diff --git a/FlagEmbedding/finetune/embedder/encoder_only/m3/modeling.py b/FlagEmbedding/finetune/embedder/encoder_only/m3/modeling.py
index c3111ea5e..4ebc18179 100644
--- a/FlagEmbedding/finetune/embedder/encoder_only/m3/modeling.py
+++ b/FlagEmbedding/finetune/embedder/encoder_only/m3/modeling.py
@@ -129,13 +129,20 @@ def _sparse_embedding(self, hidden_state, input_ids, return_embedding: bool = Tr
         if not return_embedding: return token_weights
 
         if self.training:
-            sparse_embedding = torch.zeros(
-                input_ids.size(0), input_ids.size(1), self.vocab_size,
-                dtype=token_weights.dtype,
-                device=token_weights.device
-            )
-            sparse_embedding = torch.scatter(sparse_embedding, dim=-1, index=input_ids.unsqueeze(-1), src=token_weights)
-            sparse_embedding = torch.max(sparse_embedding, dim=1).values
+            weights = token_weights.squeeze(-1)
+            # Find each token's first maximum without a batch x length x vocab tensor.
+            # Gathering the original weights preserves max(dim=1)'s tie gradients.
+            with torch.no_grad():
+                maxima = weights.new_zeros(input_ids.size(0), self.vocab_size)
+                maxima.scatter_reduce_(dim=-1, index=input_ids, src=weights, reduce="amax")
+                token_maxima = maxima.gather(-1, input_ids)
+                is_maximum = (weights == token_maxima) | (weights.isnan() & token_maxima.isnan())
+                positions = torch.arange(input_ids.size(1), device=input_ids.device).expand_as(input_ids)
+                positions = positions.masked_fill(~is_maximum, input_ids.size(1))
+                first_maxima = input_ids.new_full((input_ids.size(0), self.vocab_size), input_ids.size(1))
+                first_maxima.scatter_reduce_(dim=-1, index=input_ids, src=positions, reduce="amin")
+            sparse_embedding = weights.gather(-1, first_maxima.clamp_max(input_ids.size(1) - 1))
+            sparse_embedding = sparse_embedding.masked_fill(first_maxima == input_ids.size(1), 0.)
         else:
             # Optimize suggestion from issue #1364: https://github.com/FlagOpen/FlagEmbedding/issues/1364
             # Disable when self.training = True, otherwise will cause:
diff --git a/tests/test_m3_sparse_training_memory.py b/tests/test_m3_sparse_training_memory.py
new file mode 100644
index 000000000..0a1501325
--- /dev/null
+++ b/tests/test_m3_sparse_training_memory.py
@@ -0,0 +1,130 @@
+"""Native M3 sparse pooling: definition, gradients, and allocation budget."""
+
+import pytest
+import torch
+from tokenizers import Tokenizer
+from tokenizers.models import WordLevel
+from transformers import BertConfig, BertModel, BertTokenizerFast
+
+from FlagEmbedding.finetune.embedder.encoder_only.m3.modeling import EncoderOnlyEmbedderM3Model
+
+
+def tiny_model(dtype=torch.float32, vocab_size=128):
+    torch.manual_seed(7)
+    vocab = {"[PAD]": 0, "[UNK]": 1, "[CLS]": 2, "[SEP]": 3}
+    vocab.update({f"word{i}": i for i in range(4, vocab_size)})
+    tokenizer = BertTokenizerFast(
+        tokenizer_object=Tokenizer(WordLevel(vocab, unk_token="[UNK]")),
+        pad_token="[PAD]", unk_token="[UNK]", cls_token="[CLS]",
+        sep_token="[SEP]", eos_token="[SEP]",
+    )
+    config = BertConfig(
+        vocab_size=vocab_size, hidden_size=8, intermediate_size=16,
+        num_hidden_layers=1, num_attention_heads=2,
+        hidden_dropout_prob=0., attention_probs_dropout_prob=0., pad_token_id=0,
+    )
+    model = EncoderOnlyEmbedderM3Model(
+        {"model": BertModel(config), "sparse_linear": torch.nn.Linear(8, 1),
+         "colbert_linear": torch.nn.Linear(8, 2)},
+        tokenizer=tokenizer,
+    ).to(dtype=dtype)
+    with torch.no_grad():
+        model.sparse_linear.weight.zero_()
+        model.sparse_linear.weight[0, 0] = 1.
+        model.sparse_linear.bias.zero_()
+    return model
+
+
+def token_dictionary_oracle(model, hidden, ids):
+    """Visit occurrences of each vocabulary word; first occurrence wins ties."""
