diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/conformer.py b/egs/librispeech/ASR/pruned_transducer_stateless7/conformer.py
index 3ae7e8d61..fb8123838 100644
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/conformer.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/conformer.py
@@ -18,7 +18,7 @@
 import copy
 import math
 import warnings
-from typing import Optional, Tuple
+from typing import List, Optional, Tuple
 
 import torch
 from encoder_interface import EncoderInterface
@@ -32,7 +32,7 @@ from scaling import (
 )
 from torch import Tensor, nn
 
-from icefall.utils import make_pad_mask
+from icefall.utils import make_pad_mask, subsequent_chunk_mask
 
 
 class Conformer(EncoderInterface):
@@ -48,6 +48,26 @@ class Conformer(EncoderInterface):
         layer_dropout (float): layer-dropout rate.
         cnn_module_kernel (int): Kernel size of convolution module
         vgg_frontend (bool): whether to use vgg frontend.
+        dynamic_chunk_training (bool): whether to use dynamic chunk training, if
+            you want to train a streaming model, this is expected to be True.
+            When setting True, it will use a masking strategy to make the attention
+            see only limited left and right context.
+        short_chunk_threshold (float): a threshold to determinize the chunk size
+            to be used in masking training, if the randomly generated chunk size
+            is greater than ``max_len * short_chunk_threshold`` (max_len is the
+            max sequence length of current batch) then it will use
+            full context in training (i.e. with chunk size equals to max_len).
+            This will be used only when dynamic_chunk_training is True.
+        short_chunk_size (int): see docs above, if the randomly generated chunk
+            size equals to or less than ``max_len * short_chunk_threshold``, the
+            chunk size will be sampled uniformly from 1 to short_chunk_size.
+            This also will be used only when dynamic_chunk_training is True.
+        num_left_chunks (int): the left context (in chunks) attention can see, the
+            chunk size is decided by short_chunk_threshold and short_chunk_size.
+            A minus value means seeing full left context.
+            This also will be used only when dynamic_chunk_training is True.
+        causal (bool): Whether to use causal convolution in conformer encoder
+            layer. This MUST be True when using dynamic_chunk_training.
     """
 
     def __init__(
@@ -61,6 +81,11 @@ class Conformer(EncoderInterface):
         dropout: float = 0.1,
         layer_dropout: float = 0.075,
         cnn_module_kernel: int = 31,
+        dynamic_chunk_training: bool = False,
+        short_chunk_threshold: float = 0.75,
+        short_chunk_size: int = 25,
+        num_left_chunks: int = -1,
+        causal: bool = False,
     ) -> None:
         super(Conformer, self).__init__()
 
@@ -76,6 +101,15 @@ class Conformer(EncoderInterface):
         #   (2) embedding: num_features -> d_model
         self.encoder_embed = Conv2dSubsampling(num_features, d_model)
 
+        self.encoder_layers = num_encoder_layers
+        self.d_model = d_model
+        self.cnn_module_kernel = cnn_module_kernel
+        self.causal = causal
+        self.dynamic_chunk_training = dynamic_chunk_training
+        self.short_chunk_threshold = short_chunk_threshold
+        self.short_chunk_size = short_chunk_size
+        self.num_left_chunks = num_left_chunks
+
         self.encoder_pos = RelPositionalEncoding(d_model, dropout)
 
         encoder_layer = ConformerEncoderLayer(
@@ -85,8 +119,10 @@ class Conformer(EncoderInterface):
             dropout,
             layer_dropout,
             cnn_module_kernel,
+            causal,
         )
         self.encoder = ConformerEncoder(encoder_layer, num_encoder_layers)
+        self._init_state: List[torch.Tensor] = [torch.empty(0)]
 
     def forward(
         self, x: torch.Tensor, x_lens: torch.Tensor, warmup: float = 1.0
@@ -120,15 +156,249 @@ class Conformer(EncoderInterface):
         lengths = (((x_lens - 1) >> 1) - 1) >> 1
 
         assert x.size(0) == lengths.max().item()
-        mask = make_pad_mask(lengths)
 
