LLaMA in R with Keras and TensorFlow

Artificial Intelligence

LLaMA in R with Keras and TensorFlow

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2023年12月10日

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OpenAI’s chatGPT has woke up a collective consciousness of what Massive
Language Fashions (LLMs) are able to. With that awakening comes a each day
march of LLM information: new merchandise, new options, new fashions, new
capabilities, (and new worries). It appears we’re within the early phases of a
Cambrian explosion of LLMs and LLM powered instruments; it’s not but clear how
LLMs will influence and affect our skilled and private lives, however
it appears clear that they may, ultimately.

Since LLMs are right here to remain, it’s worthwhile to take a while to
perceive how these fashions work from a first-principles perspective.
Beginning with the mechanics might help foster sturdy intuitions that may
inform our utilization of those fashions now and sooner or later. (Particularly if
the long run is one the place LLMs are a staple of the info scientist’s
toolbox, as frequent as an lm() perform name).

And what higher approach is there to be taught than by doing. So with that
preamble, on this submit we’ll stroll by way of an implementation of an LLM,
LLaMA (Touvron et al. 2023)
particularly, in TensorFlow and Keras, with the purpose being to develop
understanding first, functionality second.

Why LLaMA? With the sheer quantity of LLM associated content material and information out
there, it might probably appear formidable to know the place to get began. Virtually weekly
it appears there’s a new mannequin introduced. Shopping some hubs of LLM
exercise (HuggingFace,
TFHub,
reddit,
HackerNews) muddies the waters even
extra. decide a selected mannequin?

Of the various LLM-related information objects up to now months, one which stands
head-and-shoulders above the group is the launch of
LLaMA,
a contemporary, foundational LLM made out there to the general public by Meta AI in
February 2023. On frequent benchmarks, LLaMA outperforms OpenAI’s GPT-3,
whereas being considerably smaller (although nonetheless giant).

LLaMA is a superb beginning place as a result of it’s a easy and trendy
structure, has glorious efficiency on benchmarks, and is open. The
mannequin structure has had just some new concepts included into it since
the unique Transformer structure first described in,
“Consideration Is All You Want”
revealed from Google (Vaswani et al. 2017). 4 totally different sizes of
LLaMA have been launched: 7 billion and 13 billion parameter fashions
educated on 1 Trillion tokens, and 33 billion and 65 billion parameter
fashions educated on 1.4 trillion tokens. This is a gigantic quantity of
coaching information these fashions have seen–the most important 65B mannequin has been
educated on roughly the “Chinchilla
compute-optimum” (Hoffmann et al. 2022)
variety of tokens, whereas the smaller LLaMAs are considerably
past that optimum. On this weblog submit we’ll give attention to the smallest, 7B
parameter LLaMA mannequin, which you’ll comfortably load domestically and run on
CPU with solely 64Gb of RAM.

Whereas not strictly essential, to observe alongside domestically, you’ll in all probability
wish to purchase the pre-trained LLaMA weights one
approach or
one other. Observe, the
weights do include their very own license, which you’ll preview
right here.

So, with out additional ado, let’s get began.

Setup

First, we’ll wish to set up the required R and Python packages, and
configure a digital setting:

remotes::install_github(c("rstudio/reticulate",
                          "rstudio/tensorflow",
                          "rstudio/keras"))
# reticulate::install_python("3.10:newest")                          
reticulate::virtualenv_create("./.venv", model = "3.10:newest")
tensorflow::install_tensorflow(envname = "./.venv", model = "launch",
                               extra_packages = "tensorflow-text")

library(purrr)
library(envir)

library(tensorflow)
library(tfautograph)
library(keras)

use_virtualenv("./.venv")
choices(tensorflow.extract.warn_tensors_passed_asis = FALSE)

attach_eval({
  import_from(glue, glue)
  import_from(jsonlite, read_json)
  import_from(withr, with_dir, with_options)
  import_from(keras$layers, Dense)
  np <- reticulate::import("numpy", convert = FALSE)

  seq_len0 <- perform(x) seq.int(from = 0L, size.out = x)
})

# reticulate::py_install("torch", pip = TRUE)
torch <- reticulate::import("torch", convert = FALSE)
with_dir("~/github/facebookresearch/llama/weights/LLaMA/7B", {
  pretrained_weights <- torch$load("consolidated.00.pth",
                                   map_location = "cpu")
  for (title in names(pretrained_weights)) {
    filename <- sprintf("%s.npy", title)
    array <- pretrained_weights[[name]]$numpy()
    np$save(filename, array)
    message(glue(
      "wrote: '{basename(filename)}' with form: {array$form}"))
  }
})

weights_path <- perform(filename) normalizePath(file.path(
  "~/github/facebookresearch/llama/weights/LLaMA/",
  glue(filename, .envir = dad or mum.body())), mustWork = TRUE)

params <- read_json(weights_path("7B/params.json"))
str(params)

