diff --git a/.github/workflows/ci_gpu.yml b/.github/workflows/ci_gpu.yml
index ac2b7e9..d52285c 100644
--- a/.github/workflows/ci_gpu.yml
+++ b/.github/workflows/ci_gpu.yml
@@ -113,6 +113,7 @@ jobs:
         run: ./test_gpt2cu
 
   build-and-test-llama3:
+    name: Build and test LLama3.2 1B
     runs-on: ubicloud-gpu-standard-1-latest
     env:
       HF_TOKEN: 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
@@ -150,17 +151,51 @@ jobs:
       - name: Build BF16 precision
         run: PRECISION=BF16 make train_llama3cu test_llama3cu
 
+      - name: Run default (BF16)
+        run: ./test_llama3cu
+
+      - name: Run no recompute GeLU (BF16)
+        run: ./test_llama3cu -r 0
+
+      - name: Run no master weights (BF16)
+        run: ./test_llama3cu -w 0
+
+      - name: Run recompute LN (BF16)
+        run: ./test_llama3cu -r 2
+
+  build-and-test-llama3-untied:
+    name: Build and test LLama3.2 1B with untie weights
+    runs-on: ubicloud-gpu-standard-1-latest
+    env:
+      HF_TOKEN: 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
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+      - run: echo "::add-mask::$HF_TOKEN"
+
+      - name: Install OpenMP
+        run: sudo apt-get update && sudo apt-get install -y libomp-dev
+
+      - name: Install dependencies
+        run: pip install -r requirements.txt
+
+      - name: Run preprocessing
+        run: python dev/data/tinyshakespeare.py --model_desc llama-3
+
+      - name: Train model
+        run: python train_llama3.py --write_tensors 1 --dtype float32 --untie 1 --depth 10
+
+      - name: Build FP32 precision
+        run: PRECISION=FP32 make test_llama3cu
+
       - name: Run default
         run: ./test_llama3cu
 
-      - name: Run no recompute GeLU
-        run: ./test_llama3cu -r 0
+      - name: Build BF16 precision
+        run: PRECISION=BF16 make train_llama3cu test_llama3cu
 
-      - name: Run no master weights
-        run: ./test_llama3cu -w 0
-
-      - name: Run recompute LN
-        run: ./test_llama3cu -r 2
+      - name: Run default
+        run: ./test_llama3cu
 
   unit-tests-gpu:
     runs-on: ubicloud-gpu-standard-1-latest
diff --git a/test_llama3.cu b/test_llama3.cu
index 03fe1ab..db82bc4 100644
--- a/test_llama3.cu
+++ b/test_llama3.cu
@@ -85,6 +85,9 @@ float* float_cpu_malloc_and_point_parameters(FloatParameterTensors* params, size
         *(ptrs[i]) = params_memory_iterator;
         params_memory_iterator += param_sizes[i];
     }
+    if(param_sizes[1] == 0) {
+        params->wlmhead = nullptr;
+    }
     return params_memory;
 }
 
diff --git a/train_llama3.cu b/train_llama3.cu
index 4177e30..7ea5a6e 100644
--- a/train_llama3.cu
+++ b/train_llama3.cu
@@ -106,6 +106,7 @@ typedef struct {
     float norm_eps; // epsilon used in layernorm, e.g. 1e-5
     float rope_theta; // theta used in ROPE attention, e.g. 500000.0 (<-- new in Llama 3)
     bool use_biases;  // we always allocate memory for biases; to match llama3 they are not used
+    bool tied_weights; // untied for large models (3.1 8B/70B/405B), tied for small (3.2 1B/3B)
 } LLama3Config;
 
 // the parameters of the model
@@ -153,7 +154,12 @@ void fill_in_parameter_sizes(size_t* param_sizes, size_t* param_sizeof, LLama3Co
     size_t ffn_channels = hidden_dim * 2; // c_fc + c_fc2 concatenated
     // now populate the parameter sizes
     param_sizes[0] = Vp * C; // wte
-    param_sizes[1] = Vp * C; // (3) lm_head (final classifier layer weights)
+    if(config.tied_weights) {
+        param_sizes[1] = 0; // no lm_head with tied weights
+    } else {
+        param_sizes[1] = Vp * C; // (3) lm_head (final classifier layer weights)
+    }
+
     param_sizes[2] = L * C; // ln1w
     param_sizes[3] = L * C; // ln1b; (1) all biases are zero it's ok
     param_sizes[4] = L * (qkv_channels) * C; // qkvw
@@ -195,6 +201,10 @@ void* malloc_and_point_parameters(ParameterTensors* params, size_t* param_elemen
         *(ptrs[i]) = (floatX*)params_memory_iterator;
         params_memory_iterator += param_elements[i] * param_sizeof[i];
     }
+    // tied weights?
+    if(param_elements[1] == 0) {
+        params->wlmhead = nullptr;
+    }
     return params_memory;
 }
 