-        x = self.encoder(
-            x, pos_emb, src_key_padding_mask=mask, warmup=warmup
-        )  # (T, N, C)
+        src_key_padding_mask = make_pad_mask(lengths)
+
+        if self.dynamic_chunk_training:
+            assert (
+                self.causal
+            ), "Causal convolution is required for streaming conformer."
+            max_len = x.size(0)
+            chunk_size = torch.randint(1, max_len, (1,)).item()
+            if chunk_size > (max_len * self.short_chunk_threshold):
+                chunk_size = max_len
+            else:
+                chunk_size = chunk_size % self.short_chunk_size + 1
+
+            mask = ~subsequent_chunk_mask(
+                size=x.size(0),
+                chunk_size=chunk_size,
+                num_left_chunks=self.num_left_chunks,
+                device=x.device,
+            )
+            x = self.encoder(
+                x,
+                pos_emb,
+                mask=mask,
+                src_key_padding_mask=src_key_padding_mask,
+                warmup=warmup,
+            )  # (T, N, C)
+        else:
+            x = self.encoder(
+                x,
+                pos_emb,
+                mask=None,
+                src_key_padding_mask=src_key_padding_mask,
+                warmup=warmup,
+            )  # (T, N, C)
+
+        x = x.permute(1, 0, 2)  # (T, N, C) ->(N, T, C)
+        return x, lengths
+
+    @torch.jit.export
+    def get_init_state(
+        self, left_context: int, device: torch.device
+    ) -> List[torch.Tensor]:
+        """Return the initial cache state of the model.
+
+        Args:
+          left_context: The left context size (in frames after subsampling).
+
+        Returns:
+          Return the initial state of the model, it is a list containing two
+          tensors, the first one is the cache for attentions which has a shape
+          of (num_encoder_layers, left_context, encoder_dim), the second one
+          is the cache of conv_modules which has a shape of
+          (num_encoder_layers, cnn_module_kernel - 1, encoder_dim).
+
+          NOTE: the returned tensors are on the given device.
+        """
+        if (
+            len(self._init_state) == 2
+            and self._init_state[0].size(1) == left_context
+        ):
+            # Note: It is OK to share the init state as it is
+            # not going to be modified by the model
+            return self._init_state
+
+        init_states: List[torch.Tensor] = [
+            torch.zeros(
+                (
+                    self.encoder_layers,
+                    left_context,
+                    self.d_model,
+                ),
+                device=device,
+            ),
+            torch.zeros(
+                (
+                    self.encoder_layers,
+                    self.cnn_module_kernel - 1,
+                    self.d_model,
+                ),
+                device=device,
+            ),
+        ]
+
+        self._init_state = init_states
+
+        return init_states
+
+    @torch.jit.export
+    def streaming_forward(
+        self,
+        x: torch.Tensor,
+        x_lens: torch.Tensor,
+        states: Optional[List[Tensor]] = None,
+        processed_lens: Optional[Tensor] = None,
+        left_context: int = 64,
+        right_context: int = 4,
+        chunk_size: int = 16,
+        simulate_streaming: bool = False,
+        warmup: float = 1.0,
+    ) -> Tuple[torch.Tensor, torch.Tensor, List[torch.Tensor]]:
+        """
+        Args:
+          x:
+            The input tensor. Its shape is (batch_size, seq_len, feature_dim).
+          x_lens:
+            A tensor of shape (batch_size,) containing the number of frames in
+            `x` before padding.
+          states:
+            The decode states for previous frames which contains the cached data.
+            It has two elements, the first element is the attn_cache which has
+            a shape of (encoder_layers, left_context, batch, attention_dim),
+            the second element is the conv_cache which has a shape of
+            (encoder_layers, cnn_module_kernel-1, batch, conv_dim).
+            Note: states will be modified in this function.
+          processed_lens:
+            How many frames (after subsampling) have been processed for each sequence.
+          left_context:
+            How many previous frames the attention can see in current chunk.
+            Note: It's not that each individual frame has `left_context` frames
+            of left context, some have more.
+          right_context:
+            How many future frames the attention can see in current chunk.
+            Note: It's not that each individual frame has `right_context` frames
+            of right context, some have more.
+          chunk_size:
