LLaMA in R with Keras and TensorFlow

OpenAI’s chatGPT has woke up a collective consciousness of what Giant
Language Fashions (LLMs) are able to. With that awakening comes a day by day
march of LLM information: new merchandise, new options, new fashions, new
capabilities, (and new worries). It appears we’re within the early levels 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 are going to, not directly.

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 can assist foster sturdy intuitions that can
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 information scientist’s
toolbox, as frequent as an lm() perform name).

And what higher method is there to study than by doing. So with that
preamble, on this put up we’ll stroll by means 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. Looking some hubs of LLM
exercise (HuggingFace,
TFHub,
reddit,
HackerNews) muddies the waters even
extra. The best way to decide a selected mannequin?

Of the numerous LLM-related information objects previously months, one which stands
head-and-shoulders above the group is the launch of
LLaMA,
a contemporary, foundational LLM made obtainable 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 fashionable
structure, has glorious efficiency on benchmarks, and is open. The
mannequin structure has had only a few 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 completely different sizes of
LLaMA have been launched: 7 billion and 13 billion parameter fashions
skilled on 1 Trillion tokens, and 33 billion and 65 billion parameter
fashions skilled on 1.4 trillion tokens. This is a gigantic quantity of
coaching knowledge these fashions have seen–the biggest 65B mannequin has been
skilled 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 put up we’ll deal with the smallest, 7B
parameter LLaMA mannequin, which you’ll be able to comfortably load regionally and run on
CPU with solely 64Gb of RAM.

Whereas not strictly vital, to comply with alongside regionally, you’ll in all probability
need to purchase the pre-trained LLaMA weights one
method or
one other. Observe, the
weights do include their very own license, which you’ll be able to preview
right here.

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

Setup

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

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$load("consolidated.00.pth",
                                   map_location = "cpu")
  for (identify in names(pretrained_weights)) {
    filename <- sprintf("%s.npy", identify)
    array <- pretrained_weights[[name]]$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 = guardian.body())), mustWork = TRUE)

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

Listing 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 means 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) > tokenizer$tokenize() 

show_tokens(immediate)

        1       450      1900       982       304     13978       367       267
       ""     "The"    "finest"     "method"      "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 count on to point out up in a
tokenizer skilled on a corpus of English textual content is “ing.” Nonetheless, when the
“ing” token reveals up is not going to at all times comply with 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. This can be 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’ll
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
   "" " ⁇ "    ""

Total, there are 32,000 tokens.

as.integer(tokenizer$vocab_size())

[1] 32000

One final remark is that the extra incessantly 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 following 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 means 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 plenty of code, there are plenty 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 flexibility to
compose with different Keras layers, however these are largely irrelevant to the
objective of this weblog put up; we might simply as simply implement this as,
for instance, a vanilla R6 class. Our TransformerBlock class has two
strategies: initialize, known as after we first create the block, and
name, known as after we run the ahead go 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() methodology.

The name methodology has a couple of easy concepts. In no explicit order, the
first one to watch is the composition sample of including residuals.

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

vanishing gradient
drawback. It’s
a skip-connection within the other-wise linear sequence of matrix
transformations. It reinjects info (throughout the ahead go), and
gradients (throughout again propagation), again into the trunk. You may assume
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” info in x, permitting the weights to
as an alternative deal with studying transformations which might be, (in corporatese
vernacular), value-adding.

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

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

There are a lot of 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 means of in a smart vary–in
the ball park of (-1, 1), usually. We’ll take a better have a look at
RMSNorm quickly.

Stripped of two tips which might 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 mainly an Consideration layer adopted by a couple of
(fancy) dense layers, with some easy composition patterns (tips)
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 an area perform that can load
    # the pretrained-weights if we provided `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 go, 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. Definitely 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 means 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$block_id))
      load_weight <- (...) NULL
    else
      load_weight <- (identify) (...) np$load(weights_path(
        "7B/layers.{self$block_id}.feed_forward.{identify}.weight.npy"))$`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 immediately. The Feedforward$name() is
only a single SwiGLU adopted by a linear projection. In its essence,
it’s a intelligent composition of three (realized) linear projections, an
element-wise multiplication, and a silu()
activation
perform.