@@ -506,8 +516,9 @@ void llama3_write_to_checkpoint(LLama3 *model, const char* checkpoint_path) {
     model_header[7] = model->config.channels;
     model_header[8] = model->config.multiple_of;
     model_header[9] = model->config.use_scaled_rope;
-    model_header[10] = 3;
-    model_header[11] = 1;
+    model_header[10] = model->config.tied_weights;
+    model_header[11] = 3;
+    model_header[12] = model->config.tied_weights ? 2 : 1;
     fwriteCheck(model_header, sizeof(int), 256, model_file);
     float float_header[256];
     float_header[0] = model->config.ffn_dim_multiplier;
@@ -580,8 +591,9 @@ void llama3_build_from_checkpoint(LLama3 *model, const char* checkpoint_path, bo
     model->config.multiple_of = header_int[8];
     model->config.use_scaled_rope = header_int[9];
     model->config.use_biases = false;
-    int major_version = header_int[10]; // currently unused, e.g. 3
-    int minor_version = header_int[11]; // currently unused, e.g. 1 (so Llama 3.1)
+    model->config.tied_weights = header_int[10];
+    int major_version = header_int[11]; // currently unused, e.g. 3
+    int minor_version = header_int[12]; // 1 or 2
     // now the float section
     model->config.ffn_dim_multiplier = header_float[0];
     model->config.norm_eps = header_float[1];
@@ -740,7 +752,9 @@ void llama3_forward(LLama3 *model, const int* inputs, size_t B, size_t T) {
         }
     }
 
-    matmul_forward_cublaslt(acts.output, acts.lnf, params.wlmhead, NULL, B, T, C, Vp, main_stream);
+    floatX* lm_head = model->config.tied_weights ? params.wte : params.wlmhead;
+    matmul_forward_cublaslt(acts.output, acts.lnf, lm_head, NULL, B, T, C, Vp, main_stream);
+
     cudaCheck(cudaDeviceSynchronize());
 }
 
@@ -836,7 +850,10 @@ void llama3_backward_and_reduce(LLama3 *model, int* inputs, const int* targets,
     // technically that is a small, inline backward() pass of calculating
     // total, final loss as the mean over all losses over all (B,T) positions in the batch
     // next: backward the classifier matmul
-    matmul_backward(model->acts.scratch_bt4c, grads.wlmhead, NULL, acts.output, acts.lnf, params.wlmhead, NULL, B, T, C, Vp, main_stream);
+    floatX* w_lm_head = model->config.tied_weights ? params.wte : params.wlmhead;
+    floatX* g_lm_head = model->config.tied_weights ? grads.wte : grads.wlmhead;
+
+    matmul_backward(model->acts.scratch_bt4c, g_lm_head, NULL, acts.output, acts.lnf, w_lm_head, NULL, B, T, C, Vp, main_stream);
     // backward the final layernorm
     floatX* residual = acts.residual3 + (L-1) * B * T * C; // last residual is in residual3
     rmsnorm_backward(dresidual, grads.lnfw, scratchF, model->acts.scratch_bt4c, residual, params.lnfw, acts.lnf_rstd, B, T, C, main_stream);
@@ -1076,6 +1093,8 @@ void llama3_update(LLama3 *model, float learning_rate, float beta1, float beta2,
         }
 
         ShardInfo tensor = llama3_get_tensor_at_layer(model, 0, i);
+        if(tensor.size == 0)
+            continue;
         ShardInfo shard = multi_gpu_get_shard_offset(tensor.size, multi_gpu_config, 1);
         ptrdiff_t local_offset_full = tensor.offset + shard.offset;
         ptrdiff_t local_offset_partial = tensor.offset / multi_gpu_config->num_processes;
@@ -1144,6 +1163,10 @@ float llama3_estimate_mfu(LLama3 *model, int num_tokens, float dt) {
     second is the attention matmul, which is also usually a small contribution.
     */
     size_t N = model->num_parameters;
+    if(!model->config.tied_weights) {
+        N -= model->param_elements[0];      // remove embedding parameters, which can be significant at 128k vocab
+    }
+
     int L = model->config.num_layers;
     int C = model->config.channels;
     int T = model->seq_len;
diff --git a/train_llama3.py b/train_llama3.py
index 30c6834..2fc64a6 100644
--- a/train_llama3.py
+++ b/train_llama3.py
@@ -312,6 +312,8 @@ class LLaMA(nn.Module):
             ln_f = RMSNorm(config.n_embd, config.norm_eps),
         ))
         self.lm_head = nn.Linear(config.n_embd, config.vocab_size, bias=False)
+        if config.tied_embeddings:
+            self.transformer.wte.weight = self.lm_head.weight
 
         # init all weights, use a torch rng object to be very careful
         self.init_rng = torch.Generator()
@@ -433,10 +435,16 @@ class LLaMA(nn.Module):
         return checkpoint
 