+            The chunk size for decoding, this will be used to simulate streaming
+            decoding using masking.
+          simulate_streaming:
+            If setting True, it will use a masking strategy to simulate streaming
+            fashion (i.e. every chunk data only see limited left context and
+            right context). The whole sequence is supposed to be send at a time
+            When using simulate_streaming.
+          warmup:
+            A floating point value that gradually increases from 0 throughout
+            training; when it is >= 1.0 we are "fully warmed up".  It is used
+            to turn modules on sequentially.
+        Returns:
+          Return a tuple containing 2 tensors:
+            - logits, its shape is (batch_size, output_seq_len, output_dim)
+            - logit_lens, a tensor of shape (batch_size,) containing the number
+              of frames in `logits` before padding.
+            - decode_states, the updated states including the information
+              of current chunk.
+        """
+
+        # x: [N, T, C]
+        # Caution: We assume the subsampling factor is 4!
+
+        #  lengths = ((x_lens - 1) // 2 - 1) // 2 # issue an warning
+        #
+        # Note: rounding_mode in torch.div() is available only in torch >= 1.8.0
+        lengths = (((x_lens - 1) >> 1) - 1) >> 1
+
+        if not simulate_streaming:
+            assert states is not None
+            assert processed_lens is not None
+            assert (
+                len(states) == 2
+                and states[0].shape
+                == (self.encoder_layers, left_context, x.size(0), self.d_model)
+                and states[1].shape
+                == (
+                    self.encoder_layers,
+                    self.cnn_module_kernel - 1,
+                    x.size(0),
+                    self.d_model,
+                )
+            ), f"""The length of states MUST be equal to 2, and the shape of
+             first element should be {(self.encoder_layers, left_context, x.size(0), self.d_model)},
+             given {states[0].shape}. the shape of second element should be
+             {(self.encoder_layers, self.cnn_module_kernel - 1, x.size(0), self.d_model)},
+             given {states[1].shape}."""
+
+            lengths -= 2  # we will cut off 1 frame on each side of encoder_embed output
+
+            src_key_padding_mask = make_pad_mask(lengths)
+
+            processed_mask = torch.arange(left_context, device=x.device).expand(
+                x.size(0), left_context
+            )
+            processed_lens = processed_lens.view(x.size(0), 1)
+            processed_mask = (processed_lens <= processed_mask).flip(1)
+
+            src_key_padding_mask = torch.cat(
+                [processed_mask, src_key_padding_mask], dim=1
+            )
+
+            embed = self.encoder_embed(x)
+
+            # cut off 1 frame on each size of embed as they see the padding
+            # value which causes a training and decoding mismatch.
+            embed = embed[:, 1:-1, :]
+
+            embed, pos_enc = self.encoder_pos(embed, left_context)
+            embed = embed.permute(1, 0, 2)  # (B, T, F) -> (T, B, F)
+
+            x, states = self.encoder.chunk_forward(
+                embed,
+                pos_enc,
+                src_key_padding_mask=src_key_padding_mask,
+                warmup=warmup,
+                states=states,
+                left_context=left_context,
+                right_context=right_context,
+            )  # (T, B, F)
+            if right_context > 0:
+                x = x[0:-right_context, ...]
+                lengths -= right_context
+        else:
+            assert states is None
+            states = []  # just to make torch.script.jit happy
+            # this branch simulates streaming decoding using mask as we are
+            # using in training time.
+            src_key_padding_mask = make_pad_mask(lengths)
+            x = self.encoder_embed(x)
+            x, pos_emb = self.encoder_pos(x)
+            x = x.permute(1, 0, 2)  # (N, T, C) -> (T, N, C)
+
+            assert x.size(0) == lengths.max().item()
+
+            num_left_chunks = -1
+            if left_context >= 0:
+                assert left_context % chunk_size == 0
+                num_left_chunks = left_context // chunk_size
+
+            mask = ~subsequent_chunk_mask(
+                size=x.size(0),
+                chunk_size=chunk_size,
+                num_left_chunks=num_left_chunks,
+                device=x.device,
+            )
+            x = self.encoder(
+                x,
+                pos_emb,
+                mask=mask,
+                src_key_padding_mask=src_key_padding_mask,
+                warmup=warmup,
+            )  # (T, N, C)
 
