smbot/nn.lua

local cos = math.cos
local exp = math.exp
local insert = table.insert
local ipairs = ipairs
local log = math.log
local max = math.max
local min = math.min
local open = io.open
local pairs = pairs
local pi = math.pi
local print = print
local remove = table.remove
local sin = math.sin
local sqrt = math.sqrt
local tostring = tostring
local uniform = math.random
local unpack = table.unpack or unpack

local Base = require("Base")

-- general utilities

local function copy(t) -- shallow copy
    local new_t = {}
    for k, v in pairs(t) do new_t[k] = v end
    return new_t
end

local function indexof(t, a)
    assert(type(t) == "table")
    for k, v in pairs(t) do if v == a then return k end end
    return nil
end

local function contains(t, a)
    return indexof(t, a) ~= nil
end

-- math utilities

local function prod(x, ...)
    if type(x) == "table" then
        return prod(unpack(x))
    end
    local ret = x
    for i = 1, select("#", ...) do
        ret = ret * select(i, ...)
    end
    return ret
end

local function normal() -- box muller
    return sqrt(-2 * log(uniform() + 1e-8) + 1e-8) * cos(2 * pi * uniform())
end

local function zeros(n, out)
    local out = out or {}
    for i = 1, n do out[i] = 0 end
    return out
end

local function allocate(t, out, init)
    out = out or {}
    local size = t
    if init ~= nil then
        return init(zeros(size, out))
    else
        return zeros(size, out)
    end
end

local function init_zeros(t, fan_in, fan_out)
    for i = 1, #t do t[i] = 0 end
    return t
end

local function init_he_uniform(t, fan_in, fan_out)
    local s = sqrt(6 / fan_in)
    for i = 1, #t do t[i] = (uniform() * 2 - 1) * s end
    return t
end

local function init_he_normal(t, fan_in, fan_out)
    local s = sqrt(2 / fan_in)
    for i = 1, #t do t[i] = normal() * s end
    return t
end

-- nodal

local function traverse(node_in, node_out, nodes, dummy_mode)
    -- i have no idea if this is any algorithm in particular.
    nodes = nodes or {}

    local seen_up = {}
    local q = {node_out}
    while #q > 0 do
        local node = remove(q, 1)
        seen_up[node] = true
        for _, parent in ipairs(node.parents) do insert(q, parent) end
    end

    if dummy_mode then seen_up[node_in] = true end

    nodes = {}
    q = {node_in}
    while #q > 0 do
        local node = remove(q, 1)
        if seen_up[node] then
            local all_parents_added = true
            for _, parent in ipairs(node.parents) do
                if not contains(nodes, parent) then
                    all_parents_added = false
                    break
                end
            end
            if not contains(nodes, node) and all_parents_added then
                insert(nodes, node)
            end
            for _, child in ipairs(node.children) do insert(q, child) end
        end
    end

    if dummy_mode then remove(nodes, indexof(nodes, node_in)) end

    return nodes
end

local function traverse_all(nodes_in, nodes_out, nodes)
    local all_in  = {children={}, parents={}}
    local all_out = {children={}, parents={}}
    for _, node in ipairs(nodes_in)  do insert(all_in.children, node) end
    for _, node in ipairs(nodes_out) do insert(all_out.parents, node) end
    return traverse(all_in, all_out, nodes or {}, true)
end

-- classes

local Weights = Base:extend()
local Layer = Base:extend()
local Model = Base:extend()
local Input = Layer:extend()
local Relu = Layer:extend()
local Gelu = Layer:extend()
local Dense = Layer:extend()
local Softmax = Layer:extend()

function Weights:init(weight_init)
    self.weight_init = weight_init
end

function Weights:allocate(fan_in, fan_out)
    self.size = prod(self.shape)
    return allocate(self.size, self, function(t)
        --print('initializing weights of size', self.size, 'with fans', fan_in, fan_out)
        return self.weight_init(t, fan_in, fan_out)
    end)
end