Maybe probably the most stunning remark to make right here is the relative
dearth of activation capabilities, 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. The whole lot 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(identify) NULL
    else
      load_weight <- (identify) (...) np$load(weights_path(
        "7B/layers.{block_id}.consideration.{identify}.weight.npy"))$`T`

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

    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. undertaking (linear remodel) x into
    #    question, key, and worth tensors
    # 2. reshape q ok v, splitting out the final dim (n_features)
    #    into n_heads impartial 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)
    ok <- x |> self$wk() |> tf$reshape(split_heads_shape)
    v <- x |> self$wv() |> tf$reshape(split_heads_shape)

    # embed positional info in question and key
    # (bsz, seqlen, n_heads, head_size)
    q %<>% apply_rotary_embedding()
    ok %<>% 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)
    ok <- tf$transpose(ok, c(0L, 2L, 3L, 1L)) # (bsz, n_heads, head_size, seqlen)

    # calculate and normalize consideration scores
    scores <- q %*% ok                       # (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)

    # regulate 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
  }
}

unique Transformers
paper (and obtainable 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 go in several question, key, and worth tensors (or motive about what
which means), because the identical enter serves all three roles. Observe that the
typical MultiHeadAttention() layer is roofed fairly totally 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 briefly unsee a few of the minutia that may act as a fog
obscuring the essence of the operation. On this occasion, if we
briefly 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()
  ok <- x

Returning to the transpose()s and reshapes(), you possibly can observe that
their objective is to make it in order that the eye calculations are
carried out throughout n_heads impartial subspaces, slightly than in a
single bigger house. The identical reasoning drives this determination as that
driving utilization of depthwise-separable convolutions in picture fashions.
Empirically, for the fastened compute finances, factoring options into
impartial subspaces performs higher than doing the identical core
operations in single bigger characteristic house. 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, checklist(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
having the ability to “look forward” and see the eye rating for a token
pairing it hasn’t seen but at a specific place within the sequence.
This want for a masks is finest regarded as a vestige from coaching,
an equipment that the mannequin wanted to study 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 right
reply is proper there, because the very subsequent token in identical sequence. The masks
prevents the mannequin from having the ability to cheat and look forward into the long run,
one thing it received’t be capable of do as soon as it’s we’re operating 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 necessary, and the
consideration layer ought to have entry to that info.
Absolutely the place of a token in a sequence is much less necessary
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 ok token sequence embedding
the identical method, 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 info. The which means or
interpretability of that positional info, or how it’s meant to
be used, and even extracted from the results of q %*% ok, is left to the
mannequin to study.

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 likely 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(checklist(xs[1:(length(xs)-1)],
                        xs[length(xs), drop = FALSE] * 2L),
                   axis = 0L)

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

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

As you possibly can see, to think about the embedding options as current 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 current in the true aircraft. Once more, the job of
decoding the which means of the options after rotation is left to the
mannequin to study.

We are able to rapidly verify 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’s yet another trick to watch earlier than transferring on: due to a few of
the mathematical properties of the rotation matrix, it’s attainable to
keep away from doing a full complicated multiply operation and nonetheless arrive on the
identical consequence. Additionally, because the rotation matrix by no means modifications, 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$stack(checklist(-x2, x1), axis = -1L)
    tf$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, word that the rotary positional embeddings are utilized inside
every Consideration layer. That is completely different from the unique Transformer
implementation, the place a positional embedding was solely added as soon as on the
head of the mannequin. Just like residual connections, you possibly can consider the
presence of those repeated injections of positional info as
relieving the remaining trainable layers from the burden of allocating
a few of their weights to the duty of “passing by means of” or “preserving”
the positional info for later layers.

Falbel and Keydana 2023),
so time spent understanding them higher is time properly
spent. For the needs of this weblog put up we’ve lined 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 put up by
Biderman et al. (2021)

Tying all of it collectively

With Tokenizer, Embedding, TransformerBlock (RMSNorm,
Consideration FeedForward and apply_rotary_embedding) all lined,
it’s time to tie all of the items collectively right into a Transformer mannequin. We
might do that utilizing %py_class% like with the opposite layers above, however
it’s simply as simple 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 likely 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)


# closing 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 ebook), however this weblog put up 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 a couple of 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 completely different instances.

Wrapping up

On this weblog put up we’ve walked by means of the LLaMA structure
carried out in R TensorFlow, together with the best way to load pretrained weights,
after which run the mannequin to generate a sentence. Observe, a lot of the code in
this weblog put up is tailor-made for didactic functions. Whereas the
implementation of the LLaMA structure lined on this weblog put up is
acceptable for coaching, there are a couple of modifications you’ll need to
make earlier than doing plenty of textual content era. These embrace issues like:

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

The modifications required to implement these optimizations for inference
balloon the code measurement and are largely about book-keeping, so we received’t go
by means of them on this weblog put up. Nonetheless, you’ll find a fuller
implementation of LLaMA in R Tensorflow, together with a cache-aware
generate() methodology 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 comfortable travels to all
exploring this thrilling LLM terrain!

Picture 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 Giant 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.