         x = x.permute(1, 0, 2)  # (T, N, C) ->(N, T, C)
 
-        return x, lengths
+        return x, lengths, states
 
 
 class ConformerEncoderLayer(nn.Module):
@@ -142,6 +412,8 @@ class ConformerEncoderLayer(nn.Module):
         dim_feedforward: the dimension of the feedforward network model (default=2048).
         dropout: the dropout value (default=0.1).
         cnn_module_kernel (int): Kernel size of convolution module.
+        causal (bool): Whether to use causal convolution in conformer encoder
+            layer. This MUST be True when using dynamic_chunk_training and streaming decoding.
 
     Examples::
         >>> encoder_layer = ConformerEncoderLayer(d_model=512, nhead=8)
@@ -158,6 +430,7 @@ class ConformerEncoderLayer(nn.Module):
         dropout: float = 0.1,
         layer_dropout: float = 0.075,
         cnn_module_kernel: int = 31,
+        causal: bool = False,
     ) -> None:
         super(ConformerEncoderLayer, self).__init__()
 
@@ -185,7 +458,9 @@ class ConformerEncoderLayer(nn.Module):
             ScaledLinear(dim_feedforward, d_model, initial_scale=0.25),
         )
 
-        self.conv_module = ConvolutionModule(d_model, cnn_module_kernel)
+        self.conv_module = ConvolutionModule(
+            d_model, cnn_module_kernel, causal=causal
+        )
 
         self.norm_final = BasicNorm(d_model)
 
@@ -214,7 +489,6 @@ class ConformerEncoderLayer(nn.Module):
             src_key_padding_mask: the mask for the src keys per batch (optional).
             warmup: controls selective bypass of of layers; if < 1.0, we will
               bypass layers more frequently.
-
         Shape:
             src: (S, N, E).
             pos_emb: (N, 2*S-1, E)
@@ -248,10 +522,12 @@ class ConformerEncoderLayer(nn.Module):
             attn_mask=src_mask,
             key_padding_mask=src_key_padding_mask,
         )[0]
+
         src = src + self.dropout(src_att)
 
         # convolution module
-        src = src + self.dropout(self.conv_module(src))
+        conv, _ = self.conv_module(src)
+        src = src + self.dropout(conv)
 
         # feed forward module
         src = src + self.dropout(self.feed_forward(src))
@@ -263,6 +539,100 @@ class ConformerEncoderLayer(nn.Module):
 
         return src
 
+    @torch.jit.export
+    def chunk_forward(
+        self,
+        src: Tensor,
+        pos_emb: Tensor,
+        states: List[Tensor],
+        src_mask: Optional[Tensor] = None,
+        src_key_padding_mask: Optional[Tensor] = None,
+        warmup: float = 1.0,
+        left_context: int = 0,
+        right_context: int = 0,
+    ) -> Tuple[Tensor, List[Tensor]]:
+        """
+        Pass the input through the encoder layer.
+
+        Args:
+            src: the sequence to the encoder layer (required).
+            pos_emb: Positional embedding tensor (required).
+            states:
+              The decode states for previous frames which contains the cached data.
+              It has two elements, the first element is the attn_cache which has
+              a shape of (left_context, batch, attention_dim),
+              the second element is the conv_cache which has a shape of
+              (cnn_module_kernel-1, batch, conv_dim).
+              Note: states will be modified in this function.
+            src_mask: the mask for the src sequence (optional).
+            src_key_padding_mask: the mask for the src keys per batch (optional).
+            warmup: controls selective bypass of of layers; if < 1.0, we will
+              bypass layers more frequently.
+            left_context:
+              How many previous frames the attention can see in current chunk.
+              Note: It's not that each individual frame has `left_context` frames
+              of left context, some have more.
+            right_context:
+              How many future frames the attention can see in current chunk.
+              Note: It's not that each individual frame has `right_context` frames
+              of right context, some have more.
+
+        Shape:
+            src: (S, N, E).
+            pos_emb: (N, 2*(S+left_context)-1, E).
+            src_mask: (S, S).
+            src_key_padding_mask: (N, S).
+            S is the source sequence length, N is the batch size, E is the feature number
+        """
+
+        assert not self.training
+        assert len(states) == 2
+        assert states[0].shape == (left_context, src.size(1), src.size(2))
+
+        # macaron style feed forward module
+        src = src + self.dropout(self.feed_forward_macaron(src))
+
+        # We put the attention cache this level (i.e. before linear transformation)
+        # to save memory consumption, when decoding in streaming fashion, the
+        # batch size would be thousands (for 32GB machine), if we cache key & val
+        # separately, it needs extra several GB memory.
+        # TODO(WeiKang): Move cache to self_attn level (i.e. cache key & val
+        # separately) if needed.
+        key = torch.cat([states[0], src], dim=0)
+        val = key
+        if right_context > 0:
+            states[0] = key[
+                -(left_context + right_context) : -right_context, ...  # noqa
+            ]
+        else:
+            states[0] = key[-left_context:, ...]
+
+        # multi-headed self-attention module
+        src_att = self.self_attn(
+            src,
+            key,
+            val,
+            pos_emb=pos_emb,
+            attn_mask=src_mask,
+            key_padding_mask=src_key_padding_mask,
+            left_context=left_context,
+        )[0]
+
+        src = src + self.dropout(src_att)
+
+        # convolution module
+        conv, conv_cache = self.conv_module(src, states[1], right_context)
+        states[1] = conv_cache
+
+        src = src + self.dropout(conv)
+
+        # feed forward module
+        src = src + self.dropout(self.feed_forward(src))
+
+        src = self.norm_final(self.balancer(src))
+
+        return src, states
+
 
