Mental Sampling in Multimodal Representations
Authors: Jianqiao Zhu, Adam Sanborn, Nick Chater
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To simulate the sampling algorithms, we use a spatial representation of semantics (rather than the graph structure used in semantic networks), and we justify this choice in the Supplementary Material. For generality, we first focus on simulating patchy environments without making detailed assumptions about any one participant s semantic space. In particular, we create a series of 2D environment using Nmode = 15 Gaussian mixtures where the means are uniformly generated from [ r, r] for both dimensions, where r = 9 and the covariance matrix is fixed as the identity matrix for all mixtures. This procedure will produce patchy environments (for example the top panel of Figure 1). We ran DS, Rw M, and MC3 on this multimodal probability landscape, and the first 100 positions for each algorithm can be found in the top panel of Figure 1. The empirical flight distances were obtained by calculating the Euclidean distance between two consecutive positions of the sampler. For MC3, only the positions of the cold chain (T = 1) were used. Power-law distributions should produce straight lines in a log-log plot. To estimate power-law exponents of flight distance, we used the normalized logarithmic binning (LBN) method as it has higher accuracy than other methods [37, 48]. In LBN, flight distances are grouped into logarithmically-increasing sized bins and the geometric midpoints are used for plotting the data. Figure 1 (bottom) shows that only MC3 can reproduce the distributional property of flight distance as a Lévy flight with estimated power-law exponent ˆµ = 1.14. Both DS (ˆµ = 0.26) and Rw M (ˆµ = 0.04) produced values outside the range of power-law exponents found in human data. Indeed, Rw M produces a highly non-linear log-log plot, differing in form as well as exponent from a Lévy flight. In the Supplemental Material, we support this result by showing how sampling from a low-dimensional semantic space representation of animal names with MC3 can produce Lévy flight exponents similar to those of produced by participants for distances. |
| Researcher Affiliation | Academia | Jian-Qiao Zhu Department of Psychology University of Warwick j.zhu@warwick.ac.uk Adam N. Sanborn Department of Psychology University of Warwick a.n.sanborn@warwick.ac.uk Nick Chater Behavioural Science Group Warwick Business School nick.chater@wbs.ac.uk |
| Pseudocode | Yes | Algorithm Metropolis-coupled Markov chain Monte Carlo |
| Open Source Code | Yes | relevant code can be found at Open Science Framework: https://osf.io/26xb5/ |
| Open Datasets | No | The paper describes a new memory retrieval experiment conducted with human participants and simulations using generated patchy environments, but it does not provide concrete access information (link, DOI, formal citation) for either the human experimental data or the specific generated datasets. |
| Dataset Splits | No | The paper does not specify any training/validation/test dataset splits, as it focuses on simulating sampling algorithms and analyzing human cognitive data rather than training machine learning models. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU models, CPU models, or memory specifications used for running the experiments or simulations. |
| Software Dependencies | No | The paper mentions 'Scikit-learn: Machine learning in Python' [33] but does not provide specific version numbers for Python or any other software dependencies used in the experiments or simulations. |
| Experiment Setup | Yes | To simulate the sampling algorithms, we use a spatial representation of semantics (rather than the graph structure used in semantic networks), and we justify this choice in the Supplementary Material. For generality, we first focus on simulating patchy environments without making detailed assumptions about any one participant s semantic space. In particular, we create a series of 2D environment using Nmode = 15 Gaussian mixtures where the means are uniformly generated from [ r, r] for both dimensions, where r = 9 and the covariance matrix is fixed as the identity matrix for all mixtures. This procedure will produce patchy environments (for example the top panel of Figure 1). We ran DS, Rw M, and MC3 on this multimodal probability landscape, and the first 100 positions for each algorithm can be found in the top panel of Figure 1. The empirical flight distances were obtained by calculating the Euclidean distance between two consecutive positions of the sampler. For MC3, only the positions of the cold chain (T = 1) were used. Power-law distributions should produce straight lines in a log-log plot. To estimate power-law exponents of flight distance, we used the normalized logarithmic binning (LBN) method as it has higher accuracy than other methods [37, 48]. In LBN, flight distances are grouped into logarithmically-increasing sized bins and the geometric midpoints are used for plotting the data. Figure 1 (bottom) shows that only MC3 can reproduce the distributional property of flight distance as a Lévy flight with estimated power-law exponent ˆµ = 1.14. Both DS (ˆµ = 0.26) and Rw M (ˆµ = 0.04) produced values outside the range of power-law exponents found in human data. Indeed, Rw M produces a highly non-linear log-log plot, differing in form as well as exponent from a Lévy flight. In the Supplemental Material, we support this result by showing how sampling from a low-dimensional semantic space representation of animal names with MC3 can produce Lévy flight exponents similar to those of produced by participants for distances. In particular, we sampled 4 different values respectively for temperature spacing {0.5, 3, 7, 10}, number of parallel chains {2, 4, 6, 10}, resulting in 16 combinations of hyperparameters. For these simulations, we set this ratio between the mean and the standard deviation equal to 8 [34]. Our motor noise had a constant standard deviation of 0.1. |