Checklist of 6
 $ dim        : int 4096
 $ multiple_of: int 256
 $ n_heads    : int 32
 $ n_layers   : int 32
 $ norm_eps   : num 1e-06
 $ vocab_size : int -1

Tokenizer

SentencePiece tokenizer from
Google. SentencePiece is accessible as a TensorFlow graph operation
by way of
tf_text.SentencepieceTokenizer,
and in addition as a Keras layer in
keras_nlp.tokenizers.SentencepieceTokenizer.
By alternative of a coin flip, we’ll use the lower-level tf_text interface.

tf_text <- reticulate::import("tensorflow_text")
tokenizer_path <- weights_path("tokenizer.mannequin")
tokenizer <- tf_text$SentencepieceTokenizer(
  tf$io$gfile$GFile(tokenizer_path, "rb")$learn(),
  add_bos = TRUE, add_eos = FALSE,
)

immediate <- "One of the best ways to draw bees"
tokenizer$tokenize(immediate)

tf.Tensor([    1   450  1900   982   304 13978   367   267], form=(8), dtype=int32)

immediate |> tokenizer$tokenize() |> tokenizer$detokenize()

tf.Tensor(b'One of the best ways to draw bees', form=(), dtype=string)

Let’s outline a show_tokens() helper perform and play with the
tokenizer somewhat.

show_tokens <- perform(what) > as.integer()
  else
    token_ids <- as.integer(what)
  tokens <- token_ids 

show_tokens(immediate)

        1       450      1900       982       304     13978       367       267
       ""     "The"    "finest"     "approach"      "to" "entice"      "be"      "es"

Observe that “bees” is 2 tokens. Not each token corresponds to a phrase.
For instance, one non-word token we will reliably anticipate to point out up in a
tokenizer educated on a corpus of English textual content is “ing.” Nevertheless, when the
“ing” token exhibits up is not going to at all times observe your intuitions, as a result of
frequent phrases get their very own token id, even when they are often decomposed into
a number of tokens.

    1  2348
   "" "ing"

        1      1985
       "" "working"

     1   8525    292
    "" "flex"  "ing"

     1   2113   9292
    ""  "received" "king"

One other factor to notice in regards to the tokenizer is that every token sequence
begins with token id 1. It is a particular beginning-of-sequence
token that we requested be added after we loaded the tokenizer with
add_bos = TRUE. There are two different such particular tokens that we are going to
encounter later: an end-of-sequence particular tokens with id 2, and an
unknown-token with id 0.

as.character(tokenizer$id_to_string(0L))

[1] "<unk>"

as.character(tokenizer$id_to_string(1L))

[1] "<s>"

as.character(tokenizer$id_to_string(2L))

[1] "</s>"

    1     0     2
   "" " ⁇ "    ""

General, there are 32,000 tokens.

as.integer(tokenizer$vocab_size())

[1] 32000

One final commentary is that the extra ceaselessly encountered tokens are
assigned decrease ids.

show_tokens(seq(50, len = 10))

 50  51  52  53  54  55  56  57  58  59
"/" "0" "1" "2" "3" "4" "5" "6" "7" "8"

show_tokens(seq(100, len = 10))

100 101 102 103 104 105 106 107 108 109
"a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

show_tokens(seq(1000, len = 10))

   1000    1001    1002    1003    1004    1005    1006    1007    1008    1009
  "ied"    "ER"  "stat"   "fig"    "me"   "von" "inter"  "roid"  "ater" "their"

show_tokens(seq(10000, len = 10))

   10000    10001    10002    10003    10004    10005    10006    10007
   "ång"  "citep"    "Sick"   "rank" "sender"   "beim"    "рак" "compat"
   10008    10009
"happens"  "diese"

show_tokens(seq(20000, len = 10))

    20000     20001     20002     20003     20004     20005     20006     20007
  "admit" "Remark"     "стя"    "Vien"      "ці"  "permut"     "cgi"    "crít"
    20008     20009
"Console"    "ctic"

show_tokens(seq(to = as.integer(tokenizer$vocab_size()) - 1, len = 10))

31990 31991 31992 31993 31994 31995 31996 31997 31998 31999
  "ὀ"  "げ"  "べ"  "边"  "还"  "黃"  "왕"  "收"  "弘"  "给"

Shifting on, the subsequent step after tokenization is embedding. An embedding
layer is successfully a dictionary lookup that converts an integer (token
id) to a 1-d float array. For this we will use the usual keras
Embedding layer.

tok_embeddings <- keras$layers$Embedding(
  input_dim = tokenizer$vocab_size(),
  output_dim = params$dim,
  embeddings_initializer =
    (...) np$load(weights_path("7B/tok_embeddings.weight.npy"))
)

tok_embeddings(3L) |> str()

