2Vh>ddlZddlmZddlmZddlmZddlmZddlmZddlm Z ddl m Z dd l m Z dd l mZGd d eZed GddeZedGddeZedGddeZedGddeZedGddeZedGddeZedGd d!eZed"Gd#d$eZed%Gd&d'eZed(Gd)d*eZed+Gd,d-eZed.Gd/d0eZed1Gd2d3eZed4Gd5d6eZed7Gd8d9eZed:Gd;dd?eZ ed@GdAdBeZ!edCGdDdEeZ"edFGdGdHeZ#edIGdJdKeZ$edLGdMdNeZ%dOZ&edPdQgdRZ'edSdTgdUZ(edVdWgdXZ)egdYdZZ*egd[d\Z+egd]d^Z,egd_d`Z-edaddbZ.edcddgddeZ/egdfdgZ0egdhdiZ1edjdkgdlZ2edmdng ddoZ3edpdqg ddrZ4edsdtg dduZ5edvdwg ddxZ6edydzg dd{Z7ed|d}Z8ed~ddZ9edddZ:ed ddZ;eddZz*LossFunctionWrapper.call.. AaDrc |dS)Nrrs rr!z*LossFunctionWrapper.call.. r"r)r map_structurermap_structure_up_torr)ry_truey_pred y_true_y_preds rcallzLossFunctionWrapper.calls_** *FF ))&.-P))&.-Ptwwvv999rct|}|jdtj|j i|jtj|j |S)Nr)r get_configupdater serialize_keras_objectrr)rconfigrs rr,zLossFunctionWrapper.get_config#sR#% t.EEdggNOP '>>tOP rcDd|vrtj|}|di|S)Nrr)r deserialize_keras_object)clsr/s r from_configzLossFunctionWrapper.from_config)s% 6>&??GF}V}rc<d|jd|jdS)Nz)rrrs r__repr__zLossFunctionWrapper.__repr__/s &twwiy8ILLr)sum_over_batch_sizeNN) __name__ __module__ __qualname__rr*r, classmethodr3r6 __classcell__rs@rr r s7(  !:  Mrr zkeras.losses.MeanSquaredErrorc0eZdZdZ dfd ZdZxZS)MeanSquaredErroraComputes the mean of squares of errors between labels and predictions. Formula: ```python loss = mean(square(y_true - y_pred)) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrmean_squared_errorrrrrrs rrzMeanSquaredError.__init__Ns  TYe  rc,tj|SNrr,r5s rr,zMeanSquaredError.get_configXt$$r)r7rANr8r9r:__doc__rr,r<r=s@rr?r?3s6( !  %rr?zkeras.losses.MeanAbsoluteErrorc0eZdZdZ dfd ZdZxZS)MeanAbsoluteErroraComputes the mean of absolute difference between labels and predictions. Formula: ```python loss = mean(abs(y_true - y_pred)) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrmean_absolute_errorrBs rrzMeanAbsoluteError.__init__ws  diu  rc,tj|SrDrEr5s rr,zMeanAbsoluteError.get_configrFr)r7rLNrGr=s@rrJrJ\s6( "  %rrJz(keras.losses.MeanAbsolutePercentageErrorc0eZdZdZ dfd ZdZxZS)MeanAbsolutePercentageErroraComputes the mean absolute percentage error between `y_true` & `y_pred`. Formula: ```python loss = 100 * mean(abs((y_true - y_pred) / y_true)) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrmean_absolute_percentage_errorrBs rrz$MeanAbsolutePercentageError.__init__#  *  rc,tj|SrDrEr5s rr,z&MeanAbsolutePercentageError.get_configrFr)r7rQNrGr=s@rrOrO6( -  %rrOz(keras.losses.MeanSquaredLogarithmicErrorc0eZdZdZ dfd ZdZxZS)MeanSquaredLogarithmicErroraComputes the mean squared logarithmic error between `y_true` & `y_pred`. Formula: ```python loss = mean(square(log(y_true + 1) - log(y_pred + 1))) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrmean_squared_logarithmic_errorrBs rrz$MeanSquaredLogarithmicError.__init__rRrc,tj|SrDrEr5s rr,z&MeanSquaredLogarithmicError.get_configrFr)r7rXNrGr=s@rrVrVrTrrVzkeras.losses.CosineSimilarityc2eZdZdZ dfd ZdZxZS)CosineSimilarityaComputes the cosine similarity between `y_true` & `y_pred`. Note that it is a number between -1 and 1. When it is a negative number between -1 and 0, 0 indicates orthogonality and values closer to -1 indicate greater similarity. This makes it usable as a loss function in a setting where you try to maximize the proximity between predictions and targets. If either `y_true` or `y_pred` is a zero vector, cosine similarity will be 0 regardless of the proximity between predictions and targets. Formula: ```python loss = -sum(l2_norm(y_true) * l2_norm(y_pred)) ``` Args: axis: The axis along which the cosine similarity is computed (the features axis). Defaults to `-1`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c6t|t||||yN)rrraxis)rrcosine_similarity)rr^rrrrs rrzCosineSimilarity.__init__s&    rc,tj|SrDrEr5s rr,zCosineSimilarity.get_configrFr)r7r_NrGr=s@rr[r[s! H'   %rr[zkeras.losses.Huberc2eZdZdZ dfd ZdZxZS)HuberaComputes the Huber loss between `y_true` & `y_pred`. Formula: ```python for x in error: if abs(x) <= delta: loss.append(0.5 * x^2) elif abs(x) > delta: loss.append(delta * abs(x) - 0.5 * delta^2) loss = mean(loss, axis=-1) ``` See: [Huber loss](https://en.wikipedia.org/wiki/Huber_loss). Args: delta: A float, the point where the Huber loss function changes from a quadratic to linear. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c6t|t||||y)N)rrrdelta)rrhuber)rrerrrrs rrzHuber.__init__8s&    rc,tj|SrDrEr5s rr,zHuber.get_configGrFr)?r7 huber_lossNrGr=s@rrcrcs! H'   %rrczkeras.losses.LogCoshc0eZdZdZ dfd ZdZxZS)LogCoshaComputes the logarithm of the hyperbolic cosine of the prediction error. Formula: ```python error = y_pred - y_true logcosh = mean(log((exp(error) + exp(-error))/2), axis=-1)` ``` where x is the error `y_pred - y_true`. Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrlog_coshrBs rrzLogCosh.__init__hs  Orc,tj|SrDrEr5s rr,zLogCosh.get_configprFr)r7rmNrGr=s@rrkrkKs:(  P%rrkzkeras.losses.Hingec0eZdZdZ dfd ZdZxZS)HingeaComputes the hinge loss between `y_true` & `y_pred`. Formula: ```python loss = maximum(1 - y_true * y_pred, 0) ``` `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1. Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrhingerBs rrzHinge.__init__s TYeLrc,tj|SrDrEr5s rr,zHinge.get_configrFr)r7rrNrGr=s@rrprpts<(  M%rrpzkeras.losses.SquaredHingec,eZdZdZ dfd ZdZxZS) SquaredHingeaComputes the squared hinge loss between `y_true` & `y_pred`. Formula: ```python loss = square(maximum(1 - y_true * y_pred, 0)) ``` `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1. Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rr squared_hingerBs rrzSquaredHinge.__init__      rc,tj|SrDrEr5s rr,zSquaredHinge.get_configrFr)r7rwNrGr=s@rrurus:LP %rruzkeras.losses.CategoricalHingec0eZdZdZ dfd ZdZxZS)CategoricalHingeaComputes the categorical hinge loss between `y_true` & `y_pred`. Formula: ```python loss = maximum(neg - pos + 1, 0) ``` where `neg=maximum((1-y_true)*y_pred)` and `pos=sum(y_true*y_pred)` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrcategorical_hingerBs rrzCategoricalHinge.__init__s  DIU  rc,tj|SrDrEr5s rr,zCategoricalHinge.get_configrFr)r7r}NrGr=s@rr{r{s:(   %rr{zkeras.losses.KLDivergencec,eZdZdZ dfd ZdZxZS) KLDivergenceaComputes Kullback-Leibler divergence loss between `y_true` & `y_pred`. Formula: ```python loss = y_true * log(y_true / y_pred) ``` `y_true` and `y_pred` are expected to be probability distributions, with values between 0 and 1. They will get clipped to the `[0, 1]` range. Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rr kl_divergencerBs rrzKLDivergence.