diff --git a/ggml-cuda.cu b/ggml-cuda.cu
index 83d53c13c1a54a..d83aefc9af33c9 100644
--- a/ggml-cuda.cu
+++ b/ggml-cuda.cu
@@ -306,11 +306,11 @@ typedef struct {
 #define QI4_K (QK_K / (4*QR4_K))
 #ifdef GGML_QKK_64
 typedef struct {
-    half    d[2];              // super-block scales/mins
+    half    dm[2];             // super-block scales/mins
     uint8_t scales[2];         // 4-bit block scales/mins
     uint8_t qs[QK_K/2];        // 4--bit quants
 } block_q4_K;
-static_assert(sizeof(block_q4_K) == 2*sizeof(ggml_fp16_t) + QK_K/2 + 2, "wrong q4_K block size/padding");
+static_assert(sizeof(block_q4_K) == sizeof(half2) + QK_K/2 + 2, "wrong q4_K block size/padding");
 #else
 typedef struct {
     half2 dm;                  // super-block scale for quantized scales/mins
@@ -737,8 +737,8 @@ static __global__ void dequantize_block_q4_K(const void * __restrict__ vx, float
     const int tid = threadIdx.x;
     const uint8_t * q = x[i].qs;
     float * y = yy + i*QK_K;
-    const float d = (float)x[i].d[0];
-    const float m = (float)x[i].d[1];
+    const float d = (float)x[i].dm[0];
+    const float m = (float)x[i].dm[1];
     y[tid+ 0] = d * (x[i].scales[0] & 0xF) * (q[tid] & 0xF) - m * (x[i].scales[0] >> 4);
     y[tid+32] = d * (x[i].scales[1] & 0xF) * (q[tid] >>  4) - m * (x[i].scales[1] >> 4);
 #endif
@@ -1155,8 +1155,8 @@ static __global__ void dequantize_mul_mat_vec_q4_k(const void * __restrict__ vx,
         const uint16_t * a = (const uint16_t *)x[i].scales;
         aux16[0] = a[0] & 0x0f0f;
         aux16[1] = (a[0] >> 4) & 0x0f0f;
-        const float d = (float)x[i].d[0];
-        const float m = (float)x[i].d[1];
+        const float d = (float)x[i].dm[0];
+        const float m = (float)x[i].dm[1];
         float sum = 0.f;
         for (int j = 0; j < K_QUANTS_PER_ITERATION; ++j) {
             sum += y[j+ 0] * (d * s[0] * (q[j+ 0] & 0xF) - m * s[2])
@@ -2845,8 +2845,8 @@ static __device__ __forceinline__ float vec_dot_q4_K_q8_1(
     aux16[0] = a[0] & 0x0f0f;
     aux16[1] = (a[0] >> 4) & 0x0f0f;
 
-    const float dall = bq4_K->d[0];
-    const float dmin = bq4_K->d[1];
+    const float dall = bq4_K->dm[0];
+    const float dmin = bq4_K->dm[1];
 
     const float d8_1 = __low2float(bq8_1[0].ds);
     const float d8_2 = __low2float(bq8_1[1].ds);
@@ -2929,7 +2929,11 @@ template <int mmq_y, int nwarps, bool need_check> static __device__ __forceinlin
 
         const block_q4_K * bxi = bx0 + i*blocks_per_row + kbxd;
 
+#if QK_K == 256
         x_dm[i * (WARP_SIZE/QI4_K) + i / QI4_K + kbxd] = bxi->dm;
+#else
+        x_dm[i * (WARP_SIZE/QI4_K) + i / QI4_K + kbxd] = {bxi->dm[0], bxi->dm[1]};
+#endif
     }
 
 #pragma unroll
@@ -3119,7 +3123,9 @@ template <int mmq_y, int nwarps, bool need_check> static __device__ __forceinlin
 
         const block_q5_K * bxi = bx0 + i*blocks_per_row + kbxd;
 
+#if QK_K == 256
         x_dm[i * (WARP_SIZE/QI5_K) + i / QI5_K + kbxd] = bxi->dm;
+#endif
     }
 
 #pragma unroll
@@ -4709,6 +4715,8 @@ static void ggml_mul_mat_q3_K_q8_1_cuda(
     const void * vx, const void * vy, float * dst, const int ncols_x, const int nrows_x,
     const int ncols_y, const int nrows_y, const int nrows_dst, cudaStream_t stream) {
 
