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Posit AI Weblog: torch time sequence, take three: Sequence-to-sequence prediction

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Posit AI Weblog: torch time sequence, take three: Sequence-to-sequence prediction

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As we speak, we proceed our exploration of multi-step time-series forecasting with torch. This publish is the third in a sequence.

  • Initially, we coated fundamentals of recurrent neural networks (RNNs), and skilled a mannequin to foretell the very subsequent worth in a sequence. We additionally discovered we might forecast fairly just a few steps forward by feeding again particular person predictions in a loop.

  • Subsequent, we constructed a mannequin “natively” for multi-step prediction. A small multi-layer-perceptron (MLP) was used to challenge RNN output to a number of time factors sooner or later.

Of each approaches, the latter was the extra profitable. However conceptually, it has an unsatisfying contact to it: When the MLP extrapolates and generates output for, say, ten consecutive time limits, there is no such thing as a causal relation between these. (Think about a climate forecast for ten days that by no means received up to date.)

Now, we’d prefer to strive one thing extra intuitively interesting. The enter is a sequence; the output is a sequence. In pure language processing (NLP), one of these activity is quite common: It’s precisely the type of scenario we see with machine translation or summarization.

Fairly fittingly, the forms of fashions employed to those ends are named sequence-to-sequence fashions (typically abbreviated seq2seq). In a nutshell, they cut up up the duty into two parts: an encoding and a decoding half. The previous is completed simply as soon as per input-target pair. The latter is completed in a loop, as in our first strive. However the decoder has extra info at its disposal: At every iteration, its processing is predicated on the earlier prediction in addition to earlier state. That earlier state would be the encoder’s when a loop is began, and its personal ever thereafter.

Earlier than discussing the mannequin intimately, we have to adapt our information enter mechanism.

We proceed working with vic_elec , offered by tsibbledata.

Once more, the dataset definition within the present publish appears to be like a bit totally different from the best way it did earlier than; it’s the form of the goal that differs. This time, y equals x, shifted to the left by one.

The explanation we do that is owed to the best way we’re going to practice the community. With seq2seq, individuals typically use a method referred to as “trainer forcing” the place, as an alternative of feeding again its personal prediction into the decoder module, you go it the worth it ought to have predicted. To be clear, that is achieved throughout coaching solely, and to a configurable diploma.

library(torch)
library(tidyverse)
library(tsibble)
library(tsibbledata)
library(lubridate)
library(fable)
library(zeallot)

n_timesteps <- 7 * 24 * 2
n_forecast <- n_timesteps

vic_elec_get_year <- operate(yr, month = NULL) {
  vic_elec %>%
    filter(yr(Date) == yr, month(Date) == if (is.null(month)) month(Date) else month) %>%
    as_tibble() %>%
    choose(Demand)
}

elec_train <- vic_elec_get_year(2012) %>% as.matrix()
elec_valid <- vic_elec_get_year(2013) %>% as.matrix()
elec_test <- vic_elec_get_year(2014, 1) %>% as.matrix()

train_mean <- imply(elec_train)
train_sd <- sd(elec_train)

elec_dataset <- dataset(
  identify = "elec_dataset",
  
  initialize = operate(x, n_timesteps, sample_frac = 1) {
    
    self$n_timesteps <- n_timesteps
    self$x <- torch_tensor((x - train_mean) / train_sd)
    
    n <- size(self$x) - self$n_timesteps - 1
    
    self$begins <- kind(pattern.int(
      n = n,
      measurement = n * sample_frac
    ))
    
  },
  
  .getitem = operate(i) {
    
    begin <- self$begins[i]
    finish <- begin + self$n_timesteps - 1
    lag <- 1
    
    listing(
      x = self$x[start:end],
      y = self$x[(start+lag):(end+lag)]$squeeze(2)
    )
    
  },
  
  .size = operate() {
    size(self$begins) 
  }
)

Dataset in addition to dataloader instantations then can proceed as earlier than.

batch_size <- 32

train_ds <- elec_dataset(elec_train, n_timesteps, sample_frac = 0.5)
train_dl <- train_ds %>% dataloader(batch_size = batch_size, shuffle = TRUE)

valid_ds <- elec_dataset(elec_valid, n_timesteps, sample_frac = 0.5)
valid_dl <- valid_ds %>% dataloader(batch_size = batch_size)

test_ds <- elec_dataset(elec_test, n_timesteps)
test_dl <- test_ds %>% dataloader(batch_size = 1)

Technically, the mannequin consists of three modules: the aforementioned encoder and decoder, and the seq2seq module that orchestrates them.

Encoder

The encoder takes its enter and runs it via an RNN. Of the 2 issues returned by a recurrent neural community, outputs and state, to date we’ve solely been utilizing output. This time, we do the other: We throw away the outputs, and solely return the state.