__init__rxrc,tj|SrDrEr5s rr,zKLDivergence.get_configrFr)r7rNrGr=s@rrrs<LP %rrzkeras.losses.Poissonc,eZdZdZ dfd ZdZxZS)PoissonarComputes the Poisson loss between `y_true` & `y_pred`. Formula: ```python loss = y_pred - y_true * log(y_pred) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrpoissonrBs rrzPoisson.__init__7s tyNrc,tj|SrDrEr5s rr,zPoisson.get_config<rFr)r7rNrGr=s@rrrs4FJO %rrzkeras.losses.BinaryCrossentropyc6eZdZdZ dfd ZdZxZS)BinaryCrossentropyaComputes the cross-entropy loss between true labels and predicted labels. Use this cross-entropy loss for binary (0 or 1) classification applications. The loss function requires the following inputs: - `y_true` (true label): This is either 0 or 1. - `y_pred` (predicted value): This is the model's prediction, i.e, a single floating-point value which either represents a [logit](https://en.wikipedia.org/wiki/Logit), (i.e, value in [-inf, inf] when `from_logits=True`) or a probability (i.e, value in [0., 1.] when `from_logits=False`). Args: from_logits: Whether to interpret `y_pred` as a tensor of [logit](https://en.wikipedia.org/wiki/Logit) values. By default, we assume that `y_pred` is probabilities (i.e., values in [0, 1]). label_smoothing: Float in range [0, 1]. When 0, no smoothing occurs. When > 0, we compute the loss between the predicted labels and a smoothed version of the true labels, where the smoothing squeezes the labels towards 0.5. Larger values of `label_smoothing` correspond to heavier smoothing. axis: The axis along which to compute crossentropy (the features axis). Defaults to `-1`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: **Recommended Usage:** (set `from_logits=True`) With `compile()` API: ```python model.compile( loss=keras.losses.BinaryCrossentropy(from_logits=True), ... ) ``` As a standalone function: >>> # Example 1: (batch_size = 1, number of samples = 4) >>> y_true = np.array([0, 1, 0, 0]) >>> y_pred = np.array([-18.6, 0.51, 2.94, -12.8]) >>> bce = keras.losses.BinaryCrossentropy(from_logits=True) >>> bce(y_true, y_pred) 0.8654 >>> # Example 2: (batch_size = 2, number of samples = 4) >>> y_true = np.array([[0, 1], [0, 0]]) >>> y_pred = np.array([[-18.6, 0.51], [2.94, -12.8]]) >>> # Using default 'auto'/'sum_over_batch_size' reduction type. >>> bce = keras.losses.BinaryCrossentropy(from_logits=True) >>> bce(y_true, y_pred) 0.8654 >>> # Using 'sample_weight' attribute >>> bce(y_true, y_pred, sample_weight=[0.8, 0.2]) 0.243 >>> # Using 'sum' reduction` type. >>> bce = keras.losses.BinaryCrossentropy(from_logits=True, ... reduction="sum") >>> bce(y_true, y_pred) 1.730 >>> # Using 'none' reduction type. >>> bce = keras.losses.BinaryCrossentropy(from_logits=True, ... reduction=None) >>> bce(y_true, y_pred) array([0.235, 1.496], dtype=float32) **Default Usage:** (set `from_logits=False`) >>> # Make the following updates to the above "Recommended Usage" section >>> # 1. Set `from_logits=False` >>> keras.losses.BinaryCrossentropy() # OR ...('from_logits=False') >>> # 2. Update `y_pred` to use probabilities instead of logits >>> y_pred = [0.6, 0.3, 0.2, 0.8] # OR [[0.6, 0.3], [0.2, 0.8]] c dt|t||||||||_||_||_yN)rrr from_logitslabel_smoothingr^)rrbinary_crossentropyrrr^rrrr^rrrrs rrzBinaryCrossentropy.__init__sE  #+  '. rctj|}|j|j|j|j d|SN)rrr^rr,r-rrr^rr/s rr,zBinaryCrossentropy.get_configA& #//#'#7#7    r)Frar7rNrGr=s@rrr@s(Xx ' ", rrz$keras.losses.BinaryFocalCrossentropyc<eZdZdZ dfd ZdZxZS)BinaryFocalCrossentropyaComputes focal cross-entropy loss between true labels and predictions. Binary cross-entropy loss is often used for binary (0 or 1) classification tasks. The loss function requires the following inputs: - `y_true` (true label): This is either 0 or 1. - `y_pred` (predicted value): This is the model's prediction, i.e, a single floating-point value which either represents a [logit](https://en.wikipedia.org/wiki/Logit), (i.e, value in [-inf, inf] when `from_logits=True`) or a probability (i.e, value in `[0., 1.]` when `from_logits=False`). According to [Lin et al., 2018](https://arxiv.org/pdf/1708.02002.pdf), it helps to apply a "focal factor" to down-weight easy examples and focus more on hard examples. By default, the focal tensor is computed as follows: `focal_factor = (1 - output) ** gamma` for class 1 `focal_factor = output ** gamma` for class 0 where `gamma` is a focusing parameter. When `gamma=0`, this function is equivalent to the binary crossentropy loss. Args: apply_class_balancing: A bool, whether to apply weight balancing on the binary classes 0 and 1. alpha: A weight balancing factor for class 1, default is `0.25` as mentioned in reference [Lin et al., 2018]( https://arxiv.org/pdf/1708.02002.pdf). The weight for class 0 is `1.0 - alpha`. gamma: A focusing parameter used to compute the focal factor, default is `2.0` as mentioned in the reference [Lin et al., 2018](https://arxiv.org/pdf/1708.02002.pdf). from_logits: Whether to interpret `y_pred` as a tensor of [logit](https://en.wikipedia.org/wiki/Logit) values. By default, we assume that `y_pred` are probabilities (i.e., values in `[0, 1]`). label_smoothing: Float in `[0, 1]`. When `0`, no smoothing occurs. When > `0`, we compute the loss between the predicted labels and a smoothed version of the true labels, where the smoothing squeezes the labels towards `0.5`. Larger values of `label_smoothing` correspond to heavier smoothing. axis: The axis along which to compute crossentropy (the features axis). Defaults to `-1`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: With the `compile()` API: ```python model.compile( loss=keras.losses.BinaryFocalCrossentropy( gamma=2.0, from_logits=True), ... ) ``` As a standalone function: >>> # Example 1: (batch_size = 1, number of samples = 4) >>> y_true = np.array([0, 1, 0, 0]) >>> y_pred = np.array([-18.6, 0.51, 2.94, -12.8]) >>> loss = keras.losses.BinaryFocalCrossentropy( ... gamma=2, from_logits=True) >>> loss(y_true, y_pred) 0.691 >>> # Apply class weight >>> loss = keras.losses.BinaryFocalCrossentropy( ... apply_class_balancing=True, gamma=2, from_logits=True) >>> loss(y_true, y_pred) 0.51 >>> # Example 2: (batch_size = 2, number of samples = 4) >>> y_true = np.array([[0, 1], [0, 0]]) >>> y_pred = np.array([[-18.6, 0.51], [2.94, -12.8]]) >>> # Using default 'auto'/'sum_over_batch_size' reduction type. >>> loss = keras.losses.BinaryFocalCrossentropy( ... gamma=3, from_logits=True) >>> loss(y_true, y_pred) 0.647 >>> # Apply class weight >>> loss = keras.losses.BinaryFocalCrossentropy( ... apply_class_balancing=True, gamma=3, from_logits=True) >>> loss(y_true, y_pred) 0.482 >>> # Using 