+#if QK_K == 256
+
     int id;
     CUDA_CHECK(cudaGetDevice(&id));
     const int compute_capability = g_compute_capabilities[id];
@@ -4740,6 +4748,7 @@ static void ggml_mul_mat_q3_K_q8_1_cuda(
         mul_mat_q3_K<need_check><<<block_nums, block_dims, 0, stream>>>
             (vx, vy, dst, ncols_x, nrows_x, ncols_y, nrows_y, nrows_dst);
     }
+#endif
 }
 
 static void ggml_mul_mat_q4_K_q8_1_cuda(
diff --git a/llama.cpp b/llama.cpp
index df103a6e54a065..e9868f5d0da77f 100644
--- a/llama.cpp
+++ b/llama.cpp
@@ -4776,7 +4776,10 @@ static void llama_model_quantize_internal(const std::string & fname_inp, const s
 
             if (name == tn(LLM_TENSOR_OUTPUT, "weight")) {
                 int nx = tensor->ne[0];
-                if (nx % QK_K == 0) {
+                if (model.arch == LLM_ARCH_FALCON || nx % QK_K != 0) {
+                    new_type = GGML_TYPE_Q8_0;
+                }
+                else if (new_type != GGML_TYPE_Q8_0) {
                     new_type = GGML_TYPE_Q6_K;
                 }
             } else if (name.find("attn_v.weight") != std::string::npos) {
@@ -4800,17 +4803,39 @@ static void llama_model_quantize_internal(const std::string & fname_inp, const s
             } else if (name.find("ffn_down.weight") != std::string::npos) {
                 if      (ftype == LLAMA_FTYPE_MOSTLY_Q2_K) new_type = GGML_TYPE_Q3_K;
                 else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_M) {
-                    new_type = i_feed_forward_w2 < 2 ? GGML_TYPE_Q5_K : GGML_TYPE_Q4_K;
+                    new_type = i_feed_forward_w2 < 2 ? GGML_TYPE_Q5_K
+                             : model.arch != LLM_ARCH_FALCON || use_more_bits(i_feed_forward_w2, n_feed_forward_w2) ? GGML_TYPE_Q4_K
+                             : GGML_TYPE_Q3_K;
+                }
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) {
+                    new_type = model.arch == LLM_ARCH_FALCON ? GGML_TYPE_Q4_K : GGML_TYPE_Q5_K;
+                }
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q4_K_M) {
+                    if (model.arch == LLM_ARCH_FALCON) {
+                        new_type = i_feed_forward_w2 < 2 ? GGML_TYPE_Q6_K :
+                                   use_more_bits(i_feed_forward_w2, n_feed_forward_w2) ? GGML_TYPE_Q5_K : GGML_TYPE_Q4_K;
+                    } else {
+                        if (use_more_bits(i_feed_forward_w2, n_feed_forward_w2)) new_type = GGML_TYPE_Q6_K;
+                    }
+                }
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q5_K_M && use_more_bits(i_feed_forward_w2, n_feed_forward_w2)) new_type = GGML_TYPE_Q6_K;
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q4_K_S && model.arch != LLM_ARCH_FALCON && i_feed_forward_w2 < 4) {
+                    new_type = GGML_TYPE_Q5_K;
                 }
-                else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) new_type = GGML_TYPE_Q5_K;
-                else if ((ftype == LLAMA_FTYPE_MOSTLY_Q4_K_M || ftype == LLAMA_FTYPE_MOSTLY_Q5_K_M) &&
-                         use_more_bits(i_feed_forward_w2, n_feed_forward_w2)) new_type = GGML_TYPE_Q6_K;
-                else if (ftype == LLAMA_FTYPE_MOSTLY_Q4_K_S && i_feed_forward_w2 < 4) new_type = GGML_TYPE_Q5_K;
                 ++i_feed_forward_w2;
             } else if (name.find("attn_output.weight") != std::string::npos) {
-                if      (ftype == LLAMA_FTYPE_MOSTLY_Q2_K  ) new_type = GGML_TYPE_Q3_K;
-                else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_M) new_type = GGML_TYPE_Q4_K;
-                else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) new_type = GGML_TYPE_Q5_K;
+                if (model.arch != LLM_ARCH_FALCON) {
+                    if      (ftype == LLAMA_FTYPE_MOSTLY_Q2_K  ) new_type = GGML_TYPE_Q3_K;
+                    else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_M) new_type = GGML_TYPE_Q4_K;
+                    else if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) new_type = GGML_TYPE_Q5_K;
+                } else {
+                    if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) new_type = GGML_TYPE_Q4_K;
+                }
+            }
+            else if (name.find("attn_qkv.weight") != std::string::npos) {
+                if (ftype == LLAMA_FTYPE_MOSTLY_Q3_K_M || ftype == LLAMA_FTYPE_MOSTLY_Q3_K_L) new_type = GGML_TYPE_Q4_K;
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q4_K_M) new_type = GGML_TYPE_Q5_K;
+                else if (ftype == LLAMA_FTYPE_MOSTLY_Q5_K_M) new_type = GGML_TYPE_Q6_K;
             }
             else if (name.find("ffn_gate.weight") != std::string::npos || name.find("ffn_up.weight") != std::string::npos) {
                 if (ftype == LLAMA_FTYPE_MOSTLY_Q2_K) new_type = GGML_TYPE_Q3_K;