     @classmethod
-    def from_pretrained_llama3_hf(cls, model_id):
+    def from_pretrained_llama3_hf(cls, model_id, untie):
         """Loads pretrained LLaMA model weights from HuggingFace"""
         from transformers import AutoModelForCausalLM, AutoTokenizer
         model_args = MODEL_DICT[model_id]
+        if untie:
+            if not model_args.tied_embeddings:
+                print("Model embeddings are not tied, --untie has no effect.")
+            else:
+                print("Untying token embeddings and LM head.")
+                model_args.tied_embeddings = False
 
         model = AutoModelForCausalLM.from_pretrained(model_id)
         checkpoint = LLaMA.adapt_llama_state_dict_keys_hf(model.state_dict(), model_args)
@@ -876,7 +884,7 @@ def write_bf16(tensor, file):
     b = t.numpy().tobytes()
     file.write(b)
 
-def write_tensors(model_tensors, L, file, dtype):
+def write_tensors(model_tensors, L, tied, file, dtype):
     # writes LLaMA 3 model's weights to a binary file
     # things get a bit more complicated though:
     # 1) We want to maintain the ability to finetune just the biases in the C code
@@ -894,7 +902,8 @@ def write_tensors(model_tensors, L, file, dtype):
     assert dtype in {"float32", "bfloat16"}
     write_fun = write_fp32 if dtype == "float32" else write_bf16
     write_fun(model_tensors["transformer.wte.weight"], file) # (V, C)
-    write_fun(model_tensors["lm_head.weight"], file) # (V, C) # <--- hack (3) here!
+    if not tied:
+        write_fun(model_tensors["lm_head.weight"], file) # (V, C) # <--- hack (3) here!
     for i in range(L): # (L, C)
         write_fun(model_tensors[f"transformer.h.{i}.ln_1.weight"], file)
     for i in range(L): # (L, C)
@@ -954,8 +963,9 @@ def write_model(model, filename, dtype):
     header_int[7] = model.config.n_embd
     header_int[8] = model.config.multiple_of
     header_int[9] = int(model.config.use_scaled_rope)
-    header_int[10] = int(model.config.version.split('.')[0]) # major version
-    header_int[11] = int(model.config.version.split('.')[1]) # minor version
+    header_int[10] = int(model.config.tied_embeddings)
+    header_int[11] = int(model.config.version.split('.')[0]) # major version
+    header_int[12] = int(model.config.version.split('.')[1]) # minor version
     # float section of the header
     header_float = torch.zeros(256, dtype=torch.float32)
     header_float[0] = model.config.ffn_dim_multiplier
@@ -967,7 +977,7 @@ def write_model(model, filename, dtype):
     with open(filename, "wb") as file:
         file.write(header_int.numpy().tobytes()) # int header
         file.write(header_float.numpy().tobytes()) # float header
-        write_tensors(params, model.config.n_layer, file, dtype) # params
+        write_tensors(params, model.config.n_layer, model.config.tied_embeddings, file, dtype) # params
     print(f"wrote {filename}")
 
 def write_state(model, x, y, logits, loss, filename):
@@ -993,7 +1003,7 @@ def write_state(model, x, y, logits, loss, filename):
         # loss (single float, result of the cross entropy loss)
         write_fp32(loss.cpu(), file)
         # gradients
-        write_tensors(grads, model.config.n_layer, file, "float32")
+        write_tensors(grads, model.config.n_layer, model.config.tied_embeddings, file, "float32")
     print(f"wrote {filename}")
 
 
@@ -1036,6 +1046,7 @@ if __name__ == "__main__":
     parser.add_argument("--output_dir", type=str, default="", help="output directory to which to write logs and checkpoints")
     parser.add_argument("--model", type=str, default="meta-llama/Llama-3.2-1B", help="chose the llama model")
     parser.add_argument("--depth", type=int, default=-1, help="load only a subset of the model's layers")
+    parser.add_argument("--untie", type=int, default=False, help="Untie token embeddings and LM-head, even if they are tied in the checkpoint.")
     # token layout for each step of the optimization
     parser.add_argument("--batch_size", type=int, default=4, help="batch size, in units of #batch dimensions")
     parser.add_argument("--sequence_length", type=int, default=64, help="sequence length")
@@ -1140,7 +1151,7 @@ if __name__ == "__main__":
 
     # init the model
     if args.use_hf:
-        model = LLaMA.from_pretrained_llama3_hf(args.model)
+        model = LLaMA.from_pretrained_llama3_hf(args.model, args.untie)
     else:  # use Meta's checkpoint
         assert args.ckpt_dir is not None and os.path.exists(args.ckpt_dir), f"llama3 ckpt dir {args.ckpt_dir} does not exist"
         assert args.tokenizer_path is not None and os.path.exists(args.tokenizer_path), f"llama3 tokenizer path {args.tokenizer_path} does not exist"