'sample_weight' attribute with focal effect >>> loss = keras.losses.BinaryFocalCrossentropy( ... gamma=3, from_logits=True) >>> loss(y_true, y_pred, sample_weight=[0.8, 0.2]) 0.133 >>> # Apply class weight >>> loss = keras.losses.BinaryFocalCrossentropy( ... apply_class_balancing=True, gamma=3, from_logits=True) >>> loss(y_true, y_pred, sample_weight=[0.8, 0.2]) 0.097 >>> # Using 'sum' reduction` type. >>> loss = keras.losses.BinaryFocalCrossentropy( ... gamma=4, from_logits=True, ... reduction="sum") >>> loss(y_true, y_pred) 1.222 >>> # Apply class weight >>> loss = keras.losses.BinaryFocalCrossentropy( ... apply_class_balancing=True, gamma=4, from_logits=True, ... reduction="sum") >>> loss(y_true, y_pred) 0.914 >>> # Using 'none' reduction type. >>> loss = keras.losses.BinaryFocalCrossentropy( ... gamma=5, from_logits=True, ... reduction=None) >>> loss(y_true, y_pred) array([0.0017 1.1561], dtype=float32) >>> # Apply class weight >>> loss = keras.losses.BinaryFocalCrossentropy( ... apply_class_balancing=True, gamma=5, from_logits=True, ... reduction=None) >>> loss(y_true, y_pred) array([0.0004 0.8670], dtype=float32) c t |t||| |||||| ||_||_||_||_||_||_y)N) rrrapply_class_balancingalphagammarrr^) rrbinary_focal_crossentropyrrr^rrr) rrrrrrr^rrrrs rrz BinaryFocalCrossentropy.__init__Lsd  %"7#+  '. %:"  rc tj|}|j|j|j|j |j |j|jd|S)N)rrr^rrr) rr,r-rrr^rrrrs rr,z"BinaryFocalCrossentropy.get_configksX& #//#'#7#7 )-)C)C    r) F?@Frrar7rNrGr=s@rrrs1J\$ ' (> rrz$keras.losses.CategoricalCrossentropyc6eZdZdZ dfd ZdZxZS)CategoricalCrossentropya Computes the crossentropy loss between the labels and predictions. Use this crossentropy loss function when there are two or more label classes. We expect labels to be provided in a `one_hot` representation. If you want to provide labels as integers, please use `SparseCategoricalCrossentropy` loss. There should be `num_classes` floating point values per feature, i.e., the shape of both `y_pred` and `y_true` are `[batch_size, num_classes]`. Args: from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. label_smoothing: Float in [0, 1]. When > 0, label values are smoothed, meaning the confidence on label values are relaxed. For example, if `0.1`, use `0.1 / num_classes` for non-target labels and `0.9 + 0.1 / num_classes` for target labels. axis: The axis along which to compute crossentropy (the features axis). Defaults to `-1`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: Standalone usage: >>> y_true = np.array([[0, 1, 0], [0, 0, 1]]) >>> y_pred = np.array([[0.05, 0.95, 0], [0.1, 0.8, 0.1]]) >>> # Using 'auto'/'sum_over_batch_size' reduction type. >>> cce = keras.losses.CategoricalCrossentropy() >>> cce(y_true, y_pred) 1.177 >>> # Calling with 'sample_weight'. >>> cce(y_true, y_pred, sample_weight=np.array([0.3, 0.7])) 0.814 >>> # Using 'sum' reduction type. >>> cce = keras.losses.CategoricalCrossentropy( ... reduction="sum") >>> cce(y_true, y_pred) 2.354 >>> # Using 'none' reduction type. >>> cce = keras.losses.CategoricalCrossentropy( ... reduction=None) >>> cce(y_true, y_pred) array([0.0513, 2.303], dtype=float32) Usage with the `compile()` API: ```python model.compile(optimizer='sgd', loss=keras.losses.CategoricalCrossentropy()) ``` c dt|t||||||||_||_||_yr)rrcategorical_crossentropyrrr^rs rrz CategoricalCrossentropy.__init__sE  $#+  '. rctj|}|j|j|j|j d|Srrrs rr,z"CategoricalCrossentropy.get_configrr)Frrar7rNrGr=s@rrrzs(BL ' ', rrz)keras.losses.CategoricalFocalCrossentropyc:eZdZdZ dfd ZdZxZS)CategoricalFocalCrossentropya Computes the alpha balanced focal crossentropy loss. Use this crossentropy loss function when there are two or more label classes and if you want to handle class imbalance without using `class_weights`. We expect labels to be provided in a `one_hot` representation. According to [Lin et al., 2018](https://arxiv.org/pdf/1708.02002.pdf), it helps to apply a focal factor to down-weight easy examples and focus more on hard examples. The general formula for the focal loss (FL) is as follows: `FL(p_t) = (1 - p_t) ** gamma * log(p_t)` where `p_t` is defined as follows: `p_t = output if y_true == 1, else 1 - output` `(1 - p_t) ** gamma` is the `modulating_factor`, where `gamma` is a focusing parameter. When `gamma` = 0, there is no focal effect on the cross entropy. `gamma` reduces the importance given to simple examples in a smooth manner. The authors use alpha-balanced variant of focal loss (FL) in the paper: `FL(p_t) = -alpha * (1 - p_t) ** gamma * log(p_t)` where `alpha` is the weight factor for the classes. If `alpha` = 1, the loss won't be able to handle class imbalance properly as all classes will have the same weight. This can be a constant or a list of constants. If alpha is a list, it must have the same length as the number of classes. The formula above can be generalized to: `FL(p_t) = alpha * (1 - p_t) ** gamma * CrossEntropy(y_true, y_pred)` where minus comes from `CrossEntropy(y_true, y_pred)` (CE). Extending this to multi-class case is straightforward: `FL(p_t) = alpha * (1 - p_t) ** gamma * CategoricalCE(y_true, y_pred)` In the snippet below, there is `num_classes` floating pointing values per example. The shape of both `y_pred` and `y_true` are `(batch_size, num_classes)`. Args: alpha: A weight balancing factor for all classes, default is `0.25` as mentioned in the reference. It can be a list of floats or a scalar. In the multi-class case, alpha may be set by inverse class frequency by using `compute_class_weight` from `sklearn.utils`. gamma: A focusing parameter, default is `2.0` as mentioned in the reference. It helps to gradually reduce the importance given to simple (easy) examples in a smooth manner. from_logits: Whether `output` is expected to be a logits tensor. By default, we consider that `output` encodes a probability distribution. label_smoothing: Float in [0, 1]. When > 0, label values are smoothed, meaning the confidence on label values are relaxed. For example, if `0.1`, use `0.1 / num_classes` for non-target labels and `0.9 + 0.1 / num_classes` for target labels. axis: The axis along which to compute crossentropy (the features axis). Defaults to `-1`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: Standalone usage: >>> y_true = [[0., 1., 0.], [0., 0., 1.]] >>> y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] >>> # Using 'auto'/'sum_over_batch_size' reduction type. >>> cce = keras.losses.CategoricalFocalCrossentropy() >>> cce(y_true, y_pred) 0.23315276 >>> # Calling with 'sample_weight'. >>> cce(y_true, y_pred, sample_weight=np.array([0.3, 0.7])) 0.1632 >>> # Using 'sum' reduction type. >>> cce = keras.losses.CategoricalFocalCrossentropy( ... reduction="sum") >>> cce(y_true, y_pred) 0.46631 >>> # Using 'none' reduction type. >>> cce = keras.losses.CategoricalFocalCrossentropy( ... reduction=None) >>> cce(y_true, y_pred) array([3.2058331e-05, 4.6627346e-01], dtype=float32) Usage with the `compile()` API: ```python model.compile(optimizer='adam', loss=keras.losses.CategoricalFocalCrossentropy()) ``` c t |t|||||||| ||_||_||_||_||_y)z4Initializes `CategoricalFocalCrossentropy` instance.)rrrrrrrr^N)rrcategorical_focal_crossentropyrrr^rr) rrrrrr^rrrrs rrz%CategoricalFocalCrossentropy.