by changing it\n from a “wide” Gaussian (Panels A and B,\n ) to a\n “narrow” Gaussian (Panels C and D,\n ). Here\n we plot average error graphs as they provide a measurement that\n allows us to compare systems with different reward functions. To\n produce the average error graphs (panels A–D, left column), we\n have averaged over 16 independent animats performing 5 blocks of 512\n trials. Every point of the graph represents the average normalised\n error of the system (i.e. the normalised absolute difference between\n the target angle and\n the decision angle )\n which, similar to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figure 3</a>, is calculated over a separate block of 128\n analysis trials (without updating the synaptic weights). Error bars\n show the standard deviation over the 16 independent animats. We\n observe that after 5 blocks of trials, the system corresponding to\n the “wide” Gaussian reward function without lateral\n connections shown in (A) has reached a lower final error than that\n of the system with lateral connections (B). When a narrow Gaussian\n reward is instead used, the system with lateral connections (D)\n recovers this difference in final error with respect to the system\n without lateral connections (C). As with the previous plot we show\n (right column panels) the gradient of the system configurations\n A–D by plotting the sum of the potential weight change\n (calculated in the same way as previously). For clarity, plots A and\n B are repeated from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018539#pone-0018539-g003\" target=\"_blank\">Figure 3</a>. We note that when a narrow Gaussian reward is\n used the system with lateral connections (D) learns over a very\n narrow band close to the target angle. In contrast the profile of\n the system without lateral connections (C) remains consistent with\n that of the wide reward, learning across a broader range of the\n population.</p>", "links"=>[], "tags"=>["neuroscience", "computer science"], "article_id"=>447295, "categories"=>["Information And Computing Sciences", "Neuroscience"], "users"=>["Paul Richmond", "Lars Buesing", "Michele Giugliano", "Eleni Vasilaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0018539.g004", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Reward_Function_Shape_/447295", "title"=>"Reward Function Shape.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 18:35:21"}

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Relative Metric

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