<tf.Tensor: form=(4096), dtype=float32, numpy=…>

immediate |> # "One of the best ways to draw bees"
  tokenizer$tokenize() |>
  tok_embeddings() |>
  str()

<tf.Tensor: form=(8, 4096), dtype=float32, numpy=…>

`TransformerBlock`

As soon as it’s tokenized and embedded, the enter then passes by way of the majority
of the mannequin, a sequence of repeating TransformerBlock layers. The 7B
mannequin has 32 of those TransformerBlock layers, whereas the 65B mannequin has
80 of them.

weights_path("7B/params.json")  |> read_json() |> _$n_layers

[1] 32

weights_path("65B/params.json") |> read_json() |> _$n_layers

[1] 80

Here’s what the transformer block seems to be like:

TransformerBlock(keras$layers$Layer) %py_class% {
  initialize <- perform(attn_head_size, attn_n_heads,
                         norm_eps = k_epsilon(), ...,
                         block_id = NULL) {
    tremendous$initialize(...)

    self$consideration <- Consideration(attn_head_size, attn_n_heads,
                                block_id = block_id)

    self$feed_forward <- FeedForward(
      hidden_dim = 4 * attn_head_size * attn_n_heads,
      block_id = block_id)

    self$attention_norm <- RMSNorm(eps = norm_eps,
                                   block_id = block_id,
                                   feeds_into = "consideration")
    self$feed_forward_norm <- RMSNorm(eps = norm_eps,
                                      block_id = block_id,
                                      feeds_into = "ffn")
  }

  name <- perform(x) >
      self$consideration()

    x <- x + x2 # add residual

    # norm and swiglu
    x2 <- x %>%
      self$feed_forward_norm() %>%
      self$feed_forward()

    x <- x + x2 # residual once more

    x
  
}

Whereas there may be not a whole lot of code, there are a whole lot of concepts packed in
there. This block varieties the principle trunk of the mannequin, so it’s price
taking the time to undergo it slowly.

We implement the TransformerBlock as a subclassed
keras.layers.Layer. That is offers us some niceties like the power to
compose with different Keras layers, however these are largely irrelevant to the
objective of this weblog submit; we may simply as simply implement this as,
for instance, a vanilla R6 class. Our TransformerBlock class has two
strategies: initialize, referred to as after we first create the block, and
name, referred to as after we run the ahead cross of the block.

In initialize, we create 4 layers: an Consideration layer, a
FeedForward layer, and a pair of RMSNorm layers. We’ll take an in depth have a look at
every of those quickly, however even earlier than we achieve this, we will see how they match
collectively by wanting on the TransformerBlock$name() technique.

The name technique has just a few easy concepts. In no specific order, the
first one to look at is the composition sample of including residuals.

x2 <- x |> ...
x <- x + x2 # add residual x to x2

vanishing gradient
downside. It’s
a skip-connection within the other-wise linear sequence of matrix
transformations. It reinjects data (in the course of the ahead cross), and
gradients (throughout again propagation), again into the trunk. You’ll be able to suppose
of those residual connections as releasing the learnable layers in-between
(the ... within the pseudo code) from the burden of getting to
“pass-through” or “protect” data in x, permitting the weights to
as an alternative give attention to studying transformations which can be, (in corporatese
vernacular), value-adding.

The subsequent composition sample to notice is the repeating utilization of a
normalization layer:

x2 <- x |> norm() |> ...
x <- x + x2

There are numerous sorts of normalization layers, however to barely
over-generalize, they’ll all be regarded as a stabilizer that helps
with coaching. Like their deep-learning cousins the regularizers, their
principal perform is to maintain values passing by way of in a smart vary–in
the ball park of (-1, 1), sometimes. We’ll take a better have a look at
RMSNorm quickly.

Stripped of two methods which can be largely there to assist the mannequin practice,
residuals and normalization, the core of the TransformerBlock is simply
this:

x |> consideration() |> feed_forward()

In a second we’ll see that that feed_foward is a barely fancier
variation of a traditional sequence of Dense layer. Earlier than we get
there we will we safely skip forward to distill the next instinct: a
TransformerBlock is principally an Consideration layer adopted by just a few
(fancy) dense layers, with some easy composition patterns (methods)
that assist with coaching. Consideration is the center of the mannequin: it’s the
most fascinating, and in addition probably the most concerned.

With the framing in place, let’s undergo and take a better have a look at
RMSNorm, FeedForward, after which with the muse in place, we’ll
flip our consideration to Consideration.

