Table 1.
Symbols used in the equations and values that were used for the parameters in the simulations
Variable | Description | Value (if applicable) |
---|---|---|
Ns | No. of spatial units | 2 |
Ne | No. of units in recurrent network (autoencoder) | 490 |
Nm | No. of place cells | 980 |
Nv | No. of cortical units (layer 1) | 980 |
Nh | No. of cortical units (layer 2) | 300 |
β | Bout length | Variable (see text) |
tb | Time elapsed within bout | [0, β] |
Rt | Reward administered at time t | {0, 1} |
σϵ | Within-bout variance | 0 (none) or 0.003 |
σφ | Interbout variance | 0 (none) or 0.11 |
σf | Place cell breadth | 0.16 |
ϕ | Sampled reward location (sudden shift) | ∼N(μ, σφ) bound to [0, 1] |
ϵ | Incremental shift | ∼N(μ, σϵ) |
lt | Reward location at time t | [0, 1] |
xt | Agent location at time t | [0, 1] |
si | Place cell centerfield | [0, 1] |
s | Spatial cell activation vector | — |
e(k) | Recurrent network (autoencoder) layer k activation vector | — |
m | Place cell activation vector (memory) | — |
mE | Episodic output | — |
mS | Schematic output | — |
mO | Combined episodic/schematic output | — |
mR | Output from replay event | — |
m∼(xt+1|ai) | Predicted output given action ai | — |
V | Cortex layer 1 activation vector | — |
H | Cortex layer 2 activation vector | — |
WSE-AE | Spatial encoder to autoencoder weights | — |
WAE-AE | Autoencoder recurrent weights | — |
WAE-PC | Autoencoder to place cell weights | — |
WCTX | Cortical weights | — |
Agent speed | 0.04 | |
at | Action taken at time t | ϵ{N, NW, W, SW, S, SE, E, NE} |
ai | Possible action at time t | ϵ{N, NW, W, SW, S, SE, E, NE} |
αt | Policy unit (episodic, schematic) at time t | [0, 1] |
αRt | Policy unit (random) at time t | [0, 1] |
δt | Temporal difference error | — |
γ | Temporal difference discounting factor | 0.95 |
λ | Learning rate (autoencoder) | δt 0.1 |
Learning rate (cortex) | 0.00001 | |
Learning rate (place cells, actor) | 0.0075 | |
Learning rate (place cells, critic) | 0.04 |