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+# Graph API: Support int4/int8 compression for K/V in fused SDPA
+
+## Introduction
+
+Int4 and int8 compression for Key and Value are exploited in fused SDPA to
+reduce the memory footprint of generative inference of LLM, especially when KV
+cache mechanism is adopted. In more details, Key and Value tensors will be
+stored in lower integral data types such as int4 and int8 for less memory
+consumption, and will be de-quantized to wider floating point data types such as
+f16 and bf16 for computation. According to the investigation and user request,
+it's also possible that Key tensor will be stored in int4 while Value tensor in
+int8 as it's more sensitive to precision.
+
+Currently, oneDNN Graph API already supports int8 data types and
+per-tensor/channel int8 quantization, but does not support int4 data types. In
+addition, due to the limited range of representation of int4 data types, grouped
+scales and zero points are required for int4 quantization and dequantization,
+which are not supported in oneDNN Graph either. With that, this document will
+concentrate more on supporting int4 data types and its quantization in oneDNN
+Graph in the following parts.
+
+To be more specific, in this RFC we are going to discuss about supporting the
+following features in oneDNN Graph API:
+
+1. Support u4/s4 data types in Graph API.
+2. Support int4 data types quantization and dequantization.
+3. Extend the existing SDPA pattern with compressed K/V inputs.
+
+## Proposals
+
+### Proposal 1: Support u4/s4 data types
+
+The proposal is to follow oneDNN primitive APIs design with adding int4 data
+types enumerations in `dnnl_data_type_t` (defined in dnnl_common_types.h). The
+new enumerations will work for both primitive and graph C APIs.
+
+```cpp
+/// Data type specification
+typedef enum {
+    /// Undefined data type, used for empty memory descriptors.
+    dnnl_data_type_undef = 0,
+    /// 16-bit/half-precision floating point.
+    dnnl_f16 = 1,
+    /// non-standard 16-bit (bfloat16 w/ 7 bit mantissa) floating point.
+    dnnl_bf16 = 2,
+    /// 32-bit/single-precision floating point.
+    dnnl_f32 = 3,
+    /// 32-bit signed integer.
+    dnnl_s32 = 4,
+    /// 8-bit signed integer.
+    dnnl_s8 = 5,
+    /// 8-bit unsigned integer.
+    dnnl_u8 = 6,
+    /// 64-bit/double-precision floating point.
+    dnnl_f64 = 7,
+    /// Boolean data type. Size is C++ implementation defined.
+    dnnl_boolean = 8,
+    /// [OFP8 standard 8-bit floating-point](https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf)
+    /// with a 5-bit exponent and a 2-bit mantissa.
+    dnnl_f8_e5m2 = 9,
+    /// [OFP8 standard 8-bit floating-point](https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf)
+    /// with a 4-bit exponent and a 3-bit mantissa.
+    dnnl_f8_e4m3 = 10,
+    /// 4-bit signed integer.
+    dnnl_s4 = 11,
+    /// 4-bit unsigned integer.
+    dnnl_u4 = 12,
+
+    /// Parameter to allow internal only data_types without undefined behavior.
+    /// This parameter is chosen to be valid for so long as sizeof(int) >= 2.
+    dnnl_data_type_max = 0x7fff,
+} dnnl_data_type_t;
+```
+
+In Graph C++ API, the enum class `logical_tensor::data_type` (defined in
+dnnl_graph.hpp) will be extended to support the int4 data types.
+
+```c++
+class logical_tensor {
+    // ...
+    /// Data Types
+    enum class data_type {
+        undef = dnnl_data_type_undef,
+        /// 16-bit/half-precision floating point.
+        f16 = dnnl_f16,
+        /// non-standard 16-bit (bfloat16 w/ 7 bit mantissa) floating point.
+        bf16 = dnnl_bf16,
+        /// 32-bit/single-precision floating point.
+        f32 = dnnl_f32,
+        /// 32-bit signed integer.
+        s32 = dnnl_s32,
+        /// 8-bit signed integer.
+        s8 = dnnl_s8,
+        /// 8-bit unsigned integer.
+        u8 = dnnl_u8,
+        /// Boolean data type. Size is C++ implementation defined.
+        boolean = dnnl_boolean,
+        /// 8-bit floating point data type with E5M2. Added by this RFC.
+        f8_e5m2 = dnnl_f8_e5m2,
+        /// 8-bit floating point data type with E4M3. Added by this RFC.
+        f8_e4m3 = dnnl_f8_e4m3,
+        /// 4-bit signed integer.
+        s4 = dnnl_s4,
+        /// 4-bit unsigned integer.
+        u4 = dnnl_u4,
+    };
+    // ...
+};
+```
+
+The new data types can be used to create logical tensors and tensors in oneDNN
+Graph API.
+
+```c++
+using namespace dnnl::graph;
+
+// create a s4 logical tensor with unknown ndim and dims.
+auto lt1 = logical_tensor(id, logical_tensor::data_type::s4);
+
+// create a u4 logical tensor with dims = (16, 8).