`RMSNorm`

RMSNorm(keras$layers$Layer) %py_class% {
  initialize <-
    perform(eps = 1e-6, ..., block_id = NULL, feeds_into = NULL) {
      tremendous$initialize(...)
      self$eps <- eps
      self$block_id <- block_id
      self$feeds_into <- feeds_into
    }

  construct <- perform(input_shape) {
    # input_shape == (batch_size, seqlen, params$dim)
    # self$w will broadcast over batch_size and seqlen dims.
    # w_shape == (1, 1, params$dim)
    w_shape <- rep(1L, size(input_shape))
    w_shape[length(input_shape)] <- as.integer(input_shape) |> tail(1L)

    # outline a neighborhood perform that may load
    # the pretrained-weights if we equipped `block_id` and `feeds_into`
    import_from({self}, block_id, feeds_into)
    initializer <-if (is.null(block_id))
      "ones"
      else if (block_id >=0) {
        (...) weights_path("7B/layers.{block_id}.{feeds_into}_norm.weight.npy") |>
               np$load() |> np$expand_dims(0:1)
      } else if(block_id == -1)
        # load weights for the ultimate output normalization layer, which isn't
        # a part of a TransformerBlock
        (...) weights_path("7B/norm.weight.npy") |>
               np$load() |> np$expand_dims(0:1)

    self$w <- self$add_weight(form = w_shape,
                              initializer = initializer,
                              trainable = TRUE)
  }

  rrms <- perform(x) {
    # reciprocal root imply sq. alongside the final axis
    x %>% # (batch_size, seqlen, n_features)
      tf$math$sq.() %>%
      tf$reduce_mean(axis = -1L, keepdims = TRUE) %>% # (batch_size, seqlen, 1)
      tf$math$add(self$eps) %>% # for numerical stability
      tf$math$rsqrt()
  }

  name <- perform(x) {
    x * self$rrms(x) * self$w
  }
}

RMSnorm() has a single trainable tensor w. Within the ahead cross, every
worth within the enter is multiplied by the reciprocal-root-mean-square of
all of the values within the characteristic axis and by w. Actually a mouthful, however
only a easy sequence of arithmetic transformations in the long run,
designed for the specific objective of adjusting the vary of values
passing by way of.

Let’s kick the tires on it:

norm <- RMSNorm()
m <- matrix(c(0, 1,
              2, 3), nrow = 2)
norm(m)

tf.Tensor(
[[0.         1.4142132 ]
 [0.44721353 1.3416406 ]], form=(2, 2), dtype=float32)

tf.Tensor(
[[0.         1.4142137 ]
 [0.44721362 1.3416408 ]], form=(2, 2), dtype=float32)

tf.Tensor(
[[0.        1.4142137]
 [0.4472136 1.3416408]], form=(2, 2), dtype=float32)

`FeedForward`

Subsequent up is FeedForward()

FeedForward(keras$layers$Layer) %py_class% {

  initialize <- perform(hidden_dim, multiple_of = 256L,
                         ..., block_id = NULL) {
    tremendous$initialize()

    if(!is.null(multiple_of)) {
      hidden_dim <- hidden_dim %>%
        { as.integer( . * (2/3)) } %>%
        { (. + multiple_of - 1) %/% multiple_of } %>%
        { . * multiple_of }
    }

    self$hidden_dim <- hidden_dim
    self$block_id <- block_id
  }

  construct <- perform(input_shape) {
    output_dim <- input_shape |> as.integer() |> tail(1)

    if(is.null(self$block_id))
      load_weight <- (...) NULL
    else
      load_weight <- (title) (...) np$load(weights_path(
        "7B/layers.{self$block_id}.feed_forward.{title}.weight.npy"))$`T`

    self$w1 <- Dense(self$hidden_dim, use_bias = FALSE,
                     kernel_initializer = load_weight("w1"))
    self$w2 <- Dense(output_dim, use_bias = FALSE,
                     kernel_initializer = load_weight("w2"))
    self$w3 <- Dense(self$hidden_dim, use_bias = FALSE,
                     kernel_initializer = load_weight("w3"))

    tremendous$construct(input_shape)
  }

  name <- perform(x) {
    import_from({self}, w1, w2, w3)
    import_from(tf$nn, silu)

    x %>%
      { silu(w1(.)) * w3(.) } %>% # SwiGLU
      w2()
  }

}

Shazeer (2020)
of SwiGLU and different variations on GLU is an exemplar of the categories
of explorations and enhancements across the Transformer structure
since its preliminary publication in
2017; a gradual accretion of
enhancements that has introduced us to at this time. The Feedforward$name() is
only a single SwiGLU adopted by a linear projection. In its essence,
it’s a intelligent composition of three (discovered) linear projections, an
element-wise multiplication, and a silu()
activation
perform.

Maybe probably the most shocking commentary to make right here is the relative
dearth of activation features, and even non-linearities, not simply in
FeedForward, however general. The silu() on this feedforward, the
reciprocal-root-mean-square in RMSnorm(), and a softmax() in
Consideration() are the one non-linear transformations in the entire
sequence of TransformerBlocks. All the pieces else is a linear
transformation!

