{ "

Arithmetic Dataset

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This creates arithmetic addition problems and solutions with workings. We've only implemented addition so far.

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It's based on a character level tokenization.

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\u7b97\u8853\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8

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\u3053\u308c\u306b\u3088\u308a\u3001\u7b97\u8853\u52a0\u7b97\u306e\u554f\u984c\u3068\u89e3\u6cd5\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u4eca\u306e\u3068\u3053\u308d\u3001\u8ffd\u52a0\u3092\u5b9f\u88c5\u3057\u305f\u3060\u3051\u3067\u3059\u3002

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\u30ad\u30e3\u30e9\u30af\u30bf\u30fc\u30ec\u30d9\u30eb\u306e\u30c8\u30fc\u30af\u30f3\u5316\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002

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Arithmetic Task Experiment Configurations

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\u7b97\u8853\u30bf\u30b9\u30af\u5b9f\u9a13\u69cb\u6210

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Evaluation

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We use the sampling function to evaluate the model on a set of problems

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\u8a55\u4fa1

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\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u4e00\u9023\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u30e2\u30c7\u30eb\u3092\u8a55\u4fa1\u3057\u307e\u3059\u3002

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Code to test generated problems

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\u751f\u6210\u3055\u308c\u305f\u554f\u984c\u3092\u30c6\u30b9\u30c8\u3059\u308b\u30b3\u30fc\u30c9

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Decode a list of token ids

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\u30c8\u30fc\u30af\u30f3 ID \u306e\u30ea\u30b9\u30c8\u3092\u30c7\u30b3\u30fc\u30c9\u3059\u308b

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Encode a given string

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\u4e0e\u3048\u3089\u308c\u305f\u6587\u5b57\u5217\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3059\u308b

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Generate multiple problems and pack them into a sequence.

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\u8907\u6570\u306e\u554f\u984c\u3092\u751f\u6210\u3057\u3001\u305d\u308c\u3089\u3092\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u307e\u3068\u3081\u307e\u3059\u3002

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Generates an integer with _^_0_^_ number of digits

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_^_0_^_\u6841\u6570\u306e\u6574\u6570\u3092\u751f\u6210\u3057\u307e\u3059

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Generates the workings for _^_0_^_. For example for _^_1_^_ it generates _^_2_^_.

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\u306e\u4f5c\u696d\u3092\u751f\u6210\u3057\u307e\u3059\u3002_^_0_^_\u305f\u3068\u3048\u3070_^_1_^_\u3001\u751f\u6210\u3059\u308b\u5834\u5408\u306a\u3069\u3067\u3059_^_2_^_\u3002

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Get a input and target pair for auto-regressive modelling

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\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u5165\u529b\u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u30da\u30a2\u3092\u53d6\u5f97

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Get arithmetic problem and answer. This is used for evaluation.

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\u7b97\u8853\u554f\u984c\u3092\u51fa\u3057\u3066\u3001\u7b54\u3048\u3092\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u8a55\u4fa1\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002

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Number of sequences per epoch

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\u30a8\u30dd\u30c3\u30af\u3042\u305f\u308a\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u6570

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Training data loader

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\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30c7\u30fc\u30bf\u30ed\u30fc\u30c0\u30fc

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This is based on code by Georges Harik (@gharik).

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\u3053\u308c\u306f\u30b8\u30e7\u30eb\u30b8\u30e5\u30fb\u30cf\u30ea\u30af (@gharik) \u306e\u30b3\u30fc\u30c9\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002

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Add the next token to the input

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\u6b21\u306e\u30c8\u30fc\u30af\u30f3\u3092\u5165\u529b\u306b\u8ffd\u52a0\u3057\u307e\u3059

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Character to token id

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\u6587\u5b57\u304b\u3089\u30c8\u30fc\u30af\u30f3 ID \u3078

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Collect the problems only

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\u554f\u984c\u3060\u3051\u96c6\u3081\u3088\u3046

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Count the number of correct answers

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\u6b63\u89e3\u306e\u6570\u3092\u6570\u3048\u308b

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Create a dataset to generate problems

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\u554f\u984c\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u4f5c\u6210

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Create a tensor with only the initial token

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\u6700\u521d\u306e\u30c8\u30fc\u30af\u30f3\u306e\u307f\u3067\u30c6\u30f3\u30bd\u30eb\u3092\u4f5c\u6210

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Discard everything after the answer in the results

