RNN-RBM

A Recurrent Temporal RBM in which the visible layer at each time step is [h_{t-1} | x_t] — the previous hidden state (context) concatenated with the current input. Training uses Contrastive Divergence on [h_t | x_{t+1}] to learn next-step prediction.

Signal flow (UNROLL_DEPTH = 2)

        x[0]              x[1]              x[2]              x[3]
          │                 │                 │                 │
          ▼                 ▼                 ▼                 ▼
      ┌───────┐         ┌───────┐         ┌───────┐         ┌───────┐
 0 ──►│       ├─ h[0] ─►│       ├─ h[1] ─►│       ├─ h[2] ─►│       ├─ h[3] ─►
      │  W0   │         │  W1   │         │  W0   │         │  W1   │
      └───────┘         └───────┘         └───────┘         └───────┘
        t=0               t=1               t=2               t=3

  vis[t]  =  [ h[t-1] | x[t] ]    (context ‖ sensory  →  input to W)
  h[t]    =  sigmoid( W · vis[t] + b_h )   (new context  →  passed right)

  Training:  CD on [ h[t] | x[t+1] ]  to predict the next sensory from h[t]

Modes

UNROLL_DEPTH	Mode	Behaviour
1	shared weights	one entity reused at every time step; sequences may have any length
N > 1	unrolled	N entities rotate as layer[t % N]; each position learns its own W

With UNROLL_DEPTH = 2 the two entities specialise for even and odd positions respectively, doubling parameter count while keeping inference identical to the shared case.

Key parameters (RNN-RBM.ipynb)

Parameter	Default	Meaning
SENSORY_SIZE	40	vocabulary size (one-hot)
CONTEXT_SIZE	256	hidden / context dimension
UNROLL_DEPTH	2	number of alternating entities
NUM_EPOCHS	100	training epochs

Papers

https://proceedings.mlr.press/v5/sutskever09a.html — The Recurrent Temporal RBM (Sutskever, Hinton, Taylor 2009) https://arxiv.org/abs/1206.6392 — Modeling temporal dependencies with RNN-RBM (Boulanger-Lewandowski et al. 2012)

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GRBM

Paper

https://medium.com/@rtdcunha/gaussian-bernoulli-restricted-boltzmann-machines-4a68b8765485 https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0171015&type=printable

Code

https://github.com/DSL-Lab/GRBM/tree/main

CRBM

Paper

https://www.ee.nthu.edu.tw/hchen/pubs/iee2003.pdf

Regularization

https://benihime91.github.io/blog/machinelearning/deeplearning/python3.x/tensorflow2.x/2020/10/08/adamW.html https://medium.com/analytics-vidhya/l1-vs-l2-regularization-which-is-better-d01068e6658c https://jamesmccaffreyblog.com/2019/05/09/the-difference-between-neural-network-l2-regularization-and-weight-decay