If the RNN in query is a GRU (and assuming that of the outputs, we take simply the ultimate time step, which is what we’ve been doing all through), there actually isn’t any distinction: The ultimate state equals the ultimate output. If it’s an LSTM, nevertheless, there’s a second type of state, the “cell state”. In that case, returning the state as an alternative of the ultimate output will carry extra info.

encoder_module <- nn_module(
  
  initialize = operate(kind, input_size, hidden_size, num_layers = 1, dropout = 0) {
    
    self$kind <- kind
    
    self$rnn <- if (self$kind == "gru") {
      nn_gru(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        dropout = dropout,
        batch_first = TRUE
      )
    } else {
      nn_lstm(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        dropout = dropout,
        batch_first = TRUE
      )
    }
    
  },
  
  ahead = operate(x) {
    
    x <- self$rnn(x)
    
    # return final states for all layers
    # per layer, a single tensor for GRU, a listing of two tensors for LSTM
    x <- x[[2]]
    x
    
  }
  
)

Decoder

Within the decoder, identical to within the encoder, the principle part is an RNN. In distinction to previously-shown architectures, although, it doesn’t simply return a prediction. It additionally experiences again the RNN’s remaining state.

decoder_module <- nn_module(
  
  initialize = operate(kind, input_size, hidden_size, num_layers = 1) {
    
    self$kind <- kind
    
    self$rnn <- if (self$kind == "gru") {
      nn_gru(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        batch_first = TRUE
      )
    } else {
      nn_lstm(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        batch_first = TRUE
      )
    }
    
    self$linear <- nn_linear(hidden_size, 1)
    
  },
  
  ahead = operate(x, state) {
    
    # enter to ahead:
    # x is (batch_size, 1, 1)
    # state is (1, batch_size, hidden_size)
    x <- self$rnn(x, state)
    
    # break up RNN return values
    # output is (batch_size, 1, hidden_size)
    # next_hidden is
    c(output, next_hidden) %<-% x
    
    output <- output$squeeze(2)
    output <- self$linear(output)
    
    listing(output, next_hidden)
    
  }
  
)

seq2seq module

seq2seq is the place the motion occurs. The plan is to encode as soon as, then name the decoder in a loop.

Should you look again to decoder ahead(), you see that it takes two arguments: x and state.

Relying on the context, x corresponds to considered one of three issues: remaining enter, previous prediction, or prior floor fact.

  • The very first time the decoder is known as on an enter sequence, x maps to the ultimate enter worth. That is totally different from a activity like machine translation, the place you’d go in a begin token. With time sequence, although, we’d prefer to proceed the place the precise measurements cease.

  • In additional calls, we wish the decoder to proceed from its most up-to-date prediction. It’s only logical, thus, to go again the previous forecast.

  • That stated, in NLP a method referred to as “trainer forcing” is usually used to hurry up coaching. With trainer forcing, as an alternative of the forecast we go the precise floor fact, the factor the decoder ought to have predicted. We do this solely in a configurable fraction of circumstances, and – naturally – solely whereas coaching. The rationale behind this method is that with out this type of re-calibration, consecutive prediction errors can shortly erase any remaining sign.

state, too, is polyvalent. However right here, there are simply two prospects: encoder state and decoder state.

  • The primary time the decoder is known as, it’s “seeded” with the ultimate state from the encoder. Notice how that is the one time we make use of the encoding.

  • From then on, the decoder’s personal earlier state will probably be handed. Bear in mind the way it returns two values, forecast and state?

seq2seq_module <- nn_module(
  
  initialize = operate(kind, input_size, hidden_size, n_forecast, num_layers = 1, encoder_dropout = 0) {
    
    self$encoder <- encoder_module(kind = kind, input_size = input_size,
                                   hidden_size = hidden_size, num_layers, encoder_dropout)
    self$decoder <- decoder_module(kind = kind, input_size = input_size,
                                   hidden_size = hidden_size, num_layers)
    self$n_forecast <- n_forecast
    
  },
  
  ahead = operate(x, y, teacher_forcing_ratio) {
    
    # put together empty output
    outputs <- torch_zeros(dim(x)[1], self$n_forecast)$to(system = system)
    
    # encode present enter sequence
    hidden <- self$encoder(x)
    
    # prime decoder with remaining enter worth and hidden state from the encoder
    out <- self$decoder(x[ , n_timesteps, , drop = FALSE], hidden)
    
    # decompose into predictions and decoder state
    # pred is (batch_size, 1)
    # state is (1, batch_size, hidden_size)
    c(pred, state) %<-% out
    
    # retailer first prediction
    outputs[ , 1] <- pred$squeeze(2)
    
    # iterate to generate remaining forecasts
    for (t in 2:self$n_forecast) {
      
      # name decoder on both floor fact or earlier prediction, plus earlier decoder state
      teacher_forcing <- runif(1) < teacher_forcing_ratio
      enter <- if (teacher_forcing == TRUE) y[ , t - 1, drop = FALSE] else pred
      enter <- enter$unsqueeze(3)
      out <- self$decoder(enter, state)
      
      # once more, decompose decoder return values
      c(pred, state) %<-% out
      # and retailer present prediction
      outputs[ , t] <- pred$squeeze(2)
    }
    outputs
  }
  
)

web <- seq2seq_module("gru", input_size = 1, hidden_size = 32, n_forecast = n_forecast)