local counter = {}
function Layer:init(name)
    assert(type(name) == "string")
    counter[name] = (counter[name] or 0) + 1
    self.name = name.."["..tostring(counter[name]).."]"
    self.parents = {}
    self.children = {}
    self.weights = {}
    --self.size_in = nil
    --self.size_out = nil
end

function Layer:make_shape(parent)
    if self.size_in == nil then self.size_in = parent.size_out end
    if self.size_out == nil then self.size_out = self.size_in end
end

function Layer:feed(child)
    assert(self.size_out ~= nil)
    child:make_shape(self)
    insert(self.children, child)
    insert(child.parents, self)
    return child
end

function Layer:forward()
    error("Unimplemented.")
end

function Layer:forward_deterministic(...)
    return self:forward(...)
end

function Layer:backward()
    error("Unimplemented.")
end

function Layer:_new_weights(init)
    local w = Weights(init)
    insert(self.weights, w)
    return w
end

function Layer:get_size()
    local size = 0
    for i, w in ipairs(self.weights) do size = size + prod(w.size) end
    return size
end

function Layer:init_weights()
    for i, w in ipairs(self.weights) do
        --print("allocating weights", i, "of", self.name)
        for j, v in ipairs(w) do w[j] = nil end -- FIXME: HACK
        w:allocate(self.size_in, self.size_out)
    end
end

function Layer:_propagate(edges, deterministic)
    assert(#edges == 1, #edges) -- override this if you need multiple parents.
    if deterministic then
        return self:forward_deterministic(edges[1])
    else
        return self:forward(edges[1])
    end
end

function Layer:propagate(values, deterministic)
    local edges = {}
    for i, parent in ipairs(self.parents) do
        if values[parent] ~= nil then
            local X = values[parent]
            insert(edges, X)
        end
    end
    assert(#edges > 0, #edges)
    local Y = self:_propagate(edges, deterministic)
    return Y
end

function Input:init(size)
    Layer.init(self, "Input")
    assert(type(size) == 'number')
    self.size_in = size
    self.size_out = size
end

function Input:forward(X)
    assert(#X == self.size_in)
    return X
end

function Input:backward(dY)
    assert(#dY == self.size_out)
    return zeros(#dY)
end

function Relu:init()
    Layer.init(self, "Relu")
end

function Relu:forward(X)
    assert(#X == self.size_in)
    self.cache = self.cache or zeros(self.size_out)
    local Y = self.cache

    for i = 1, #X do Y[i] = X[i] >= 0 and X[i] or 0 end

    assert(#Y == self.size_out)
    return Y
end

function Relu:backward(dY)
    assert(#dY == self.size_out)
    self.dcache = self.dcache or zeros(self.size_in)
    local Y = self.cache
    local dX = self.dcache

    for i = 1, #dY do dX[i] = Y[i] >= 0 and dY[i] or 0 end

    assert(#Y == self.size_in)
    return Y
end

function Gelu:init()
    Layer.init(self, "Gelu")
end

function Gelu:forward(X)
    assert(#X == self.size_in)
    self.cache = self.cache or zeros(self.size_out)
    local Y = self.cache

    -- NOTE: approximate form of GELU exploiting similarities to sigmoid curve.
    for i = 1, #X do
        Y[i] = X[i] / (1 + exp(-1.704 * X[i]))
    end

    assert(#Y == self.size_out)
    return Y
end

function Dense:init(dim)
    Layer.init(self, "Dense")
    assert(type(dim) == "number")
    self.dim = dim
    self.size_out = dim
    self.coeffs = self:_new_weights(init_he_normal) -- should be normal, but...
    self.biases = self:_new_weights(init_zeros)
end

function Dense:make_shape(parent)
    self.size_in = parent.size_out
    self.coeffs.shape = {self.size_in, self.dim}
    self.biases.shape = self.dim
end

function Dense:forward(X)
    assert(#X == self.size_in)
    self.cache = self.cache or zeros(self.size_out)
    local Y = self.cache

    for i = 1, self.dim do
        local res = 0
        local c = (i - 1) * #X
        for j = 1, #X do
            res = res + X[j] * self.coeffs[c + j]
        end
        Y[i] = res + self.biases[i]
    end