`Consideration`

Lastly, let’s flip our consideration to Consideration().

Consideration(keras$layers$Layer) %py_class% {
  initialize <- perform(head_size, n_heads,
                         ..., block_id = NULL) {
    tremendous$initialize(...)

    self$head_size <- head_size
    self$n_heads <- n_heads

    if (is.null(block_id))
      load_weight <- perform(title) NULL
    else
      load_weight <- (title) (...) np$load(weights_path(
        "7B/layers.{block_id}.consideration.{title}.weight.npy"))$`T`

    Dense <- perform(title) keras$layers$Dense(
      items = n_heads * head_size,
      use_bias = FALSE,
      kernel_initializer = load_weight(title)
    )

    self$wq <- Dense("wq")
    self$wk <- Dense("wk")
    self$wv <- Dense("wv")
    self$wo <- Dense("wo")
  }

  name <- perform(x) {
    c(batch_size, seqlen, n_features) %<-% tf$unstack(tf$form(x))

    # 1. venture (linear remodel) x into
    #    question, key, and worth tensors
    # 2. reshape q okay v, splitting out the final dim (n_features)
    #    into n_heads unbiased subspaces,
    #    every with measurement head_size.
    #    (n_features == head_size * n_heads)
    split_heads_shape <- c(batch_size, seqlen,
                           self$n_heads, self$head_size)
    q <- x |> self$wq() |> tf$reshape(split_heads_shape)
    okay <- x |> self$wk() |> tf$reshape(split_heads_shape)
    v <- x |> self$wv() |> tf$reshape(split_heads_shape)

    # embed positional data in question and key
    # (bsz, seqlen, n_heads, head_size)
    q %<>% apply_rotary_embedding()
    okay %<>% apply_rotary_embedding()

    # reshape:
    #   transfer heads out of the final 2 axes,
    #   so later matmuls are carried out throughout the subspaces (heads)
    #   between (seqlen, head_size) axes
    v <- tf$transpose(v, c(0L, 2L, 1L, 3L)) # (bsz, n_heads, seqlen, head_size)
    q <- tf$transpose(q, c(0L, 2L, 1L, 3L)) # (bsz, n_heads, seqlen, head_size)
    okay <- tf$transpose(okay, c(0L, 2L, 3L, 1L)) # (bsz, n_heads, head_size, seqlen)

    # calculate and normalize consideration scores
    scores <- q %*% okay                       # (bsz, n_heads, seqlen, seqlen)
    scores <- scores / sqrt(self$head_size) # scale

    # apply causal masks, so the mannequin cannot "look forward" throughout coaching
    masks <- make_mask(seqlen, dtype = scores$dtype)
    scores %<>% { . + masks }

    scores <- tf$nn$softmax(scores, axis = -1L)

    # alter values tensor with consideration scores
                      # scores (bsz, n_heads, seqlen, seqlen)
                      # v      (bsz, n_heads, seqlen, head_size)
    output <- scores %*% v   # (bsz, n_heads, seqlen, head_size)

    # mix heads again right into a single options dim,
    # so Consideration output_shape==input_shape
    output <- output |>
      tf$transpose(c(0L, 2L, 1L, 3L)) |> # (bsz, seqlen, n_heads, head_size)
      tf$reshape(tf$form(x))            # (bsz, seqlen, n_heads * head_size)

    # yet another trainable linear projection for good luck
    output <- self$wo(output) # (bsz, seqlen, n_heads * head_size)

    output
  }
}

authentic Transformers
paper (and out there as a keras
builtin underneath keras$layers$MultiHeadAttention()). The core novelty is
the addition of the apply_rotary_embedding() perform, which we’ll
describe shortly. The extra novelty is balanced by the simplicity
from the truth that the layer is performing self-attention—we don’t want
to cross in several question, key, and worth tensors (or purpose about what
meaning), for the reason that similar enter serves all three roles. Observe that the
standard MultiHeadAttention() layer is roofed fairly completely in
the 2nd Version of Deep Studying with R,
together with a full implementation of consideration in base R.