__init__QsY  *#+  '.   rctj|}|j|j|j|j |j |jd|S)N)rrr^rr)rr,r-rrr^rrrs rr,z'CategoricalFocalCrossentropy.get_confignsO& #//#'#7#7     r)rrFrrar7rNrGr=s@rrrs.k^ ' -: rrz*keras.losses.SparseCategoricalCrossentropyc6eZdZdZ dfd ZdZxZS)SparseCategoricalCrossentropyaO Computes the crossentropy loss between the labels and predictions. Use this crossentropy loss function when there are two or more label classes. We expect labels to be provided as integers. If you want to provide labels using `one-hot` representation, please use `CategoricalCrossentropy` loss. There should be `# classes` floating point values per feature for `y_pred` and a single floating point value per feature for `y_true`. In the snippet below, there is a single floating point value per example for `y_true` and `num_classes` floating pointing values per example for `y_pred`. The shape of `y_true` is `[batch_size]` and the shape of `y_pred` is `[batch_size, num_classes]`. Args: from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. axis: The axis along which to compute crossentropy (the features axis). Defaults to `-1`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: >>> y_true = [1, 2] >>> y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] >>> # Using 'auto'/'sum_over_batch_size' reduction type. >>> scce = keras.losses.SparseCategoricalCrossentropy() >>> scce(y_true, y_pred) 1.177 >>> # Calling with 'sample_weight'. >>> scce(y_true, y_pred, sample_weight=np.array([0.3, 0.7])) 0.814 >>> # Using 'sum' reduction type. >>> scce = keras.losses.SparseCategoricalCrossentropy( ... reduction="sum") >>> scce(y_true, y_pred) 2.354 >>> # Using 'none' reduction type. >>> scce = keras.losses.SparseCategoricalCrossentropy( ... reduction=None) >>> scce(y_true, y_pred) array([0.0513, 2.303], dtype=float32) Usage with the `compile()` API: ```python model.compile(optimizer='sgd', loss=keras.losses.SparseCategoricalCrossentropy()) ``` c Vt|t||||||||_||_y)N)rrrr ignore_classr^)rrsparse_categorical_crossentropyrr)rrrrr^rrrs rrz&SparseCategoricalCrossentropy.__init__s>  +#%  '(rctj|}|j|j|jd|S)N)rr)rr,r-rrrs rr,z(SparseCategoricalCrossentropy.get_configs:& #// $ 1 1   r)FNr7rarNrGr=s@rrr|s(AJ'  .)*rrzkeras.losses.CTCc*eZdZdZdfd ZdZxZS)CTCaCTC (Connectionist Temporal Classification) loss. Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. c4t|t|||yr)rrctcrBs rrz CTC.__init__s 49EJrc,tj|SrDrEr5s rr,zCTC.get_configrFr)r7rNrGr=s@rrrs&K%rrzkeras.losses.Dicec2eZdZdZ dfd ZdZxZS)DiceaPComputes the Dice loss value between `y_true` and `y_pred`. Formula: ```python loss = 1 - (2 * sum(y_true * y_pred)) / (sum(y_true) + sum(y_pred)) ``` Args: reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. axis: Tuple for which dimensions the loss is calculated. Defaults to `None`. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Returns: Dice loss value. Example: >>> y_true = [[[[1.0], [1.0]], [[0.0], [0.0]]], ... [[[1.0], [1.0]], [[0.0], [0.0]]]] >>> y_pred = [[[[0.0], [1.0]], [[0.0], [1.0]]], ... [[[0.4], [0.0]], [[0.0], [0.9]]]] >>> axis = (1, 2, 3) >>> loss = keras.losses.Dice(axis=axis, reduction=None)(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([0.5, 0.75757575], shape=(2,), dtype=float32) >>> loss = keras.losses.Dice()(y_true, y_pred) >>> assert loss.shape == () >>> loss array(0.6164384, shape=(), dtype=float32) >>> y_true = np.array(y_true) >>> y_pred = np.array(y_pred) >>> loss = keras.losses.Dice(axis=axis, reduction=None)(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([0.5, 0.75757575], shape=(2,), dtype=float32) cDt|t||||||_yr])rrdicer^)rrrr^rrs rrz Dice.__init__5s+  tyD   rcjtj|}|jd|ji|S)Nr^)rr,r-r^rs rr,zDice.get_configAs*& vtyy)* r)r7rNNrGr=s@rrrs!4p(   rrzkeras.losses.Tverskyc6eZdZdZ dfd ZdZxZS)TverskyaLComputes the Tversky loss value between `y_true` and `y_pred`. This loss function is weighted by the alpha and beta coefficients that penalize false positives and false negatives. With `alpha=0.5` and `beta=0.5`, the loss value becomes equivalent to Dice Loss. Args: alpha: The coefficient controlling incidence of false positives. Defaults to `0.5`. beta: The coefficient controlling incidence of false negatives. Defaults to `0.5`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Returns: Tversky loss value. Reference: - [Salehi et al., 2017](https://arxiv.org/abs/1706.05721) c dt|t||||||||_||_||_y)N)rrrrbetar^)rrtverskyrrr^)rrrrrr^rrs rrzTversky.__init__msC       rctj|}|j|j|j|j d|S)N)rrr^)rr,r-rrr^rs rr,zTversky.get_configs9& jj$))TYY G  r)?rr7rNNrGr=s@rrrGs'"L '  ,rrzkeras.losses.Circlec6eZdZdZ dfd ZdZxZS)Circlea Computes Circle Loss between integer labels and L2-normalized embeddings. This is a metric learning loss designed to minimize within-class distance and maximize between-class distance in a flexible manner by dynamically adjusting the penalty strength based on optimization status of each similarity score. To use Circle Loss effectively, the model should output embeddings without an activation function (such as a `Dense` layer with `activation=None`) followed by UnitNormalization layer to ensure unit-norm embeddings. Args: gamma: Scaling factor that determines the largest scale of each similarity score. Defaults to `80`. margin: The relaxation factor, below this distance, negatives are up weighted and positives are down weighted. Similarly, above this distance negatives are down weighted and positive are up weighted. Defaults to `0.4`. remove_diagonal: Boolean, whether to remove self-similarities from the positive mask. Defaults to `True`. reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Examples: Usage with the `compile()` API: ```python model = models.Sequential([ keras.layers.Input(shape=(224, 224, 3)), keras.layers.Conv2D(16, (3, 3), activation='relu'), keras.layers.Flatten(), keras.layers.Dense(64, activation=None), # No activation keras.layers.UnitNormalization() # L2 normalization ]) model.compile(optimizer="adam", loss=keras.losses.Circle()) ``` Reference: - [Yifan Sun et al., 2020](https://arxiv.org/abs/2002.10857) c dt|t||||||||_||_||_y)N)rrrrmarginremove_diagonal)rrcirclerrr)rrrrrrrrs rrzCircle.