Standard encoder block

Block with a closed-loop SSM. In SpaceTime, we only consider using one ClosedLoopBlock as the last-layer in a single-layer decoder

In SpaceTime, we only consider using one ClosedLoopBlock as the last-layer in a single-layer decoder. However, other architectures

Same as mean, but compute mean over entire input

Zero-center values

Standardize lag terms, i.e., z = (x - mean(x)) / std(x) - Computed as (1 / std(x)) * x - mean(x) * (1 / std(x)) to fit with inverse call,

Closed-loop implementation of Companion SSM: - Instantiate A, B, C; so we can compute both: - Open-loop inference: -> y_{n + h}

Open-loop implementation of Companion SSM: -> y_t = C \sum_{i = 0}^{k - 1 - i} A^k B u_i where A is companion matrix

X and Y are complex64 tensors but stored as float32 tensors, with last dimension = 2.

X is a complex64 tensors but stored as float32 tensors, with last dimension = 2.

Day of month encoded as value between [-0.5, 0.5]

Hour of day encoded as value between [-0.5, 0.5]

Day of year encoded as value between [-0.5, 0.5]

Computes order-N differencing over input sequence

Hour of day encoded as value between [-0.5, 0.5]

Minute of hour encoded as value between [-0.5, 0.5]

Month of year encoded as value between [-0.5, 0.5]

Computes moving average residuals over input sequence

Computes both order-N differencing and moving average residuals over input sequence

Minute of hour encoded as value between [-0.5, 0.5]

Open-loop implementation of Shift SSM: -> y_t = C \sum_{i = 0}^{k - 1 - i} S^k B u_i where S is shift matrix

Trade off speed (20-25% faster) for more memory (20-25%)

Week of year encoded as value between [-0.5, 0.5]