diff --git a/.clang-tidy b/.clang-tidy
index 7c7f85ee9c..12e89fb63d 100644
--- a/.clang-tidy
+++ b/.clang-tidy
@@ -10,6 +10,7 @@ Checks: '
 clang-analyzer*,
 clang-diagnostic-missing-prototypes,
 cppcoreguidelines-init-variables,
+cppcoreguidelines-special-member-functions,
 bugprone*,
 -bugprone-crtp-constructor-accessibility,
 -bugprone-easily-swappable-parameters,
@@ -72,4 +73,8 @@ CheckOptions:
  - key: facebook-cuda-safe-kernel-call-check.HandlerName
    # This is PyTorch's handler; you may need to define your own
    value: C10_CUDA_KERNEL_LAUNCH_CHECK
+ - key: cppcoreguidelines-special-member-functions.AllowSoleDefaultDtor
+   value: true
+ - key: cppcoreguidelines-special-member-functions.AllowImplicitlyDeletedCopyOrMove
+   value: true
 ...
diff --git a/include/fbgemm/Fbgemm.h b/include/fbgemm/Fbgemm.h
index dd373fab7c..cea268a62d 100644
--- a/include/fbgemm/Fbgemm.h
+++ b/include/fbgemm/Fbgemm.h
@@ -79,9 +79,9 @@ class PackMatrix {
  public:
   PackMatrix() = delete; // no default constructor
   PackMatrix(const PackMatrix&) = delete; // no copy
-  PackMatrix& operator==(const PackMatrix&) = delete; // no copy
+  PackMatrix& operator=(const PackMatrix&) = delete; // no copy
   PackMatrix(PackMatrix&&) = delete; // no move
-  PackMatrix& operator==(PackMatrix&& rhs) noexcept = delete; // no move
+  PackMatrix& operator=(PackMatrix&& rhs) noexcept = delete; // no move
 
   /**
    * @param rows total number of rows in the matrix
@@ -515,11 +515,11 @@ class FBGEMM_API PackWeightMatrixForGConv {
 
   PackWeightMatrixForGConv() = delete; // no default constructor
   PackWeightMatrixForGConv(const PackWeightMatrixForGConv&) = delete; // no copy
-  PackWeightMatrixForGConv& operator==(const PackWeightMatrixForGConv&) =
+  PackWeightMatrixForGConv& operator=(const PackWeightMatrixForGConv&) =
       delete; // no copy
 
   PackWeightMatrixForGConv(PackWeightMatrixForGConv&&) = delete; // no move
-  PackWeightMatrixForGConv& operator==(PackWeightMatrixForGConv&&) =
+  PackWeightMatrixForGConv& operator=(PackWeightMatrixForGConv&&) =
       delete; // no move
 
   /**
@@ -715,6 +715,11 @@ class FBGEMM_API PackAWithIm2Col
       bool b_symmetric = false,
       const BlockingFactors* params = nullptr);
 
+  PackAWithIm2Col(const PackAWithIm2Col&) = delete;
+  PackAWithIm2Col(PackAWithIm2Col&&) = delete;
+  PackAWithIm2Col& operator=(const PackAWithIm2Col&) = delete;
+  PackAWithIm2Col& operator=(PackAWithIm2Col&&) = delete;
+
   /**
    * Activation matrices are not constant so cannot amortize the cost of
    * pre-packing.
@@ -799,6 +804,11 @@ class FBGEMM_API PackAWithRowOffset final
       std::int32_t* row_offset = nullptr,
       const BlockingFactors* params = nullptr);
 