__init__sD  +    .rctj|}|j|j|j|j d|S)N)rrr)rr,r-rrrrs rr,zCircle.get_configs?& ++#'#7#7   r)gT@皙?Tr7rNrGr=s@rrrs'6t' /, rrz/keras.losses.CategoricalGeneralizedCrossEntropyc2eZdZdZ dfd ZdZxZS)"CategoricalGeneralizedCrossEntropyaComputes the Generalized Cross Entropy loss between `y_true` & `y_pred`. Generalized Cross Entropy (GCE) is a noise-robust loss function that provides better robustness against noisy labels than standard cross entropy. It generalizes both cross entropy and mean absolute error through the parameter q, where values closer to 1 make the loss more robust to noisy labels. Formula: ```python loss = (1 - p**q) / q ``` where `p` is the predicted probability for the true class and `q` is the noise parameter. Args: q: Float in range `(0, 1)`. It is the noise parameter. Controls the behavior of the loss: - As `q` approaches 0: Behaves more like cross entropy - As `q` approaches 1: Behaves more like mean absolute error Defaults to `0.5` reduction: Type of reduction to apply to the loss. In almost all cases this should be `"sum_over_batch_size"`. Supported options are `"sum"`, `"sum_over_batch_size"`, `"mean"`, `"mean_with_sample_weight"` or `None`. `"sum"` sums the loss, `"sum_over_batch_size"` and `"mean"` sum the loss and divide by the sample size, and `"mean_with_sample_weight"` sums the loss and divides by the sum of the sample weights. `"none"` and `None` perform no aggregation. Defaults to `"sum_over_batch_size"`. name: Optional name for the loss instance. dtype: The dtype of the loss's computations. Defaults to `None`, which means using `keras.backend.floatx()`. `keras.backend.floatx()` is a `"float32"` unless set to different value (via `keras.backend.set_floatx()`). If a `keras.DTypePolicy` is provided, then the `compute_dtype` will be utilized. Example: ```python y_true = np.array([0, 1, 0, 1]) y_pred = np.array([[0.7, 0.3], [0.2, 0.8], [0.6, 0.4], [0.4, 0.6]]) keras.losses.CategoricalGeneralizedCrossEntropy()(y_true, y_pred) ``` References: - [Zhang, Sabuncu, 2018](https://arxiv.org/abs/1805.07836) ("Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels") cd|cxkrdkstdtdt| t||||||_y)Nrr$z q must be in the interval (0, 1))rrrq) ValueErrorrr%categorical_generalized_cross_entropyr)rrrrrrs rrz+CategoricalGeneralizedCrossEntropy.__init__sW1yqy?@ @?@ @  1  rcjtj|}|jd|ji|S)Nr)rr,r-rrs rr,z-CategoricalGeneralizedCrossEntropy.get_config-s1& TVV   r)rr7rNrGr=s@rrrs!0h ' 4 $rrctjd}tjd}tjtj||}fd}fd}tj|||}|S)zCConverts binary labels into -1/1 for hinge loss/metric calculation.rr$cdzdz S)Nrrhrr'sr_convert_binary_labelsz>convert_binary_labels_to_hinge.._convert_binary_labels=sV|c!!rcSrDrrsr_return_labels_unconvertedzBconvert_binary_labels_to_hinge.._return_labels_unconvertedAs r)requalall logical_orcond)r' are_zerosare_ones is_binaryrrupdated_y_trues` rconvert_binary_labels_to_hinger7sg &!$Iyy#H 8<>I"XX)+EN rzkeras.metrics.hingezkeras.losses.hingectj|}tj||j}tj|}t |}tj tj d||zz ddS)aComputes the hinge loss between `y_true` & `y_pred`. Formula: ```python loss = mean(maximum(1 - y_true * y_pred, 0), axis=-1) ``` Args: y_true: The ground truth values. `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are provided they will be converted to -1 or 1 with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Hinge loss values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.choice([-1, 1], size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.hinge(y_true, y_pred) rrhrrar^)rconvert_to_tensorcastrrmeanmaximumr'r(s rrrrrKsg< " "6 *F XXfFLL 1F  " "6 *F +F 3F 88CKKfvo 5s;" EErzkeras.metrics.squared_hingezkeras.losses.squared_hingec  tj|}tj||j}t |}tj tj tjd||zz ddS)aComputes the squared hinge loss between `y_true` & `y_pred`. Formula: ```python loss = mean(square(maximum(1 - y_true * y_pred, 0)), axis=-1) ``` Args: y_true: The ground truth values. `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1 with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Squared hinge loss values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.choice([-1, 1], size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.squared_hinge(y_true, y_pred) rhrrar)rrrrrrsquarerrs rrwrwpse< " "6 *F XXffll +F +F 3F 88 3;;sVf_4c:;" rzkeras.metrics.categorical_hingezkeras.losses.categorical_hingecRtj|}tj||j}tj||zd}tj d|z |zd}tjd|j}tj ||z dz|S)a<Computes the categorical hinge loss between `y_true` & `y_pred`. Formula: ```python loss = maximum(neg - pos + 1, 0) ``` where `neg=maximum((1-y_true)*y_pred)` and `pos=sum(y_true*y_pred)` Args: y_true: The ground truth values. `y_true` values are expected to be either `{-1, +1}` or `{0, 1}` (i.e. a one-hot-encoded tensor) with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Categorical hinge loss values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.randint(0, 3, size=(2,)) >>> y_true = np.eye(np.max(y_true) + 1)[y_true] >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.categorical_hinge(y_true, y_pred) rarrhr)rrrrsummaxr)r'r(posnegzeros rr}r}sB " "6 *F XXffll +F ''&6/ +C ''3<6) 3C 88C &D ;;sSy3 --r)z keras.metrics.mean_squared_errorzkeras.losses.mean_squared_errorzkeras._legacy.losses.msezkeras._legacy.losses.MSEzkeras._legacy.metrics.msezkeras._legacy.metrics.MSEctj|}tj||j}t||\}}tjtj ||z dS)aLComputes the mean squared error between labels and predictions. Formula: ```python loss = mean(square(y_true - y_pred), axis=-1) ``` Example: >>> y_true = np.random.randint(0, 2, size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.mean_squared_error(y_true, y_pred) Args: y_true: Ground truth values with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Mean squared error values with shape = `[batch_size, d0, .. dN-1]`. rrar)rrrrrrrs rrArAsYB " "6 *F  " "6 >F3FFCNFF 88CJJv/b 99r)z!keras.metrics.mean_absolute_errorz keras.losses.mean_absolute_errorzkeras._legacy.losses.MAEzkeras._legacy.losses.maezkeras._legacy.metrics.MAEzkeras._legacy.metrics.maectj|}tj||j}t||\}}tjtj ||z dS)a>Computes the mean absolute error between labels and predictions. ```python loss = mean(abs(y_true - y_pred), axis=-1) ``` Args: y_true: Ground truth values with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Mean absolute error values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.randint(0, 2, size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.mean_absolute_error(y_true, y_pred) rrar)rrrrrabsrs