# coaching RNNs on the GPU at the moment prints a warning which will litter 
# the console
# see https://github.com/mlverse/torch/points/461
# alternatively, use 
# system <- "cpu"
system <- torch_device(if (cuda_is_available()) "cuda" else "cpu")

web <- web$to(system = system)

The coaching process is primarily unchanged. We do, nevertheless, have to resolve about teacher_forcing_ratio, the proportion of enter sequences we need to carry out re-calibration on. In valid_batch(), this could at all times be 0, whereas in train_batch(), it’s as much as us (or fairly, experimentation). Right here, we set it to 0.3.

optimizer <- optim_adam(web$parameters, lr = 0.001)

num_epochs <- 50

train_batch <- operate(b, teacher_forcing_ratio) {
  
  optimizer$zero_grad()
  output <- web(b$x$to(system = system), b$y$to(system = system), teacher_forcing_ratio)
  goal <- b$y$to(system = system)
  
  loss <- nnf_mse_loss(output, goal)
  loss$backward()
  optimizer$step()
  
  loss$merchandise()
  
}

valid_batch <- operate(b, teacher_forcing_ratio = 0) {
  
  output <- web(b$x$to(system = system), b$y$to(system = system), teacher_forcing_ratio)
  goal <- b$y$to(system = system)
  
  loss <- nnf_mse_loss(output, goal)
  
  loss$merchandise()
  
}

for (epoch in 1:num_epochs) {
  
  web$practice()
  train_loss <- c()
  
  coro::loop(for (b in train_dl) {
    loss <-train_batch(b, teacher_forcing_ratio = 0.3)
    train_loss <- c(train_loss, loss)
  })
  
  cat(sprintf("nEpoch %d, coaching: loss: %3.5f n", epoch, imply(train_loss)))
  
  web$eval()
  valid_loss <- c()
  
  coro::loop(for (b in valid_dl) {
    loss <- valid_batch(b)
    valid_loss <- c(valid_loss, loss)
  })
  
  cat(sprintf("nEpoch %d, validation: loss: %3.5f n", epoch, imply(valid_loss)))
}
Epoch 1, coaching: loss: 0.37961 

Epoch 1, validation: loss: 1.10699 

Epoch 2, coaching: loss: 0.19355 

Epoch 2, validation: loss: 1.26462 

# ...
# ...

Epoch 49, coaching: loss: 0.03233 

Epoch 49, validation: loss: 0.62286 

Epoch 50, coaching: loss: 0.03091 

Epoch 50, validation: loss: 0.54457

It’s attention-grabbing to check performances for various settings of teacher_forcing_ratio. With a setting of 0.5, coaching loss decreases much more slowly; the other is seen with a setting of 0. Validation loss, nevertheless, shouldn’t be affected considerably.

The code to examine test-set forecasts is unchanged.

web$eval()

test_preds <- vector(mode = "listing", size = size(test_dl))

i <- 1

coro::loop(for (b in test_dl) {
  
  output <- web(b$x$to(system = system), b$y$to(system = system), teacher_forcing_ratio = 0)
  preds <- as.numeric(output)
  
  test_preds[[i]] <- preds
  i <<- i + 1
  
})

vic_elec_jan_2014 <- vic_elec %>%
  filter(yr(Date) == 2014, month(Date) == 1)

test_pred1 <- test_preds[[1]]
test_pred1 <- c(rep(NA, n_timesteps), test_pred1, rep(NA, nrow(vic_elec_jan_2014) - n_timesteps - n_forecast))

test_pred2 <- test_preds[[408]]
test_pred2 <- c(rep(NA, n_timesteps + 407), test_pred2, rep(NA, nrow(vic_elec_jan_2014) - 407 - n_timesteps - n_forecast))

test_pred3 <- test_preds[[817]]
test_pred3 <- c(rep(NA, nrow(vic_elec_jan_2014) - n_forecast), test_pred3)


preds_ts <- vic_elec_jan_2014 %>%
  choose(Demand) %>%
  add_column(
    mlp_ex_1 = test_pred1 * train_sd + train_mean,
    mlp_ex_2 = test_pred2 * train_sd + train_mean,
    mlp_ex_3 = test_pred3 * train_sd + train_mean) %>%
  pivot_longer(-Time) %>%
  update_tsibble(key = identify)


preds_ts %>%
  autoplot() +
  scale_colour_manual(values = c("#08c5d1", "#00353f", "#ffbf66", "#d46f4d")) +
  theme_minimal()

One-week-ahead predictions for January, 2014.

Determine 1: One-week-ahead predictions for January, 2014.

Evaluating this to the forecast obtained from final time’s RNN-MLP combo, we don’t see a lot of a distinction. Is that this stunning? To me it’s. If requested to invest concerning the purpose, I might in all probability say this: In all the architectures we’ve used to date, the principle provider of data has been the ultimate hidden state of the RNN (one and solely RNN within the two earlier setups, encoder RNN on this one). It is going to be attention-grabbing to see what occurs within the final a part of this sequence, once we increase the encoder-decoder structure by consideration.

Thanks for studying!

Picture by Suzuha Kozuki on Unsplash

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