 class ConformerEncoder(nn.Module):
     r"""ConformerEncoder is a stack of N encoder layers
@@ -301,6 +671,8 @@ class ConformerEncoder(nn.Module):
             pos_emb: Positional embedding tensor (required).
             mask: the mask for the src sequence (optional).
             src_key_padding_mask: the mask for the src keys per batch (optional).
+            warmup: controls selective bypass of of layers; if < 1.0, we will
+              bypass layers more frequently.
 
         Shape:
             src: (S, N, E).
@@ -312,7 +684,7 @@ class ConformerEncoder(nn.Module):
         """
         output = src
 
-        for i, mod in enumerate(self.layers):
+        for layer_index, mod in enumerate(self.layers):
             output = mod(
                 output,
                 pos_emb,
@@ -323,6 +695,79 @@ class ConformerEncoder(nn.Module):
 
         return output
 
+    @torch.jit.export
+    def chunk_forward(
+        self,
+        src: Tensor,
+        pos_emb: Tensor,
+        states: List[Tensor],
+        mask: Optional[Tensor] = None,
+        src_key_padding_mask: Optional[Tensor] = None,
+        warmup: float = 1.0,
+        left_context: int = 0,
+        right_context: int = 0,
+    ) -> Tuple[Tensor, List[Tensor]]:
+        r"""Pass the input through the encoder layers in turn.
+
+        Args:
+            src: the sequence to the encoder (required).
+            pos_emb: Positional embedding tensor (required).
+            states:
+              The decode states for previous frames which contains the cached data.
+              It has two elements, the first element is the attn_cache which has
+              a shape of (encoder_layers, left_context, batch, attention_dim),
+              the second element is the conv_cache which has a shape of
+              (encoder_layers, cnn_module_kernel-1, batch, conv_dim).
+              Note: states will be modified in this function.
+            mask: the mask for the src sequence (optional).
+            src_key_padding_mask: the mask for the src keys per batch (optional).
+            warmup: controls selective bypass of of layers; if < 1.0, we will
+              bypass layers more frequently.
+            left_context:
+              How many previous frames the attention can see in current chunk.
+              Note: It's not that each individual frame has `left_context` frames
+              of left context, some have more.
+            right_context:
+              How many future frames the attention can see in current chunk.
+              Note: It's not that each individual frame has `right_context` frames
+              of right context, some have more.
+        Shape:
+            src: (S, N, E).
+            pos_emb: (N, 2*(S+left_context)-1, E).
+            mask: (S, S).
+            src_key_padding_mask: (N, S).
+            S is the source sequence length, T is the target sequence length, N is the batch size, E is the feature number
+
+        """
+        assert not self.training
+        assert len(states) == 2
+        assert states[0].shape == (
+            self.num_layers,
+            left_context,
+            src.size(1),
+            src.size(2),
+        )
+        assert states[1].size(0) == self.num_layers
+
+        output = src
+
+        for layer_index, mod in enumerate(self.layers):
+            cache = [states[0][layer_index], states[1][layer_index]]
+            output, cache = mod.chunk_forward(
+                output,
+                pos_emb,
+                states=cache,
+                src_mask=mask,
+                src_key_padding_mask=src_key_padding_mask,
+                warmup=warmup,
+                left_context=left_context,
+                right_context=right_context,
+            )
+            states[0][layer_index] = cache[0]
+            states[1][layer_index] = cache[1]
+
+        return output, states
+
 
 class RelPositionalEncoding(torch.nn.Module):
     """Relative positional encoding module.
@@ -347,24 +792,25 @@ class RelPositionalEncoding(torch.nn.Module):
         self.pe = None
         self.extend_pe(torch.tensor(0.0).expand(1, max_len))
 