rrLrLsX> " "6 *F  " "6 >F3FFCNFF 88CGGFVO,2 66r)z,keras.metrics.mean_absolute_percentage_errorz+keras.losses.mean_absolute_percentage_errorzkeras._legacy.losses.mapezkeras._legacy.losses.MAPEzkeras._legacy.metrics.mapezkeras._legacy.metrics.MAPEctj|}tj||j}tjtj|j}t ||\}}tj ||z tjtj ||z }dtj|dzS)aComputes the mean absolute percentage error between `y_true` & `y_pred`. Formula: ```python loss = 100 * mean(abs((y_true - y_pred) / y_true), axis=-1) ``` Division by zero is prevented by dividing by `maximum(y_true, epsilon)` where `epsilon = keras.backend.epsilon()` (default to `1e-7`). Args: y_true: Ground truth values with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Mean absolute percentage error values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.random(size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.mean_absolute_percentage_error(y_true, y_pred) rgY@rar) rrrrepsilonrrrr)r'r(rdiffs rrQrQ sL " "6 *F  " "6 >F##GOO$5V\\JG3FFCNFF 77FVOs{{3776?G'LL MD 388Dr* **r)z,keras.metrics.mean_squared_logarithmic_errorz+keras.losses.mean_squared_logarithmic_errorzkeras._legacy.losses.mslezkeras._legacy.losses.MSLEzkeras._legacy.metrics.mslezkeras._legacy.metrics.MSLEctjtj}tj|}tj||j}t ||\}}tj tj||dz}tj tj||dz}tjtj||z dS)a4Computes the mean squared logarithmic error between `y_true` & `y_pred`. Formula: ```python loss = mean(square(log(y_true + 1) - log(y_pred + 1)), axis=-1) ``` Note that `y_pred` and `y_true` cannot be less or equal to 0. Negative values and 0 values will be replaced with `keras.backend.epsilon()` (default to `1e-7`). Args: y_true: Ground truth values with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Mean squared logarithmic error values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.randint(0, 2, size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.mean_squared_logarithmic_error(y_true, y_pred) rrhrar) rrrrrrlogrrr)r'r(r first_log second_logs rrXrX9sL##GOO$56G  " "6 *F  " "6 >F3FFCNFF FG4s:;IVW5;>> y_true = [[0., 1.], [1., 1.], [1., 1.]] >>> y_pred = [[1., 0.], [1., 1.], [-1., -1.]] >>> loss = keras.losses.cosine_similarity(y_true, y_pred, axis=-1) [-0., -0.99999994, 0.99999994] rr)rrrrr r)r'r(r^s rr_r_hsk@ " "6 *F  " "6 >F3FFCNFF vD )F vD )F GGFVO$ / //rzkeras.losses.huberzkeras.metrics.huberc (tj|}tj||j}t||\}}tj||j}tj||}tj |}tjd|j}tj tj||k|tj|z||z|tj|zz dS)a Computes Huber loss value. Formula: ```python for x in error: if abs(x) <= delta: loss.append(0.5 * x^2) elif abs(x) > delta: loss.append(delta * abs(x) - 0.5 * delta^2) loss = mean(loss, axis=-1) ``` See: [Huber loss](https://en.wikipedia.org/wiki/Huber_loss). Example: >>> y_true = [[0, 1], [0, 0]] >>> y_pred = [[0.6, 0.4], [0.4, 0.6]] >>> loss = keras.losses.huber(y_true, y_pred) 0.155 Args: y_true: tensor of true targets. y_pred: tensor of predicted targets. delta: A float, the point where the Huber loss function changes from a quadratic to linear. Defaults to `1.0`. Returns: Tensor with one scalar loss entry per sample. rrrar) rrrrsubtractrrwherer)r'r(reerror abs_errorhalfs rrfrfsB " "6 *F  " "6 >F3FFCNFF  ! !%v|| >> y_true = [[0., 1.], [0., 0.]] >>> y_pred = [[1., 1.], [0., 0.]] >>> loss = keras.losses.log_cosh(y_true, y_pred) 0.108 Args: y_true: Ground truth values with shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values with shape = `[batch_size, d0, .. dN]`. Returns: Logcosh error values with shape = `[batch_size, d0, .. dN-1]`. rrc@|tj|dzzz S)Ng)rsoftplus)r log2s r_logcoshzlog_cosh.._logcoshs 3<<D))D00rrar)rrrrrr)r'r(rrs @rrmrms{H " "6 *F  " "6 >F3FFCNFF  V\\ BD1 88HVf_-B 77r)zkeras.metrics.kl_divergencezkeras.losses.kl_divergencezkeras._legacy.losses.KLDzkeras._legacy.losses.kldz0keras._legacy.losses.kullback_leibler_divergencezkeras._legacy.metrics.KLDzkeras._legacy.metrics.kldz1keras._legacy.metrics.kullback_leibler_divergencecptj|}tj||j}tj|t j d}tj|t j d}tj |tj||z zdS)aComputes Kullback-Leibler divergence loss between `y_true` & `y_pred`. Formula: ```python loss = y_true * log(y_true / y_pred) ``` `y_true` and `y_pred` are expected to be probability distributions, with values between 0 and 1. They will get clipped to the `[0, 1]` range. Args: y_true: Tensor of true targets. y_pred: Tensor of predicted targets. Returns: KL Divergence loss values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.randint(0, 2, size=(2, 3)).astype(np.float32) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.kl_divergence(y_true, y_pred) >>> assert loss.shape == (2,) >>> y_true = ops.clip(y_true, 1e-7, 1) >>> y_pred = ops.clip(y_pred, 1e-7, 1) >>> assert np.array_equal( ... loss, np.sum(y_true * np.log(y_true / y_pred), axis=-1)) r$rar)rrrcliprrrrrs rrrsX " "6 *F  " "66<< 8F XXfgoo/ 3F XXfgoo/ 3F 776CGGFVO442 >>rzkeras.metrics.poissonzkeras.losses.poissonc:tj|}tj||j}tjtj|j}tj ||tj ||zzz dS)aComputes the Poisson loss between y_true and y_pred. Formula: ```python loss = y_pred - y_true * log(y_pred) ``` Args: y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`. Returns: Poisson loss values with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = np.random.randint(0, 2, size=(2, 3)) >>> y_pred = np.random.random(size=(2, 3)) >>> loss = keras.losses.poisson(y_true, y_pred) >>> assert loss.shape == (2,) >>> y_pred = y_pred + 1e-7 >>> assert np.allclose( ... loss, np.mean(y_pred - y_true * np.log(y_pred), axis=-1), ... atol=1e-5) rrar)rrrrrrr)r'r(rs rrr$sqB " "6 *F  " "6 >F##GOO$5V\\JG 88FVcggfw.>&???b IIrz&keras.metrics.categorical_crossentropyz%keras.losses.categorical_crossentropyct|trtd|dt|t j |}t j ||j}|jddk(r*tjd|jdtd|rDt j t j|d|j}|d |z z||z z}t j|||| S) aComputes the categorical crossentropy loss. Args: y_true: Tensor of one-hot true targets. y_pred: Tensor of predicted targets. from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. label_smoothing: Float in [0, 1]. If > `0` then smooth the labels. For example, if `0.1`, use `0.1 / num_classes` for non-target labels and `0.9 + 0.1 / num_classes` for target labels. axis: Defaults to `-1`. The dimension along which the entropy is computed. Returns: Categorical crossentropy loss value. Example: >>> y_true = [[0, 1, 0], [0, 0, 1]] >>> y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] >>> loss = keras.losses.categorical_crossentropy(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([0.0513, 2.303], dtype=float32) -`axis` must be of type `int`. Received: axis= of type rar$zIn loss categorical_crossentropy, expected y_pred.shape to be (batch_size, num_classes) with num_classes > 1. Received: y_pred.shape=B. Consider using 'binary_crossentropy' if you only have 2 classes. stacklevelrhrr^) isinstanceboolrtyperrrrshapewarningswarn SyntaxWarningr)r'r(rrr^ num_classess rrrKsD$ "V9T$ZL :   " "6 *F XXffll +F ||B1  <JO O   hhsyy04fllC 301 k )   ' 'Kd rz,keras.metrics.categorical_focal_crossentropyz+keras.losses.categorical_focal_crossentropyct|trtd|dt|t j |}t j ||j}|jddk(r*tjd|jdtd|rDt j t j|d|j}|d |z z||z z}|rt j|| }|t j||d z }t j|tj d tj z }| t j"|z} t j$d |z |} t j&| |} t j&| | } t j| | } | S) a4Computes the categorical focal crossentropy loss. Args: y_true: Tensor of one-hot true targets. y_pred: Tensor of predicted targets. alpha: A weight balancing factor for all classes, default is `0.25` as mentioned in the reference. It can be a list of floats or a scalar. In the multi-class case, alpha may be set by inverse class frequency by using `compute_class_weight` from `sklearn.utils`. gamma: A focusing parameter, default is `2.0` as mentioned in the reference. It helps to gradually reduce the importance given to simple examples in a smooth manner. When `gamma` = 0, there is no focal effect on the categorical crossentropy. from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. label_smoothing: Float in [0, 1]. If > `0` then smooth the labels. For example, if `0.1`, use `0.1 / num_classes` for non-target labels and `0.9 + 0.1 / num_classes` for target labels. axis: Defaults to `-1`. The dimension along which the entropy is computed. Returns: Categorical focal crossentropy loss value. Example: >>> y_true = [[0, 1, 0], [0, 0, 1]] >>> y_pred = [[0.05, 0.9, 0.05], [0.1, 0.85, 0.05]] >>> loss = keras.losses.categorical_focal_crossentropy(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([2.63401289e-04, 6.75912094e-01], dtype=float32) r r rar$zIn loss categorical_focal_crossentropy, expected y_pred.shape to be (batch_size, num_classes) with num_classes > 1. Received: y_pred.shape=r r rrhrT)r^keepdims)rrrrrrrrrrrrsoftmaxrrrrrpowermultiply) r'r(rrrrr^routputccemodulating_factorweighting_factor focal_cces rrrsb$ "V9T$ZL :   " "6 *F XXffll +F ||B1  <JO O   hhsyy04fllC 301 k ) V$/ cggf4$? ?F XXfgoo/w7H1H IF 'CGGFO #C #,6||$5u= -s3I -I rz-keras.metrics.sparse_categorical_crossentropyz,keras.losses.sparse_categorical_crossentropyct|jt|jk(r)|jddk(rtj|d}|tj|dd}tj|tj ||j }|tj ||j z}|tj tj|d|j z}tj||||}|Dtj}tj||d}tj|||S)aComputes the sparse categorical crossentropy loss. Args: y_true: Ground truth values. y_pred: The predicted values. from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. ignore_class: Optional integer. The ID of a class to be ignored during loss computation. This is useful, for example, in segmentation problems featuring a "void" class (commonly -1 or 255) in segmentation maps. By default (`ignore_class=None`), all classes are considered. axis: Defaults to `-1`. The dimension along which the entropy is computed. Returns: Sparse categorical crossentropy loss value. Examples: >>> y_true = [1, 2] >>> y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] >>> loss = keras.losses.sparse_categorical_crossentropy(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([0.0513, 2.303], dtype=float32) rar$rNrr)mask) lenrrsqueeze not_equalrr expand_dimsrreshaperrset_keras_mask)r'r(rrr^ res_shape valid_maskress rrrsJ 6<<C --&,,r2Ba2GV"-IIf%cr* ]]6388L&,,+OP #((:v||<<#(( OOJ +V\\    - -   C[[Y7 ii C-s4 Jrz!keras.metrics.binary_crossentropyz keras.losses.binary_crossentropyctj|}tj||j}|r|d|z zd|zz}tjtj ||||S)aComputes the binary crossentropy loss. Args: y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`. y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`. from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. label_smoothing: Float in `[0, 1]`. If > `0` then smooth the labels by squeezing them towards 0.5, that is, using `1. - 0.5 * label_smoothing` for the target class and `0.5 * label_smoothing` for the non-target class. axis: The axis along which the mean is computed. Defaults to `-1`. Returns: Binary crossentropy loss value. shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = [[0, 1], [0, 0]] >>> y_pred = [[0.6, 0.4], [0.4, 0.6]] >>> loss = keras.losses.binary_crossentropy(y_true, y_pred) >>> assert loss.shape == (2,) >>> loss array([0.916 , 0.714], dtype=float32) rhr)rr)rrrrrr)r'r(rrr^s rrr) skD " "6 *F XXffll +F301C/4II 88 KH  rz'keras.metrics.binary_focal_crossentropyz&keras.losses.binary_focal_crossentropyctj|}tj||j}|r|d|z zd|zz}|rtj|}tj ||d}||zd|z d|z zz} tj d| z |} | |z} |r||zd|z d|z zz} | | z} tj| |S)a Computes the binary focal crossentropy loss. According to [Lin et al., 2018](https://arxiv.org/pdf/1708.02002.pdf), it helps to apply a focal factor to down-weight easy examples and focus more on hard examples. By default, the focal tensor is computed as follows: `focal_factor = (1 - output) ** gamma` for class 1 `focal_factor = output ** gamma` for class 0 where `gamma` is a focusing parameter. When `gamma` = 0, there is no focal effect on the binary crossentropy loss. If `apply_class_balancing == True`, this function also takes into account a weight balancing factor for the binary classes 0 and 1 as follows: `weight = alpha` for class 1 (`target == 1`) `weight = 1 - alpha` for class 0 where `alpha` is a float in the range of `[0, 1]`. Args: y_true: Ground truth values, of shape `(batch_size, d0, .. dN)`. y_pred: The predicted values, of shape `(batch_size, d0, .. dN)`. apply_class_balancing: A bool, whether to apply weight balancing on the binary classes 0 and 1. alpha: A weight balancing factor for class 1, default is `0.25` as mentioned in the reference. The weight for class 0 is `1.0 - alpha`. gamma: A focusing parameter, default is `2.0` as mentioned in the reference. from_logits: Whether `y_pred` is expected to be a logits tensor. By default, we assume that `y_pred` encodes a probability distribution. label_smoothing: Float in `[0, 1]`. If > `0` then smooth the labels by squeezing them towards 0.5, that is, using `1. - 0.5 * label_smoothing` for the target class and `0.5 * label_smoothing` for the non-target class. axis: The axis along which the mean is computed. Defaults to `-1`. Returns: Binary focal crossentropy loss value with shape = `[batch_size, d0, .. dN-1]`. Example: >>> y_true = [[0, 1], [0, 0]] >>> y_pred = [[0.6, 0.4], [0.4, 0.6]] >>> # In this instance, the first sample in the second batch is the >>> # 'easier' example. >>> focal_loss = keras.losses.binary_focal_crossentropy( ... y_true, y_pred, gamma=2) >>> assert loss.shape == (2,) >>> focal_loss array([0.330, 0.206], dtype=float32) >>> # Compare with binary_crossentropy >>> bce_loss = keras.losses.binary_focal_crossentropy( ... y_true, y_pred) >>> bce_loss array([0.916, 0.714], dtype=float32) >>> # Binary focal crossentropy loss attributes more importance to the >>> # harder example which results in a higher loss for the first batch >>> # when normalized by binary cross entropy loss >>> focal_loss/bce_loss array([0.360, 0.289] rhrF)targetrrr$r)rrrrsigmoidrrr) r'r(rrrrrr^bcep_t focal_factor focal_bceweights rrrW sZ " "6 *F XXffll +F301C/4IIV$ ! ! C 6/QZAJ7 7C99S3Y.Ls"I%1v:!e)"<<Y& 88ID ))rzkeras.losses.ctcc6ttj|dk7r!tdtj|ttj|dk7r!tdtj|d}tj|d}tj|d}|tj|fdz}tj tj ||k7d d}tj||||| S) aCTC (Connectionist Temporal Classification) loss. Args: y_true: A tensor of shape `(batch_size, max_length)` containing the true labels in integer format. `0` always represents the blank/mask index and should not be used for classes. y_pred: A tensor of shape `(batch_size, max_length, num_classes)` containing logits (the output of your model). They should *not* be normalized via softmax. r z{Targets `y_true` are expected to be a tensor of shape `(batch_size, max_length)` in integer format. Received: y_true.shape=zuLogits `y_pred` are expected to be a tensor of shape `(batch_size, max_length, num_classes)`. Received: y_pred.shape=rr$int32rrar) mask_index)r%rrronesrrctc_loss)r'r(r: batch_length input_length label_lengths rrr s 399V " &&)ii&7%8 :   399V " &&)ii&7%8 :  J99V$Q'L99V$Q'L#((L?'"JJL88 *$2.gL << lz rzkeras.losses.dicechtj|}tj||j}|}|}tj||z|}tj d|ztj||tj||zt jz}d|z S)aComputes the Dice loss value between `y_true` and `y_pred`. Formula: ```python loss = 1 - (2 * sum(y_true * y_pred)) / (sum(y_true) + sum(y_pred)) ``` Args: y_true: tensor of true targets. y_pred: tensor of predicted targets. axis: tuple for which dimensions the loss is calculated Returns: Dice loss value. Example: >>> y_true = [[[[1.0], [1.0]], [[0.0], [0.0]]], ... [[[1.0], [1.0]], [[0.0], [0.0]]]] >>> y_pred = [[[[0.0], [1.0]], [[0.0], [1.0]]], ... [[[0.4], [0.0]], [[0.0], [0.9]]]] >>> axis = (1, 2, 3) >>> loss = keras.losses.dice(y_true, y_pred, axis=axis) >>> assert loss.shape == (2,) >>> loss array([0.5, 0.75757575], shape=(2,), dtype=float32) >>> loss = keras.losses.dice(y_true, y_pred) >>> assert loss.shape == () >>> loss array(0.6164384, shape=(), dtype=float32) rrr$rrrrrdividerr)r'r(r^inputstargets intersectionrs rrr sF " "6 *F XXffll +F FG776G+$7L :: l T" ''&t $ % //   D t8Orzkeras.losses.tverskyctj|}tj||j}|}|}tj||z|}tjd|z |z|}tj|d|z z|} tj ||||zz| |zzt jz} d| z S)aComputes the Tversky loss value between `y_true` and `y_pred`. This loss function is weighted by the alpha and beta coefficients that penalize false positives and false negatives. With `alpha=0.5` and `beta=0.5`, the loss value becomes equivalent to Dice Loss. Args: y_true: tensor of true targets. y_pred: tensor of predicted targets. alpha: coefficient controlling incidence of false positives. beta: coefficient controlling incidence of false negatives. axis: tuple for which dimensions the loss is calculated. Returns: Tversky loss value. Reference: - [Salehi et al., 2017](https://arxiv.org/abs/1706.05721) rr$rA) r'r(rrr^rCrDrEfprrs rrr s0 " "6 *F XXffll +F FG776G+$7L !g+'d 3B AJ'd 3BjjrEz!BI-0AAG w;rzkeras.losses.circlec tj|}tj|d}||ntj|}||ntj|d}|}d|z}|} d|z } dtj|tj|z } tj | d} t |||\} } tj| | j} tj| | j} || z}|| z}tj |d}|| z }|| z}tj |d}| | z }| | z }d|z|z|z}||z|z}tjtj| |tdd}tjtj| |tdd}tj||z}tj||d kD|S) a]Computes the Circle loss. It is designed to minimize within-class distances and maximize between-class distances in L2 normalized embedding space. Args: y_true: Tensor with ground truth labels in integer format. y_pred: Tensor with predicted L2 normalized embeddings. ref_labels: Optional integer tensor with labels for reference embeddings. If `None`, defaults to `y_true`. ref_embeddings: Optional tensor with L2 normalized reference embeddings. If `None`, defaults to `y_pred`. remove_diagonal: Boolean, whether to remove self-similarities from positive mask. Defaults to `True`. gamma: Float, scaling factor for the loss. Defaults to `80`. margin: Float, relaxation factor for the loss. Defaults to `0.4`. Returns: Circle loss value. r9r$r)rrraz-infrr)rrrmatmul transposerr r logsumexprfloatrrr*)r'r( ref_labelsref_embeddingsrrr optim_pos optim_neg delta_pos delta_negpairwise_cosine_distances positive_mask negative_mask pos_weights neg_weights pos_dists neg_dists pos_wdists neg_wdistsp_lossn_loss circle_losss rrrD s< " "6 *F XXfg &F  !   " "> 2 &-388J3PJIF IIF I !CJJ n-%!!$ ,Es K#6'$ M= HH6<<MHH6<<M77K -K++k3/K77K -K++k3/K55I55Iek)I5J$y0J ]] -U6]; F]] -U6]; F ,,v/K ; a8 rz2keras.losses.categorical_generalized_cross_entropyc4tjtj|dtj|d}tj||j}tj ||zd}dtj ||z |z }|S)aComputes the Generalized Cross Entropy loss. Generalized Cross Entropy (GCE) is a noise-robust loss function that provides better robustness against noisy labels than standard cross entropy. It generalizes both cross entropy and mean absolute error through the parameter q, where values closer to 1 make the loss more robust to noisy labels. Formula: ```python loss = (1 - p**q) / q ``` where `p` is the predicted probability for the true class and `q` is the noise parameter. Args: y_true: Ground truth labels. Expected to contain *integer class indices* with shape `[batch_size]` or `[batch_size, 1]`. y_pred: The predicted class probabilities, with shape `[batch_size, num_classes]`. q: Float in range `(0, 1)`. It is the noise parameter. Controls the behavior of the loss: - As `q` approaches 0: Behaves more like cross entropy - As `q` approaches 1: Behaves more like mean absolute error Returns: GCE loss values with shape `[batch_size]`. ``` References: - [Zhang, Sabuncu, 2018](https://arxiv.org/abs/1805.07836) ("Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels") intra)rrr$)rone_hotrrrrr)r'r(ry_true_one_hotpgce_losss rrr s|L[[ SYYv->r-BNXXnfll;N 'b1ACIIaO#q(H Or)ra)rh)Frra)rrFrra)FNra)FrrFrrarD)rrN)NNTPr)=r keras.srcrrrkeras.src.api_exportrkeras.src.losses.lossrrkeras.src.savingr keras.src.utils.numerical_utilsr r r r?rJrOrVr[rcrkrprur{rrrrrrrrrrrrrrrrwr}rArLrQrXr_rfrmrrrrrrrrrrrrrrrrksr-&@.?5"M$"MJ-.%%*%%/%%P./%%+%%0%%P89(%"5(%:(%V89(%"5(%:(%V-.3%*3%/3%l"#3% 3%$3%l$%%%!%%&%%P"#&% &%$&%R)*%%&%%+%%P-.'%*'%/'%T)*&%&&%+&%R$% %! %& %F/0z,z1zz45x1x6xv45d1d6dN9:V#6V;Vr:;a$7a<aH !% %"%6!"F F#FR$%@!@&@F#$X X%Xv?@L)<LAL^( F  F>%$   @)( .  .F : :8 7 74  +  +F !A !AH./$00$0N#%:;<.=.b#8#8L  #? #?L J  JB0/BD6  6r65   W  Wt76@B6  6r+*BD%  %P10   `*  `*F !"""J!"0#0f$%&&&R#$ T%TnBC/D/r