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\u7d50\u679c\u306e\u56de\u7b54\u306e\u5f8c\u306b\u7d9a\u304f\u3082\u306e\u306f\u3059\u3079\u3066\u7834\u68c4\u3057\u3066\u304f\u3060\u3055\u3044

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Find which sequences have finished

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\u3069\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u7d42\u4e86\u3057\u305f\u304b\u8abf\u3079\u308b

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Get a set of problems and answers

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\u4e00\u9023\u306e\u554f\u984c\u3068\u56de\u7b54\u3092\u5165\u624b

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Get the answers

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\u7b54\u3048\u3092\u30b2\u30c3\u30c8

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Get the model output

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\u30e2\u30c7\u30eb\u51fa\u529b\u3092\u53d6\u5f97

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Get the model prediction (greedy)

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\u30e2\u30c7\u30eb\u4e88\u6e2c\u3092\u53d6\u5f97 (\u6b32\u5f35\u308a)

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Get the sampled results

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\u30b5\u30f3\u30d7\u30eb\u7d50\u679c\u3092\u53d6\u5f97

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If all the sequences have completed we skip this

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\u3059\u3079\u3066\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u5b8c\u4e86\u3057\u305f\u3089\u3053\u308c\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u307e\u3059\u3002

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Log a sample

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\u30b5\u30f3\u30d7\u30eb\u3092\u30ed\u30b0\u306b\u8a18\u9332\u3059\u308b

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Log the score

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\u30b9\u30b3\u30a2\u3092\u8a18\u9332\u3059\u308b

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Make a problem with a pre_explanation or not

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Creates an arithmetic addition problem with workings and answer.

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pre_explanation \u3067\u554f\u984c\u3092\u8d77\u3053\u3059\u304b\u3057\u306a\u3044\u304b

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\u8a08\u7b97\u3068\u89e3\u3092\u542b\u3080\u7b97\u8853\u52a0\u7b97\u554f\u984c\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002

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Maximum number of digits per operand integer

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\u30aa\u30da\u30e9\u30f3\u30c9\u6574\u6570\u3042\u305f\u308a\u306e\u6700\u5927\u6841\u6570

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Move to device

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\u30c7\u30d0\u30a4\u30b9\u306b\u79fb\u52d5

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No need of a validation dataset

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\u691c\u8a3c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u4e0d\u8981

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Number of problems in evaluation

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\u8a55\u4fa1\u4e2d\u306e\u554f\u984c\u306e\u6570

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Number of sequences that have completed

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\u5b8c\u4e86\u3057\u305f\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u6570

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Number of times to run evaluations per epoch

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\u30a8\u30dd\u30c3\u30af\u3054\u3068\u306b\u8a55\u4fa1\u3092\u5b9f\u884c\u3059\u308b\u56de\u6570

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Number of tokens in the vocabulary

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\u30dc\u30ad\u30e3\u30d6\u30e9\u30ea\u30fc\u306e\u30c8\u30fc\u30af\u30f3\u306e\u6570

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Number of training sequences per epoch

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\u30a8\u30dd\u30c3\u30af\u3042\u305f\u308a\u306e\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u6570

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Override with the question

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\u8cea\u554f\u3067\u4e0a\u66f8\u304d

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Sample upto sequence length

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\u30b7\u30fc\u30b1\u30f3\u30b9\u9577\u307e\u3067\u306e\u30b5\u30f3\u30d7\u30eb

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Sampled results

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\u30b5\u30f3\u30d7\u30eb\u7d50\u679c

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Skip if all have finished

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\u3059\u3079\u3066\u7d42\u4e86\u3057\u305f\u3089\u30b9\u30ad\u30c3\u30d7

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Skip in the first epoch

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\u6700\u521d\u306e\u30a8\u30dd\u30c3\u30af\u3092\u30b9\u30ad\u30c3\u30d7

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Token id of the new line character - this marks end of the answer

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\u6539\u884c\u6587\u5b57\u306e\u30c8\u30fc\u30af\u30f3ID-\u3053\u308c\u3067\u56de\u7b54\u306e\u6700\u5f8c\u306b\u306a\u308a\u307e\u3059

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Token id to string

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\u30c8\u30fc\u30af\u30f3 ID \u3092\u6587\u5b57\u5217\u306b

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Training data loader

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\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30c7\u30fc\u30bf\u30ed\u30fc\u30c0\u30fc

\n", "\n": "\n", "Arithmetic Dataset": "\u7b97\u8853\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8", "This creates arithmetic problems.": "\u3053\u308c\u306f\u7b97\u8853\u4e0a\u306e\u554f\u984c\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059\u3002" }