-    def extend_pe(self, x: Tensor) -> None:
+    def extend_pe(self, x: Tensor, left_context: int = 0) -> None:
         """Reset the positional encodings."""
+        x_size_1 = x.size(1) + left_context
         if self.pe is not None:
             # self.pe contains both positive and negative parts
             # the length of self.pe is 2 * input_len - 1
-            if self.pe.size(1) >= x.size(1) * 2 - 1:
+            if self.pe.size(1) >= x_size_1 * 2 - 1:
                 # Note: TorchScript doesn't implement operator== for torch.Device
                 if self.pe.dtype != x.dtype or str(self.pe.device) != str(
                     x.device
                 ):
                     self.pe = self.pe.to(dtype=x.dtype, device=x.device)
                 return
-        # Suppose `i` means to the position of query vecotr and `j` means the
+        # Suppose `i` means to the position of query vector and `j` means the
         # position of key vector. We use position relative positions when keys
         # are to the left (i>j) and negative relative positions otherwise (i<j).
-        pe_positive = torch.zeros(x.size(1), self.d_model)
-        pe_negative = torch.zeros(x.size(1), self.d_model)
-        position = torch.arange(0, x.size(1), dtype=torch.float32).unsqueeze(1)
+        pe_positive = torch.zeros(x_size_1, self.d_model)
+        pe_negative = torch.zeros(x_size_1, self.d_model)
+        position = torch.arange(0, x_size_1, dtype=torch.float32).unsqueeze(1)
         div_term = torch.exp(
             torch.arange(0, self.d_model, 2, dtype=torch.float32)
             * -(math.log(10000.0) / self.d_model)
@@ -382,22 +828,30 @@ class RelPositionalEncoding(torch.nn.Module):
         pe = torch.cat([pe_positive, pe_negative], dim=1)
         self.pe = pe.to(device=x.device, dtype=x.dtype)
 
-    def forward(self, x: torch.Tensor) -> Tuple[Tensor, Tensor]:
+    def forward(
+        self,
+        x: torch.Tensor,
+        left_context: int = 0,
+    ) -> Tuple[Tensor, Tensor]:
         """Add positional encoding.
 
         Args:
             x (torch.Tensor): Input tensor (batch, time, `*`).
+            left_context (int): left context (in frames) used during streaming decoding.
+                this is used only in real streaming decoding, in other circumstances,
+                it MUST be 0.
 
         Returns:
             torch.Tensor: Encoded tensor (batch, time, `*`).
             torch.Tensor: Encoded tensor (batch, 2*time-1, `*`).
 
         """
-        self.extend_pe(x)
+        self.extend_pe(x, left_context)
+        x_size_1 = x.size(1) + left_context
         pos_emb = self.pe[
             :,
             self.pe.size(1) // 2
-            - x.size(1)
+            - x_size_1
             + 1 : self.pe.size(1) // 2  # noqa E203
             + x.size(1),
         ]
@@ -405,7 +859,7 @@ class RelPositionalEncoding(torch.nn.Module):
 
 
 class RelPositionMultiheadAttention(nn.Module):
-    r"""Multi-Head Attention layer with simplified relative position encoding
+    r"""Multi-Head Attention layer with relative position encoding
 
     See reference: "Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context"
 
@@ -441,7 +895,24 @@ class RelPositionMultiheadAttention(nn.Module):
         )
 