+const logical_tensor::dims shape = {16, 8}
+auto lt2 = logical_tensor(id, logical_tensor::data_type::u4, shape);
+```
+
+### Proposal 2: Extend Quantize and Dequantize Operations
+
+The recommended proposal is that oneDNN Graph API will support int4 data type
+through graph fusion following the way that int8 is supported, instead of
+directly adding int4 data types in computation operations.
+
+Based on the request, int4 quantization happens in runtime (scales and zps are
+stored as tensors on device). Graph API will support int4 quantization through
+operations `DynamicDequantize` and `DynamicQuantize`. In the future, it's
+possible that we will also extend the static version of `Quantize` and
+`Dequantize` to support int4 quantization. But for now, we wil focus on
+`DynamicQuantize` and `DynamicDequantize` due to the request urgency and the
+feature use scenario.
+
+According to the request from frameworks, for int4 quantization, grouped scales
+are required for each hidden dimension to maintain the model accuracy. The
+requirement for grouped zero points is not promised. See [int4
+Quantize](https://docs.nvidia.com/deeplearning/tensorrt/operators/docs/Quantize.html?highlight=int4)
+and
+[Dequantize](https://docs.nvidia.com/deeplearning/tensorrt/operators/docs/Dequantize.html)
+in TensorRT and
+[QuantizeLinear](https://onnx.ai/onnx/operators/onnx__QuantizeLinear.html) in
+ONNX.
+
+Currently, `DynamicDequantize` and `DynamicQuantize` in Graph API accept a
+required f32 1D tensor as the scale factor, and an optional 1D tensor as the
+zero points( can be either s8/u8/f32 ). What's more, two optional attributes are
+provided: `qtype` is used to specify which quantization type is used,
+`per_tensor` or `per_channel`. And `axis` specifies on which dimension
+`per_channel` quantization will be applied. To support int4 data types,
+`DynamicQuantize` and `DynamicDequantize` operations in oneDNN Graph opset will
+be extended:
+
+1. `DynamicQuantize` will be extended to support u4/s4 output, and scales and
+   zero points with groups. The library may raise an error if groups are not
+   provided for a `DynamicQuantize` op with u4/s4 output.
+2. `DynamicDequantize` will be extended to support u4/s4 input, and scales and
+   zero points with groups. The library may raise an error if groups are not
+   provided for a `DynamicDequantize` op with u4/s4 input.
+
+Besides the input or output data types, new attributes will be added for
+DynamicQuantize and DynamicDequantize:
+
+1. Add `per_group` to the supported values of `qtype` attribute, and the default
+   value will be unchanged.
+2. The existing attribute `axis` will ignored if `per_group` quantization is
+   specified.
+3. Add a new attribute `group_shape` to support `per_group` quantization
+   type. The value of `group_shape` attribute is a vector of `s64` data. On the
+   dimension where the group quantization is applied, the dimension indicates
+   the number of elements that share the same scaling factor and zero points in
+   each quantization group( which is `group_size` ).  And the other dimensions
+   should be all `1`. The attribute is required when `per_group` quantization
+   type is specified for `qtype`. If `per_group` quantization is not specified
+   and `group_shape` attribute is given, it will be ignored. 
+4. The `scale` and `zp` input will be extended to a `n`-dimensional tensor
+   (`n` = dims(input)) for `per_group` quantization. The shape requirements for
+   `scale` and `zp` are as follows:
+   1. For `per_tensor` and `per_channel` quantization, the `scale` and `zp`
+      inputs should be `1d` tensors.
+   2. For `per_group` quantization:
+      - On the dimension where the group quantization is applied, the dimension
+      should equal to `src_dim / group_size`.
+      - On other dimensions, the dimension should match the input.
+
+For example, if the shape of Key tensor is `4x8x4`, and the group shape is
+`1x4x1`, which means each scaling factor will be adopted for 4 times. One
+possible scale would be:
+
+![alt text](img/grouped_scale.png)
+
+The usage of the new attribute will be like:
+
+```cpp
+using namespace dnnl::graph;
+
+const dim K = 10, N = 20;
+const size_t nG = 2, G = N / nG;
+
+dims src_dims = {K, N};
+dims scale_dims = {K, N/G};
+dims group_shape = {1, G}
+
+// In real case, users do not have to provide the concrete shapes of logical
+// tensors until compilation stage. 
+logical_tensor src_desc {0, data_type::u4, src_dims, layout_type::strided};
+logical_tensor scale_desc {
+        1, data_type::f32, scale_dims, layout_type::strided};
+logical_tensor dst_desc {2, data_type::f32, src_dims, layout_type::strided};
+
+op deq = op(0, op::kind::DynamicDequantize, {src_desc, scale_desc},
+        {dst_desc}, "deq");
+// Specify the quantization type as per_group quantization.
+deq.set_attr<std::string>(op::attr::qtype, "per_group");
+// Axis indicates on which dimension the quantization will be applied.
+deq.set_attr<int64_t>(op::attr::axis, 1);
+// Group size indicates the the size of each group.