+    weights = torch.relu(model.sparse_linear(hidden)).squeeze(-1)
+    excluded = {model.tokenizer.cls_token_id, model.tokenizer.eos_token_id,
+                model.tokenizer.pad_token_id, model.tokenizer.unk_token_id}
+    rows = []
+    for row, tokens in enumerate(ids.tolist()):
+        entries = []
+        for word in range(model.vocab_size):
+            positions = [index for index, token in enumerate(tokens) if token == word]
+            if not positions or word in excluded:
+                entries.append(weights.new_zeros(()))
+            else:
+                entries.append(weights[row, positions].max(dim=0).values)
+        rows.append(torch.stack(entries))
+    return torch.stack(rows)
+
+
+@pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
+@pytest.mark.parametrize("pattern", ["distinct", "positive_ties", "negative_and_zero"])
+def test_sparse_training_values_and_first_maximum_gradients(dtype, pattern):
+    model = tiny_model(dtype)
+    ids = torch.tensor([[2, 5, 6, 5, 7, 6, 3, 0], [2, 7, 7, 8, 9, 8, 3, 1]])
+    hidden = torch.arange(128, dtype=dtype).reshape(2, 8, 8) / 64.
+    if pattern == "distinct":
+        hidden[:, :, 0] = torch.tensor([[1., 2., 3., 4., 1., 2., 5., 6.],
+                                       [1., 3., 2., 4., 1., 2., 5., 6.]])
+    elif pattern == "positive_ties":
+        hidden[:, :, 0] = 2.
+    else:
+        hidden[:, :, 0] = torch.tensor([[1., -2., 0., -1., 3., 0., 5., 6.],
+                                       [1., 0., -2., 1., 3., -1., 5., 6.]])
+    hidden.requires_grad_()
+    actual = model._sparse_embedding(hidden, ids)
+    expected = token_dictionary_oracle(model, hidden, ids)
+    torch.testing.assert_close(actual, expected)
+    coefficients = torch.linspace(.1, 1.3, model.vocab_size, dtype=dtype)[None, :]
+    parameters = (hidden, model.sparse_linear.weight, model.sparse_linear.bias)
+    actual_gradients = torch.autograd.grad((actual * coefficients).sum(), parameters, retain_graph=True)
+    expected_gradients = torch.autograd.grad((expected * coefficients).sum(), parameters)
+    for actual_gradient, expected_gradient in zip(actual_gradients, expected_gradients):
+        torch.testing.assert_close(actual_gradient, expected_gradient)
+    assert torch.count_nonzero(actual[:, [0, 1, 2, 3]]) == 0
+    assert torch.count_nonzero(actual[:, 10:]) == 0
+    if pattern == "positive_ties":
+        assert actual_gradients[0][0, 1, 0] > 0
+        assert actual_gradients[0][0, 3, 0] == 0
+
+
+def test_sparse_training_retains_nan_propagation():
+    model = tiny_model()
+    ids = torch.tensor([[2, 5, 5, 6, 3]])
+    hidden = torch.ones(1, 5, 8)
+    hidden[0, 2, 0] = float("nan")
+    actual = model._sparse_embedding(hidden, ids)
+    expected = token_dictionary_oracle(model, hidden, ids)
+    torch.testing.assert_close(actual, expected, equal_nan=True)
+
+
+@pytest.mark.parametrize("sub_batch_size", [-1, 1])
+def test_native_encoder_sparse_backward_matches_dictionary_definition(sub_batch_size):
+    model = tiny_model()
+    model.sub_batch_size = sub_batch_size
+    ids = torch.tensor([[2, 5, 6, 5, 3, 0], [2, 7, 7, 8, 3, 0]])
+    features = {"input_ids": ids, "attention_mask": ids.ne(0).long()}
+    actual = model.encode(features)[1]
+    hidden = model.model(**features, return_dict=True).last_hidden_state
+    expected = token_dictionary_oracle(model, hidden, ids)
+    torch.testing.assert_close(actual, expected)
+    coefficients = torch.linspace(.1, 1.3, model.vocab_size)[None, :]
+    parameters = (model.model.embeddings.word_embeddings.weight,
+                  model.sparse_linear.weight, model.sparse_linear.bias)
+    actual_gradients = torch.autograd.grad((actual * coefficients).sum(), parameters)
+    expected_gradients = torch.autograd.grad((expected * coefficients).sum(), parameters)
+    for actual_gradient, expected_gradient in zip(actual_gradients, expected_gradients):
+        torch.testing.assert_close(actual_gradient, expected_gradient)
+
+
+@pytest.mark.parametrize("sequence_length", [64, 96])
+def test_sparse_training_allocation_scales_with_tokens_plus_vocabulary(sequence_length):
+    model = tiny_model()
+    batch_size = 2
+    ids = torch.arange(sequence_length).remainder(model.vocab_size).repeat(batch_size, 1)
+    hidden = torch.ones(batch_size, sequence_length, 8, requires_grad=True)
+    with torch.profiler.profile(activities=[torch.profiler.ProfilerActivity.CPU], profile_memory=True) as profile:
+        sparse = model._sparse_embedding(hidden, ids)
+        sparse.sum().backward()
+    # A generous constant-size multiple of the input token count and output vocabulary.
+    # The original batch x sequence x vocabulary allocation exceeds this budget.
+    budget = 16 * batch_size * (sequence_length + model.vocab_size)
+    largest_allocation = max(event.cpu_memory_usage for event in profile.events())
+    assert largest_allocation <= budget, (largest_allocation, budget)
+    assert torch.isfinite(hidden.grad).all()