Loss function to directly aim the target.

math.ipynb

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    "import math"
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    "p = 0.1"
   ]
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  {
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   "source": [
    "y = 0"
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     "execution_count": 4,
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   "source": [
    "-(y*math.log(p) + (1-y)*math.log(1-p))"
   ]
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     "execution_count": 5,
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   "source": [
    "-math.log(1-abs(y-p))"
   ]
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    "y = 1"
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   "source": [
    "-(y*math.log(p) + (1-y)*math.log(1-p))"
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   "source": [
    "-math.log(1-abs(y-p))"
   ]
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   "cell_type": "markdown",
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   "source": []
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   "cell_type": "code",
   "execution_count": 9,
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   "source": [
    "y = 0.3"
   ]
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   "source": [
    "-(y*math.log(p) + (1-y)*math.log(1-p)) # hazardous (were written with y: {0, 1} in mind)"
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     "execution_count": 11,
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   "source": [
    "-math.log(1-abs(y-p)) # works as if: y=1, p=0.8 or y=0, p=0.2"
   ]
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  {
   "cell_type": "markdown",
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   "cell_type": "markdown",
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   "source": [
    "### Label smoothing is natural this way as you can say that the label should be (0.5, 0.1, 0.2, 0.2), for example.\n",
    "### It would be interesting to see how mixup works with this loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = torch.tensor([0.30, 0.10, 0.50, 0.10]) # p\n",
    "targs = torch.tensor([0.80, 0.10, 0.05, 0.05]) # y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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     "data": {
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       "tensor([0.6931, -0.0000, 0.5978, 0.0513])"
      ]
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     "execution_count": 14,
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   ],
   "source": [
    "-torch.log(1 - (targs-probs).abs())"
   ]
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   "cell_type": "code",
   "execution_count": 15,
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   "outputs": [
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       "tensor(0.3356)"
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     "execution_count": 15,
     "metadata": {},
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   ],
   "source": [
    "-torch.log(1 - (targs-probs).abs()).mean()"
   ]
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