Bigger batch size improves training by too much

I am writing a classifier that takes a surname and predicts a language it belongs to. I found that small batch sizes (256 and less) perform poorly compared to big batch sizes (2048 and more). Could someone give me some insight on why this is happening and how to fix it? Thank you.

Training code:

def indices_to_packed(names, input_size):
    names = [F.one_hot(item, input_size).float() for item in names]
    names_packed = pack_sequence(names, enforce_sorted=False)
    return names_packed

def infer(model, data, labels, lengths, device):
    data_packed = indices_to_packed(data, model.rnn.input_size)
    data_packed, labels, lengths = data_packed.to(device), labels.to(device), lengths.to(device)
    preds = model(data_packed, lengths)
    loss = loss_fn(preds, labels)
    return loss, preds

results = {}
epochs = 100
for BATCH_SIZE in [4096, 2048, 256]:
    train_loader = data.DataLoader(train_data, BATCH_SIZE, sampler=train_sampler, collate_fn=partial(my_collate, input_size=input_size, output_size=output_size))
    val_loader = data.DataLoader(val_data, BATCH_SIZE, sampler=val_sampler, collate_fn=partial(my_collate, input_size=input_size, output_size=output_size))
    model = LSTM(input_size, HIDDEN_SIZE, NUM_LAYERS, DROPOUT, output_size)
    optimizer = torch.optim.Adam(model.parameters())
    model.to(device)
    train_losses = []
    val_losses = []
    cur_losses = {}
    duration = 0
    for epoch in range(epochs):
        start = time.time()
        train_loss = 0
        model.train()
        # Using PackedSequence
        for names, langs, lengths in train_loader:
            optimizer.zero_grad()
            loss, _ = infer(model, names, langs, lengths, device)
            loss.backward()
            optimizer.step()
            train_loss += loss

        train_loss /= len(train_data)    
        train_losses.append(train_loss.cpu().detach().numpy())

        model.eval()
        val_loss = 0
        with torch.no_grad():
            for names, langs, lengths in val_loader:
                loss, _ = infer(model, names, langs, lengths, device)
                val_loss += loss
        val_loss /= len(val_data)
        val_losses.append(val_loss.cpu().detach().numpy())        
        
        cur_duration = time.time() - start
        duration += cur_duration
        
        log_line = (f"BATCH_SIZE: {BATCH_SIZE} epoch: {epoch} train loss: "
                    f"{train_loss:.5f} val loss: {val_loss:.5f}")
        print(log_line)
    cur_losses["train_losses"] = train_losses
    cur_losses["val_losses"] = val_losses
    results[BATCH_SIZE] = {"losses" : cur_losses, "duration" : duration, "model": model}

Model:

class LSTM(nn.Module):
def __init__(self, input_size, hidden_size, num_layers, dropout, output_size):
    super().__init__()
    
    self.rnn = nn.LSTM(input_size, hidden_size, num_layers, dropout=DROPOUT)
    self.linear = nn.Linear(hidden_size, output_size)
    self.softmax = nn.LogSoftmax(dim=1)

def forward(self, x, lengths):
    lstm_out, _ = self.rnn(x)
    # https://discuss.pytorch.org/t/get-each-sequences-last-item-from-packed-sequence/41118/7
    sum_batch_sizes = torch.cat((
        torch.zeros(2, dtype=torch.int64),
        torch.cumsum(lstm_out.batch_sizes, 0)
    ))
    sorted_lengths = lengths[lstm_out.sorted_indices]
    last_seq_idxs = sum_batch_sizes[sorted_lengths] + torch.arange(lengths.size(0))
    last_seq_items = lstm_out.data[last_seq_idxs]
    lstm_last_out = last_seq_items[lstm_out.unsorted_indices]
    linear_out = self.linear(lstm_last_out)
    softmax_out = self.softmax(linear_out)

    return softmax_out

Losses with different batch sizes: