TheAlgorithms/Python · error · ValueError

gamma value must be non-negative

Error message

gamma value must be non-negative

What it means

Raised by the kernel helper class inside sequential_minimum_optimization.py when the RBF kernel is selected with a negative gamma. _check() runs during setup and validates that the RBF width parameter is non-negative, because a negative gamma would produce an exploding (non-decaying) exponential kernel that is mathematically invalid for RBF.

Source

Thrown at machine_learning/sequential_minimum_optimization.py:424

        self.degree = np.float64(degree)
        self.coef0 = np.float64(coef0)
        self.gamma = np.float64(gamma)
        self._kernel_name = kernel
        self._kernel = self._get_kernel(kernel_name=kernel)
        self._check()

    def _polynomial(self, v1, v2):
        return (self.gamma * np.inner(v1, v2) + self.coef0) ** self.degree

    def _linear(self, v1, v2):
        return np.inner(v1, v2) + self.coef0

    def _rbf(self, v1, v2):
        return np.exp(-1 * (self.gamma * np.linalg.norm(v1 - v2) ** 2))

    def _check(self):
        if self._kernel == self._rbf and self.gamma < 0:
            raise ValueError("gamma value must be non-negative")

    def _get_kernel(self, kernel_name):
        maps = {"linear": self._linear, "poly": self._polynomial, "rbf": self._rbf}
        return maps[kernel_name]

    def __call__(self, v1, v2):
        return self._kernel(v1, v2)

    def __repr__(self):
        return self._kernel_name


def count_time(func):
    def call_func(*args, **kwargs):
        import time

        start_time = time.time()
        func(*args, **kwargs)

View on GitHub (pinned to f5988cc097)

Solutions

1. Set gamma to a non-negative value; typical starting points are 1/n_features or values from a logspace grid like 0.001-10.
2. If you intended gamma = 1/(2*sigma^2), compute it explicitly so the result is positive.
3. Switch to kernel='linear' if you do not need the RBF kernel at all.

Example fix

# before
model = SMO(train_samples, train_labels, kernel='rbf', gamma=-0.5)

# after
model = SMO(train_samples, train_labels, kernel='rbf', gamma=0.5)

gamma = 1.0 / train_samples.shape[1]  # positive default
assert gamma >= 0, 'gamma must be non-negative for rbf'

def is_valid_gamma(g) -> bool:
    return isinstance(g, (int, float)) and not isinstance(g, bool) and g >= 0

When it happens

Trigger: Constructing the SMO classifier (or its kernel object) with kernel='rbf' and a gamma value less than 0. Other kernels (linear, poly) never trigger this check even with negative gamma.

Common situations: Typosigning gamma (e.g. gamma=-0.1 instead of 0.1), copying hyperparameters from a convention where gamma means inverse width (1/(2*sigma^2)) and mixing up signs, or sweeping gamma over a log range that includes negatives.

Related errors

• rbf kernel requires gamma
• gamma must be > 0
• Length of predicted and actual array must be same.
• y_true can have values -1 or 1 only.
• Test samples' feature length does not equal to that of train

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/8a4bf33995d5c83e. Report an issue: GitHub.