To develop an understanding of the mechanics in a layer like this, it’s
useful to quickly unsee among the minutia that may act as a fog
obscuring the essence of the operation. On this occasion, if we
quickly strip out the transpose()s and reshape()s (as intelligent and
very important as they’re), that is what’s left:

name <- perform(x) > self$wq()
  okay <- x

Returning to the transpose()s and reshapes(), you’ll be able to observe that
their objective is to make it in order that the eye calculations are
carried out throughout n_heads unbiased subspaces, somewhat than in a
single bigger area. The identical reasoning drives this resolution as that
driving utilization of depthwise-separable convolutions in picture fashions.
Empirically, for the fastened compute finances, factoring options into
unbiased subspaces performs higher than doing the identical core
operations in single bigger characteristic area. As with all issues, there may be
a steadiness to strike between n_heads (the variety of subspaces) and
head_dim (the scale of every subspace). The LLaMA authors have struck
the steadiness like this on the varied mannequin sizes:

lapply(c("7B", "13B", "30B", "65B"), (measurement) {
  p <- read_json(weights_path("{measurement}/params.json"))
  with(p, listing(llama_size = measurement,
               n_heads = n_heads,
               head_dim = dim %/% n_heads))
}) |> dplyr::bind_rows()

# A tibble: 4 × 3
  llama_size n_heads head_dim
  <chr>        <int>    <int>
1 7B              32      128
2 13B             40      128
3 30B             52      128
4 65B             64      128

Subsequent lets flip our consideration to the causal consideration masks.

make_mask <- perform(seqlen, dtype = k_floatx()) {
  x <- tf$vary(seqlen)
  masks <- tf$the place(x[, tf$newaxis] < x[tf$newaxis, ],
                   tf$fixed(-Inf, dtype = dtype),
                   tf$fixed(0, dtype = dtype))

  # broadcast over batch and heads dim
  masks[tf$newaxis, tf$newaxis, , ] # (1, 1, seqlen, seqlen)
}

The masks is a strictly higher triangular matrix stuffed with -Inf
values. Including the masks to the eye scores prevents the mannequin from
with the ability to “look forward” and see the eye rating for a token
pairing it hasn’t seen but at a selected place within the sequence.
This want for a masks is finest regarded as a vestige from coaching,
an equipment that the mannequin wanted to be taught with and now it might probably’t perform with out.
Throughout coaching, gradients are calculated for predictions from all
token positions in a sequence, together with predictions tokens the place the proper
reply is proper there, because the very subsequent token in similar sequence. The masks
prevents the mannequin from with the ability to cheat and look forward into the long run,
one thing it received’t have the ability to do as soon as it’s we’re working it for inference.

tf.Tensor(
[[[[  0. -inf -inf -inf -inf]
   [  0.   0. -inf -inf -inf]
   [  0.   0.   0. -inf -inf]
   [  0.   0.   0.   0. -inf]
   [  0.   0.   0.   0.   0.]]]], form=(1, 1, 5, 5), dtype=float32)

Rotary Place Embedding

Su et al. (2022) within the paper titled
“RoFormer: Enhanced Transformer with Rotary Place Embedding”.

Some context:

The naked Consideration() mechanism doesn’t depart any chance for a
token’s place in a sequence to have an effect on the eye scores, since
solely token-pairs are scored. Consideration treats its enter like a
bag-of-tokens.
The place of a token in a sequence is clearly essential, and the
consideration layer ought to have entry to that data.
Absolutely the place of a token in a sequence is much less essential
than the relative place between tokens. (Particularly so for lengthy
sequences).

Which leads us into the complicated aircraft. If we think about the options as
complicated numbers, we will rotate them, and we will calculate angles between
them. From the Roformers paper:

Particularly, incorporating the relative place embedding is
simple: merely rotate the affine-transformed phrase embedding
vector by quantity of angle multiples of its place index and thus
interprets the instinct behind Rotary Place Embedding

Increasing barely: the rotation matrix is designed in order that
subsequently, after rotating our q and okay token sequence embedding
the identical approach, the angle between token options is a perform of the
relative distance between these tokens within the token sequence. The
relative angle between two tokens is invariant to absolutely the
place of these tokens within the full sequence.

In brief, the rotation injects positional data. The which means or
interpretability of that positional data, or how it’s meant to
be used, and even extracted from the results of q %*% okay, is left to the
mannequin to be taught.

Right here is the code:

apply_rotary_embedding <- perform(x) {
  c(., seqlen, ., head_size) %<-%
    tf$unstack(tf$form(x))

  rotation_matrix <- compute_rotation_matrix(seqlen, head_size)

  x %>%
    view_as_complex() %>%
    { . * rotation_matrix } %>%
    view_as_real()

}

compute_rotation_matrix <-
  perform(seqlen, feature_dim, theta = 10000) {
    # `feature_dim` right here goes to be consideration$head_size
    # `seqlen` goes to match the token sequence size.

    t <- tf$vary(seqlen, dtype = tf$float32)
    freqs <- tf$vary(begin = 0, restrict = 1, delta = 1 / (feature_dim %/% 2),
                      dtype = tf$float32)
    tf_assert(tf$measurement(freqs) == feature_dim %/% 2)
    freqs <- 1.0 / (theta ^ freqs)

    # outer product; (seqlen, head_size/2)
    freqs <- tf$einsum('a,b->ab', t, freqs)

    rot_mat <- tf$complicated(tf$cos(freqs), tf$sin(freqs))