    assert(#Y == self.size_out)
    return Y
end

function Softmax:init()
    Layer.init(self, "Softmax")
end

function Softmax:forward(X)
    assert(#X == self.size_in)
    self.cache = self.cache or zeros(self.size_out)
    local Y = self.cache

    local alpha = 0
    local num = {} -- TODO: cache
    local den = 0

    for i = 1, #X do alpha = max(alpha, X[i]) end
    for i = 1, #X do num[i] = exp(X[i] - alpha) end
    for i = 1, #X do den = den + num[i] end
    for i = 1, #X do Y[i] = num[i] / den end

    assert(#Y == self.size_out)
    return Y
end

function Model:init(nodes_in, nodes_out)
    assert(#nodes_in > 0, #nodes_in)
    assert(#nodes_out > 0, #nodes_out)
    --if #nodes_in == 0 and type(nodes_in) == "table" then nodes_in = {nodes_in} end
    --if #nodes_out == 0 and type(nodes_out) == "table" then nodes_out = {nodes_out} end

    self.nodes_in = nodes_in
    self.nodes_out = nodes_out

    -- find all the used (inbetween) nodes in the graph.
    self.nodes = traverse_all(self.nodes_in, self.nodes_out)
end

function Model:reset()
    self.n_param = 0
    for _, node in ipairs(self.nodes) do
        node:init_weights()
        self.n_param = self.n_param + node:get_size()
    end
end

function Model:forward(inputs)
    local values = {}
    local outputs = {}
    for i, node in ipairs(self.nodes) do
        --print(i, node.name)
        if contains(self.nodes_in, node) then
            local X = inputs[node]
            assert(X ~= nil, ("missing input for node %s"):format(node.name))
            values[node] = node:_propagate({X})
        else
            values[node] = node:propagate(values)
        end
        if contains(self.nodes_out, node) then
            outputs[node] = values[node]
        end
    end
    return outputs
end

function Model:collect()
    -- return a flat array of all the weights in the graph.
    -- if Lua had slices, we wouldn't need this. future library idea?
    assert(self.n_param >= 0, self.n_param)
    local W = zeros(self.n_param)
    local i = 0
    for _, node in ipairs(self.nodes) do
        for _, w in ipairs(node.weights) do
            for j, v in ipairs(w) do
                W[i+j] = v
            end
            i = i + #w
        end
    end
    return W
end

function Model:distribute(W)
    -- inverse operation of collect().
    local i = 0
    for _, node in ipairs(self.nodes) do
        for _, w in ipairs(node.weights) do
            for j, v in ipairs(w) do
                w[j] = W[i+j]
            end
            i = i + #w
        end
    end
end

function Model:default_filename()
    return ('network%07i.txt'):format(self.n_param)
end

function Model:save(fn)
    local fn = fn or self:default_filename()
    local f = open(fn, 'w')
    if f == nil then error("Failed to save network to file "..fn) end
    local W = self:collect()
    for i, v in ipairs(W) do
        f:write(v)
        f:write('\n')
    end
    f:close()
end

function Model:load(fn)
    local fn = fn or self:default_filename()
    local f = open(fn, 'r')
    if f == nil then
        error("Failed to load network from file "..fn)
    end

    local W = zeros(self.n_param)
    local i = 0
    for line in f:lines() do
        i = i + 1
        local n = tonumber(line)
        if n == nil then
            error("Failed reading line "..tostring(i).." of file "..fn)
        end
        W[i] = n
    end
    f:close()

    self:distribute(W)
end

return {
    copy = copy,
    indexof = indexof,
    contains = contains,
    prod = prod,
    normal = normal,
    zeros = zeros,
    allocate = allocate,
    init_zeros = init_zeros,
    init_he_uniform = init_he_uniform,
    init_he_normal = init_he_normal,
    traverse = traverse,
    traverse_all = traverse_all,

    Weights = Weights,
    Layer   = Layer,
    Model   = Model,
    Input   = Input,
    Relu    = Relu,
    Gelu    = Gelu,
    Dense   = Dense,
    Softmax = Softmax,
}