smbot/nn.lua

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

local bor = bit.bor

local Base = require("Base")

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

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

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

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 allocate(t, out, init)
    -- FIXME: this code is fucking disgusting.

    out = out or {}
    assert(type(out) == "table", type(out))
    if type(t) == "number" then
        local size = t
        if init ~= nil then
            return init(zeros(size, out))
        else
            return zeros(size, out)
        end
    end
    local topsize = t[1]
    t = copy(t)
    remove(t, 1)
    if #t == 1 then t = t[1] end
    for i = 1, topsize do
        local res = allocate(t, nil, init)
        assert(res ~= nil)
        insert(out, res)
    end
    return out
end

local Weights = Base:extend()
local Layer = Base:extend()
local Model = Base:extend()
local Input = Layer:extend()
local Relu = 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)
    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 w = Weights(init_he_uniform)
w.size = {16, 16}
w:allocate(16, 16)
print(w)
do return end

local w = zeros(16)
for i = 1, #w do w[i] = normal() * 1920 / 2560 end
print(w)
--]]

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

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

function Layer:getsize()
    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 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 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.size = {self.dim, self.size_in}
    self.biases.size = 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.coeffs do
        local res = 0
        local c = self.coeffs[i]
        for j = 1, #X do
            res = res + X[j] * 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

local function levelorder(field, node_in, nodes)
    -- horribly inefficient.
    nodes = nodes or {}
    local q = {node_in}
    while #q > 0 do
        local node = q[1]
        remove(q, 1)
        insert(nodes, node)
        for _, child in ipairs(node[field]) do
            q[#q+1] = child
        end
    end
    return nodes
end

local function traverse(node_in, node_out, nodes)
    nodes = nodes or {}
    local down = levelorder('children', node_in, {})
    local up   = levelorder('parents', node_out, {})
    local seen = {}
    for _, node in ipairs(up) do
        seen[node] = bor(seen[node] or 0, 1)
    end
    for _, node in ipairs(down) do
        seen[node] = bor(seen[node] or 0, 2)
        if seen[node] == 3 then
            insert(nodes, node)
        end
    end
    return nodes
end

local function traverse_all(nodes_in, nodes_out, nodes)
    local all_in = {children={}}
    local all_out = {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 {})
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:getsize()
    end
end

function Model:forward(X)
    local values = {}
    local outputs = {}
    for i, node in ipairs(self.nodes) do
        --print(i, node.name)
        if contains(self.nodes_in, node) then
            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

return {
    uniform = uniform,
    normal = normal,

    zeros = zeros,
    init_zeros = init_zeros,
    init_he_uniform = init_he_uniform,
    init_he_normal = init_he_normal,

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