    # the positional embedding will probably be broadcast throughout batch and heads dim
    rot_mat[tf$newaxis, , tf$newaxis, ] #(1, seqlen, 1, headdim/2)
  }

view_as_complex <- perform(x) {
  tf$complicated(x[all_dims(), `::2`],
             x[all_dims(), `2::2`])
}

view_as_real <- perform(x) {
  # xs = (..., f);  xs2 = (..., f*2)
  xs <- tf$form(x)
  xs2 <- tf$concat(listing(xs[1:(length(xs)-1)],
                        xs[length(xs), drop = FALSE] * 2L),
                   axis = 0L)

  x2 <- tf$stack(listing(Re(x), Im(x)), axis = -1L)

  # (..., f, 2) -> (..., f*2)
  tf$reshape(x2, xs2)
}

As you’ll be able to see, to think about the embedding options as present within the
complicated aircraft, we merely deal with adjoining pairs of floats within the
underlying array as the true and imaginary a part of a posh quantity. We
rotate the embeddings within the complicated aircraft, then return to imagining
the options as present in the true aircraft. Once more, the job of
decoding the which means of the options after rotation is left to the
mannequin to be taught.

We are able to rapidly affirm that the rotary embeddings solely rotate options
and don’t scale them:

close to <- perform (x, y, tol = 1e-6) abs(x - y) < tol
all(close to(1, Mod(compute_rotation_matrix(2048L, 128L))))

tf.Tensor(True, form=(), dtype=bool)

There may be yet another trick to look at earlier than shifting on: due to a few of
the mathematical properties of the rotation matrix, it’s doable to
keep away from doing a full complicated multiply operation and nonetheless arrive on the
similar consequence. Additionally, for the reason that rotation matrix by no means adjustments, it makes
sense to solely compute it as soon as and cache it, like so:

precomputed_rotation_matrix <- compute_rotation_matrix(
  seqlen = 2048L, # LLaMA max seqlen
  feature_dim = with(params, dim %/% n_heads)  # head_size
)

apply_rotary_embedding_faster <- perform(x) {

  rotate_every_two <- perform(x) {
    x1 <- x[all_dims(), `::2`]
    x2 <- x[all_dims(), `2::2`]
    x_ <- tf$stack(listing(-x2, x1), axis = -1L)
    tf$reshape(x_, tf$form(x))
  }

  repeat_each_twice <- perform(x) {
    tf$`repeat`(x, 2L, axis = -1L)
  }

  seqlen <- tf$form(x)[2]
  rot <- precomputed_rotation_matrix[, NA:seqlen, , ]

  cos <- Re(rot) |> repeat_each_twice()
  sin <- Im(rot) |> repeat_each_twice()

  (x * cos) + (rotate_every_two(x) * sin)
}

rand <- tf$random$uniform(form(3, 8, params$n_heads, 128))
all(apply_rotary_embedding(rand) ==
    apply_rotary_embedding_faster(rand))

tf.Tensor(True, form=(), dtype=bool)

apply_rotary_embedding <- apply_rotary_embedding_faster

Lastly, observe that the rotary positional embeddings are utilized inside
every Consideration layer. That is totally different from the unique Transformer
implementation, the place a positional embedding was solely added as soon as on the
head of the mannequin. Much like residual connections, you’ll be able to consider the
presence of those repeated injections of positional data as
relieving the remaining trainable layers from the burden of allocating
a few of their weights to the duty of “passing by way of” or “preserving”
the positional data for later layers.

Falbel and Keydana 2023),
so time spent understanding them higher is time properly
spent. For the needs of this weblog submit we’ve coated the factors
wanted and we’ll transfer on to tying all items collectively. To go deeper and
develop a extra mathematically knowledgeable perceive of RoPE, two glorious
beginning factors are:

The unique paper by Su et al. (2022)
This weblog submit by
Biderman et al. (2021)

Tying all of it collectively

With Tokenizer, Embedding, TransformerBlock (RMSNorm,
Consideration FeedForward and apply_rotary_embedding) all coated,
it’s time to tie all of the items collectively right into a Transformer mannequin. We
may do that utilizing %py_class% like with the opposite layers above, however
it’s simply as straightforward to maneuver over to utilizing the Keras useful API at this
level.

layer_transformer_block <- create_layer_wrapper(TransformerBlock)
layer_rms_norm <- create_layer_wrapper(RMSNorm)

# enter to the mannequin will probably be output from the tokenizer
enter <- layer_input(form(NA)) #, dtype = "int32")

x <- enter |>
  tok_embeddings()  # instantiated earlier within the blog-post

for(block_id in seq_len0(params$n_layers)) >
    layer_transformer_block(attn_head_size = params$dim %/% params$n_heads,
                            attn_n_heads = params$n_heads,
                            norm_eps = params$norm_eps,
                            block_id = block_id)


