How deeply does Domain-Specific Small Language Models cover operator?

Explains operator semantics, typing, graph construction, validation, and a linear-regression example, but defers the complete operator catalog.

Operator in Domain-Specific Small Language Models

A computation node in an ONNX graph that performs a specific operation during model execution.

An operator is a computation node in an ONNX directed graph. It consumes typed tensor inputs, performs a defined operation, and passes results to downstream nodes. Standard operators cover common machine-learning workloads; custom operators extend the graph when standard operations are insufficient. section 5.1 section 5.2

Operators matter operationally because they define both graph semantics and deployment constraints:

Express numerical computation through matrix operations, reductions, image transformations, neural-network layers, and activation functions. section 5.2
Require explicit input and output shapes and element types because ONNX is strongly typed. section 5.2
Run through ONNX Runtime and its execution providers across CPUs, GPUs, and edge devices, with performance depending on the deployment target. section 5.1 section 5.7

Linear regression as two operators

The expression Y = XA + B becomes a graph containing MatMul(X, A) followed by Add(XA, B). Python bindings construct its typed values with make_tensor_value_info, create nodes with make_node, assemble the graph with make_graph, and validate it with check_model. section 5.2

Table 5.1 The most relevant ONNX operators for LLMs

Operator	Description
`Add`	Performs element-wise binary addition. It supports multidirectional broadcasting (like NumPy).
`And`	Returns the tensor resulted from performing the and logical operation elementwise on the input tensors
`ArgMax`	Computes the indices of the max elements of the input tensor’s element along the provided axis
`ArgMin`	Computes the indices of the min elements of the input tensor’s element along the provided axis
`Atan`	Calculates the arctangent (inverse of tangent) of the given input tensor, element-wise
`AveragePool`	Consumes an input tensor and applies average pooling across the tensor according to kernel sizes, stride sizes, and pad lengths. Average pooling consists of computing the average on all values of a subset of the input tensor according to the kernel size and downsampling the data into the output tensor for further processing.
`BatchNormalization`	Applies batch normalization to deep neural networks
`Conv`	Applies convolution to the input tensor
`DFT`	Computes the discrete fourier transform of the input
`Det`	Calculates the determinant of a square matrix (or a batch of square matrices)
`Div`	Performs element-wise binary division of the input
`Equal`	Returns the tensor resulted from performing the equal logical operation element-wise on the input tensors
`Exp`	Calculates the exponential of the given input tensor, element-wise
`Floor`	Takes one input tensor and produces an output tensor where the floor is y = floor(x), applied element-wise
`GreaterOrEqual`	Returns the tensor resulted from performing the `greater_equal` logical operation element-wise on the input tensors
`Identity`	The identity operator
`IsNaN`	Returns which elements of the input are NaN
`LayerNormalization`	Layer normalization defined as a function
`LessOrEqual`	Returns the tensor resulted from performing the less equal logical operation element-wise on the input tensors
`Loop`	The generic loop construct
`MatMul`	The matrix product
`MaxPool`	Consumes an input tensor and applies max pooling across the tensor according to kernel sizes, stride sizes, and pad lengths. The max pooling operation consists of computing the max on all values of a subset of the input tensor according to the kernel size and downsampling the data into the output tensor for further processing.
`Mean`	Element-wise mean of each of the input tensors
`Pad`	Given a tensor containing the data to be padded, a tensor containing the number of start and end pad values for axis, and, optionally, a mode and a constant value, a padded tensor is generated as output.
`QuantizeLinear`	The linear quantization operator. It consumes a high-precision tensor, a scale, and a zero point to compute the low-precision/quantized tensor.
`Reciprocal`	Takes one input tensor and produces one output tensor where the reciprocal, y = 1/x, is applied to the tensor element-wise
`RegexFullMatch`	Performs a full regex match on each element of the input tensor. If an element fully matches the regex pattern specified as an attribute, the corresponding element in the output is true, and it is false otherwise.
`Reshape`	Reshapes the input tensor. First input is the data tensor; second input is a shape tensor which specifies the output shape. It outputs the reshaped tensor.
`Softmax`	Computes the normalized exponential values for the given input: `Softmax(input, axis) = Exp(input) / ReduceSum(Exp(input), axis=axis, keepdims=1)` The axis attribute indicates the dimension along which `Softmax` will be performed. The output tensor has the same shape and contains the `Softmax` values of the corresponding input.
`Transpose`	Transposes the input tensor
`Unique`	Finds the unique elements of a tensor. When an optional attribute axis is provided, unique subtensors sliced along the axis are returned. Otherwise, the input tensor is flattened, and unique values of the flattened tensor are returned.

Browse representative ONNX operators and their tensor-level behavior, including broadcasting, reductions, pooling, and activation operations. section 5.2

How Domain-Specific Small Language Models covers it

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Domain-Specific Small Language Models. The section links point to the parts of the book it draws on.