Sunday, March 3, 2024

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


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

  • 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 a couple of 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 mission 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 isn’t any causal relation between these. (Think about a climate forecast for ten days that by no means acquired up to date.)

Now, we’d wish to attempt 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 kinds of fashions employed to those ends are named sequence-to-sequence fashions (usually abbreviated seq2seq). In a nutshell, they break 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 attempt. 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 knowledge enter mechanism.

We proceed working with vic_elec , offered by tsibbledata.

Once more, the dataset definition within the present publish seems to be a bit completely 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 rationale we do that is owed to the best way we’re going to practice the community. With seq2seq, folks usually use a way referred to as “instructor forcing” the place, as an alternative of feeding again its personal prediction into the decoder module, you move it the worth it ought to have predicted. To be clear, that is accomplished 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(12 months, month = NULL) {
  vic_elec %>%
    filter(12 months(Date) == 12 months, 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,
      dimension = 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 this point we’ve solely been utilizing output. This time, we do the alternative: 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, nonetheless, 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, an inventory 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 reviews 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.

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

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

  • The very first time the decoder is named on an enter sequence, x maps to the ultimate enter worth. That is completely different from a activity like machine translation, the place you’ll move in a begin token. With time collection, although, we’d wish 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 move again the previous forecast.

  • That stated, in NLP a way referred to as “instructor forcing” is often used to hurry up coaching. With instructor forcing, as an alternative of the forecast we move the precise floor reality, the factor the decoder ought to have predicted. We try this solely in a configurable fraction of instances, and – naturally – solely whereas coaching. The rationale behind this system 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 named, it’s “seeded” with the ultimate state from the encoder. Observe 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(gadget = gadget)
    
    # 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 reality 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
  }
  
)

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

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

internet <- internet$to(gadget = gadget)

The coaching process is primarily unchanged. We do, nonetheless, 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 all the time be 0, whereas in train_batch(), it’s as much as us (or quite, experimentation). Right here, we set it to 0.3.

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

num_epochs <- 50

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

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

for (epoch in 1:num_epochs) {
  
  internet$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)))
  
  internet$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 match performances for various settings of teacher_forcing_ratio. With a setting of 0.5, coaching loss decreases much more slowly; the alternative is seen with a setting of 0. Validation loss, nonetheless, is just not affected considerably.

The code to examine test-set forecasts is unchanged.

internet$eval()

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

i <- 1

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

vic_elec_jan_2014 <- vic_elec %>%
  filter(12 months(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 take a position concerning the motive, I might in all probability say this: In the entire architectures we’ve used to this point, the principle service of knowledge has been the ultimate hidden state of the RNN (one and solely RNN within the two earlier setups, encoder RNN on this one). It will likely be attention-grabbing to see what occurs within the final a part of this collection, once we increase the encoder-decoder structure by consideration.

Thanks for studying!

Photograph by Suzuha Kozuki on Unsplash

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