# last output projection into logits of output tokens
x <- x |>
  layer_rms_norm(block_id = -1, eps = params$norm_eps) |>
  layer_dense(
    tokenizer$vocab_size(), use_bias = FALSE,
    kernel_initializer = (...) np$load(weights_path("7B/output.weight.npy"))$`T`
  )

# slice out the logits for the final token
with_options(c(tensorflow.extract.warn_negatives_pythonic = FALSE), {
  output <- x[, -1, ]
})

llama <- keras_model(enter, output) %>%
  compile(jit_compile = TRUE)

next_token_probs <- immediate %>%
  tokenizer$tokenize() %>%
  llama()

next_token_probs

tf.Tensor(
[[-2.4503722e+00 -3.4463339e+00  1.3200411e+01 ...  4.8804146e-01
  -1.3277926e+00  9.9985600e-03]], form=(1, 32000), dtype=float32)

Deep Studying with
R e book), however this weblog submit is lengthy sufficient
already. So for now, let’s simply take the argmax().

sampler <- (logits) tf$argmax(logits, axis = -1L, output_type = "int32")

(next_token <- sampler(next_token_probs))

tf.Tensor([304], form=(1), dtype=int32)

tokenizer$detokenize(next_token) |> as.character()

[1] "to"

Let’s run it for just a few tokens and let LLaMa end the sentence:

prompt_tokens <- tokenizer$tokenize("One of the best ways to draw bees")

for (i in 1:20) {

  next_token_probs <- prompt_tokens |> llama()
  next_token <- sampler(next_token_probs)

  prompt_tokens %<>% { tf$concat(c(., next_token), axis = -1L) }

  # finish of sentence
  if (as.logical(next_token == tokenizer$string_to_id(".")))
    break
}

prompt_tokens |>
  tokenizer$detokenize() |>
  as.character() |>
  strwrap(60) |> writeLines()

One of the best ways to draw bees to your backyard is to plant a
number of flowers that bloom at totally different occasions.

Wrapping up

On this weblog submit we’ve walked by way of the LLaMA structure
carried out in R TensorFlow, together with the right way to load pretrained weights,
after which run the mannequin to generate a sentence. Observe, a lot of the code in
this weblog submit is tailor-made for didactic functions. Whereas the
implementation of the LLaMA structure coated on this weblog submit is
applicable for coaching, there are just a few modifications you’ll wish to
make earlier than doing a whole lot of textual content era. These embody issues like:

Within the Consideration layer, caching the okay and v tensors. Then,
after the primary ahead cross with the preliminary immediate, solely feeding
the mannequin the one new token from the sampler(), somewhat than
feeding the mannequin all of the tokens of the complete immediate on every ahead
cross.
Solely producing the causal masks make_mask() and rotary_matrix
slices as soon as per ahead cross, as an alternative of inside every Consideration
name.
Updating the TransformerBlock to be cache-aware and to cross
by way of the suitable arguments to Consideration()
Wrapping all the extra book-keeping logic in a customized
TransformerDecoder() class.

The adjustments required to implement these optimizations for inference
balloon the code measurement and are largely about book-keeping, so we received’t go
by way of them on this weblog submit. Nevertheless, you’ll find a fuller
implementation of LLaMA in R Tensorflow, together with a cache-aware
generate() technique that solely feeds the mannequin one token at a time throughout
the principle inference loop, (and compiles to XLA!),
right here.

That’s all for now. Thanks for studying and blissful travels to all
exploring this thrilling LLM terrain!

Photograph by Sébastien Goldberg on Unsplash

Biderman, Stella, Sid Black, Charles Foster, Leo Gao, Eric Hallahan, Horace He, Ben Wang, and Phil Wang. 2021. “Rotary Embeddings: A Relative Revolution.” weblog.eleuther.ai/rotary-embeddings/.

Falbel, Daniel, and Sigrid Keydana. 2023. “Posit AI Weblog: De-Noising Diffusion with Torch.” https://blogs.rstudio.com/tensorflow/posts/2023-04-13-denoising-diffusion/.

Hoffmann, Jordan, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, et al. 2022. “Coaching Compute-Optimum Massive Language Fashions.” https://arxiv.org/abs/2203.15556.

Shazeer, Noam. 2020. “GLU Variants Enhance Transformer.” https://arxiv.org/abs/2002.05202.

Su, Jianlin, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu. 2022. “RoFormer: Enhanced Transformer with Rotary Place Embedding.” https://arxiv.org/abs/2104.09864.

Touvron, Hugo, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, et al. 2023. “LLaMA: Open and Environment friendly Basis Language Fashions.” https://doi.org/10.48550/ARXIV.2302.13971.

Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. 2017. “Consideration Is All You Want.” https://arxiv.org/abs/1706.03762.

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