+  PackAWithRowOffset(const PackAWithRowOffset&) = delete;
+  PackAWithRowOffset(PackAWithRowOffset&&) = delete;
+  PackAWithRowOffset& operator=(const PackAWithRowOffset&) = delete;
+  PackAWithRowOffset& operator=(PackAWithRowOffset&&) = delete;
+
   /**
    * Activation matrices are not constant so cannot amortize the cost of
    * pre-packing.
@@ -890,6 +900,10 @@ class FBGEMM_API PackAWithQuantRowOffset final
       int groups = 1,
       std::int32_t* row_offset = nullptr,
       const BlockingFactors* params = nullptr);
+  PackAWithQuantRowOffset(const PackAWithQuantRowOffset&) = delete;
+  PackAWithQuantRowOffset(PackAWithQuantRowOffset&&) = delete;
+  PackAWithQuantRowOffset& operator=(const PackAWithQuantRowOffset&) = delete;
+  PackAWithQuantRowOffset& operator=(PackAWithQuantRowOffset&&) = delete;
 
   /**
    * Activation matrices are not constant so cannot amortize the cost of
diff --git a/include/fbgemm/FbgemmI8DepthwiseAvx2.h b/include/fbgemm/FbgemmI8DepthwiseAvx2.h
index 7f5e60fe70..ed55480ae7 100644
--- a/include/fbgemm/FbgemmI8DepthwiseAvx2.h
+++ b/include/fbgemm/FbgemmI8DepthwiseAvx2.h
@@ -8,7 +8,6 @@
 
 #pragma once
 
-#include <array>
 #include <cstdint>
 #include "fbgemm/ConvUtils.h"
 #include "fbgemm/FbgemmBuild.h"
@@ -27,6 +26,10 @@ class FBGEMM_API PackedDepthWiseConvMatrix {
    * @param smat the source unpacked weight in GRS layout
    */
   PackedDepthWiseConvMatrix(int OC, int kernel_prod, const std::int8_t* smat);
+  PackedDepthWiseConvMatrix(const PackedDepthWiseConvMatrix&) = delete;
+  PackedDepthWiseConvMatrix(PackedDepthWiseConvMatrix&&) = delete;
+  PackedDepthWiseConvMatrix& operator=(const PackedDepthWiseConvMatrix&) = delete;
+  PackedDepthWiseConvMatrix& operator=(PackedDepthWiseConvMatrix&&) = delete;
   virtual ~PackedDepthWiseConvMatrix();
 
   const std::int8_t* PackedMat() const {
diff --git a/include/fbgemm/FbgemmI8DirectconvAvx2.h b/include/fbgemm/FbgemmI8DirectconvAvx2.h
index 09fc9fcf17..2c2e8eb0bc 100644
--- a/include/fbgemm/FbgemmI8DirectconvAvx2.h
+++ b/include/fbgemm/FbgemmI8DirectconvAvx2.h
@@ -31,6 +31,11 @@ class FBGEMM_API PackedDirectConvMatrix {
       int OC_per_G,
       int filter_prod,
       const std::int8_t* smat);
+  PackedDirectConvMatrix(const PackedDirectConvMatrix&) = delete;
+  PackedDirectConvMatrix(PackedDirectConvMatrix&&) = delete;
+  PackedDirectConvMatrix& operator=(const PackedDirectConvMatrix&) = delete;
+  PackedDirectConvMatrix& operator=(PackedDirectConvMatrix&&) = delete;
+
   virtual ~PackedDirectConvMatrix();
 
   const std::int8_t* PackedMat() const {
diff --git a/include/fbgemm/FbgemmPackMatrixB.h b/include/fbgemm/FbgemmPackMatrixB.h
index c67a829ca3..a88b705ace 100644
--- a/include/fbgemm/FbgemmPackMatrixB.h
+++ b/include/fbgemm/FbgemmPackMatrixB.h
@@ -126,6 +126,10 @@ class PackedGemmMatrixB {
     packed_ = true;
     pmat_passed_in = true;
   }
+  PackedGemmMatrixB(const PackedGemmMatrixB&) = delete;
+  PackedGemmMatrixB(PackedGemmMatrixB&&) = delete;
+  PackedGemmMatrixB& operator=(const PackedGemmMatrixB&) = delete;
+  PackedGemmMatrixB& operator=(PackedGemmMatrixB&&) = delete;
 
   void initializeParam() {
     if (!cpuinfo_initialize()) {