+deq.set_attr<int64_t>(op::attr::group_shape, group_shape);
+
+// Create graph and add the op to the graph
+graph g(dnnl::engine::kind::gpu);
+g.add_op(deq);
+
+// ...
+```
+
+##### Limitation
+
+With the introduction of the new attribute `group_shape`, Graph API now
+enables users to define group quantization across multiple dimensions. This
+design aims to accommodate potential quantization types, such as per-token
+quantization, where the group size is defined as H*D. However, these
+quantization types are not yet supported by the current implementation. As for
+grouped quantization, the backend currently facilitates quantization on one of
+the last two dimensions, while all other inputs will be deemed invalid.
+
+#### Alternative options
+
+Similar to the discussion of int8 and fp8 data types, an alternative solution
+may be supporting int4 data types directly in computation operations like MatMul
+and Convolution. But it will bloat and complicate the opset and op schema of
+oneDNN Graph. Hence it's not considered here.
+
+In addition, currrently oneDNN Graph does not support the direct int8
+quantization and dequantization between int8 and f16/bf16 data types. To align
+with current integration flow and maintain the consistency of library design,
+quantization and dequantization between int4 and f16/bf16 data types will also
+be implemented with a combination of quantization ops and `TypeCast`. An
+alternative solution may be to extend quantization ops to support data type
+conversion directly between int4 and f16/bf16 data types. But it will
+unnecessarily complicates the fusion patterns in oneDNN Graph. For example,
+an int4 quantization will be expressed in two different ways: 
+
+1. With a single `Quantize(f16 -> int4)`
+2. With two operations `TypeCast(f16 -> f32) -> Quantize(f32 -> int4)`
+
+It will require extensions for all patterns related to mixed data type
+quantization. Hence the option is not considered here.
+
+### Proposal 3: Extend SDPA pattern with compressed K/V
+
+#### Pattern definition
+
+With the reference to int4 GQA pattern in
+[PyTorch](https://pytorch.org/blog/int4-decoding/), the proposed fusion pattern
+for SDPA with compressed K/V in oneDNN Graph API is defined as:
+
+![alt text](img/sdpa_pattern.png)
+
+As illustrated in the figure above, K cache and V cache are stored on user side
+in int4 or int8 data types. `DynamicDequantize` is used to convert int4 data to
+f32, then an optional `TypeCast` is used to convert f32 data types to f16 or
+bf16 data types when needed. Two `MatMul`s are used to compute the matrix
+multiplication of Q and K, as well as  score and V. oneDNN Graph will fuse the
+pattern into a single partition with optimized CPU and GPU implementations.
+
+To get rid of the ambiguity of the computation type of the MatMul ops in the
+pattern and give users the control of leveraging higher precision data types to
+keep the model accuracy, we propose to follow the design of floating point math
+mode in primitive API. Once the math mode is specified, the backend will
+automatically perform either implicit down-conversion to lower-precision
+integral type values or up-conversion from int4/int8 to floating points, such as
+f16, based on user input. For compressed SDPA, since the Key tensor will be in
+integral types like int4 and `MatMul`s are expected to compute in f16/bf16,
+users must explicitly set the math mode. Put it in another way, the API allows
+users to control the computation type of the SDPA fusion. What's more, following
+the design of floating point math mode also helps to maintain a consistent API
+semantics between graph API and primitive API. 
+
+Currently, oneDNN Graph API supports setting floating-point math mode during the
+construction of graph object, which will affect the whole graph. 
+
+As primitive API has supported a second argument for enforcing an integral
+primitive to comply with the floating-point math mode, oneDNN Graph API need to
+accommodate to the change. The new API will be like:
+
+```cpp
+/// @param mode Floating-point math mode.
+/// @param apply_to_int Use of floating-point arithmetic for integer primitives.
+void set_fpmath_mode(fpmath_mode mode,  bool apply_to_int = false);
+```
+
+Users can use the new API like:
+
+```cpp
+using namespace dnnl::graph;
+
+graph g(kind);
+g.set_fpmath_mode( math_mode, /*apply_to_int=*/true);
+
+op foo(id, kind, "foo"); g.add_op(foo);
+op bar(id, kind, "bar"); g.add_op(bar);
+g.finalize();
+partitions p = g.get_partitions();
+
+// All the partitions from the same graph should share the same math mode
+compiled_partition cp0 = p[0].compile(inputs, outputs, engine);
+compiled_partition cp1 = p[1].compile(inputs, outputs, engine);
+cp0.execute(…);
+cp1.execute(…);
+```
+
+User can still set graph-level fpmath mode through graph constructor, and only
+one method will be allowed for setting the graph-level fpmath mode. Otherwise,
+the library will report an error.
+
+#### Alternative option
+
+Considering the fact that the framework users can create different graphs if
+they require different floating point math mode, the current API capability is
+enough for covering the user request. An alternative solution is to specify the
+floating point math mode on partition. But it may require new APIs and may cause
+confusion when the modes on graph and partition are incompatible. Hence it's not
+considered here.
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