         # linear transformation for positional encoding.
-        self.linear_pos = ScaledLinear(embed_dim, num_heads, bias=True)
+        self.linear_pos = ScaledLinear(embed_dim, embed_dim, bias=False)
+        # these two learnable bias are used in matrix c and matrix d
+        # as described in "Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context" Section 3.3
+        self.pos_bias_u = nn.Parameter(torch.Tensor(num_heads, self.head_dim))
+        self.pos_bias_v = nn.Parameter(torch.Tensor(num_heads, self.head_dim))
+        self.pos_bias_u_scale = nn.Parameter(torch.zeros(()).detach())
+        self.pos_bias_v_scale = nn.Parameter(torch.zeros(()).detach())
+        self._reset_parameters()
+
+    def _pos_bias_u(self):
+        return self.pos_bias_u * self.pos_bias_u_scale.exp()
+
+    def _pos_bias_v(self):
+        return self.pos_bias_v * self.pos_bias_v_scale.exp()
+
+    def _reset_parameters(self) -> None:
+        nn.init.normal_(self.pos_bias_u, std=0.01)
+        nn.init.normal_(self.pos_bias_v, std=0.01)
 
     def forward(
         self,
@@ -452,6 +923,7 @@ class RelPositionMultiheadAttention(nn.Module):
         key_padding_mask: Optional[Tensor] = None,
         need_weights: bool = True,
         attn_mask: Optional[Tensor] = None,
+        left_context: int = 0,
     ) -> Tuple[Tensor, Optional[Tensor]]:
         r"""
         Args:
@@ -465,6 +937,9 @@ class RelPositionMultiheadAttention(nn.Module):
             need_weights: output attn_output_weights.
             attn_mask: 2D or 3D mask that prevents attention to certain positions. A 2D mask will be broadcasted for all
                 the batches while a 3D mask allows to specify a different mask for the entries of each batch.
+            left_context (int): left context (in frames) used during streaming decoding.
+                this is used only in real streaming decoding, in other circumstances,
+                it MUST be 0.
 
         Shape:
             - Inputs:
@@ -510,14 +985,18 @@ class RelPositionMultiheadAttention(nn.Module):
             key_padding_mask=key_padding_mask,
             need_weights=need_weights,
             attn_mask=attn_mask,
+            left_context=left_context,
         )
 
-    def rel_shift(self, x: Tensor) -> Tensor:
+    def rel_shift(self, x: Tensor, left_context: int = 0) -> Tensor:
         """Compute relative positional encoding.
 
         Args:
             x: Input tensor (batch, head, time1, 2*time1-1).
                 time1 means the length of query vector.
+            left_context (int): left context (in frames) used during streaming decoding.
+                this is used only in real streaming decoding, in other circumstances,
+                it MUST be 0.
 
         Returns:
             Tensor: tensor of shape (batch, head, time1, time2)
@@ -525,14 +1004,19 @@ class RelPositionMultiheadAttention(nn.Module):
           the key, while time1 is for the query).
         """
         (batch_size, num_heads, time1, n) = x.shape
-        assert n == 2 * time1 - 1
+
+        time2 = time1 + left_context
+        assert (
+            n == left_context + 2 * time1 - 1
+        ), f"{n} == {left_context} + 2 * {time1} - 1"
+
         # Note: TorchScript requires explicit arg for stride()
         batch_stride = x.stride(0)
         head_stride = x.stride(1)
         time1_stride = x.stride(2)
         n_stride = x.stride(3)
         return x.as_strided(
-            (batch_size, num_heads, time1, time1),
+            (batch_size, num_heads, time1, time2),
             (batch_stride, head_stride, time1_stride - n_stride, n_stride),
             storage_offset=n_stride * (time1 - 1),
         )
@@ -554,6 +1038,7 @@ class RelPositionMultiheadAttention(nn.Module):
         key_padding_mask: Optional[Tensor] = None,
         need_weights: bool = True,
         attn_mask: Optional[Tensor] = None,
+        left_context: int = 0,
     ) -> Tuple[Tensor, Optional[Tensor]]:
         r"""
         Args:
@@ -571,6 +1056,9 @@ class RelPositionMultiheadAttention(nn.Module):
             need_weights: output attn_output_weights.
             attn_mask: 2D or 3D mask that prevents attention to certain positions. A 2D mask will be broadcasted for all
                 the batches while a 3D mask allows to specify a different mask for the entries of each batch.
+            left_context (int): left context (in frames) used during streaming decoding.
+                this is used only in real streaming decoding, in other circumstances,
+                it MUST be 0.
 
         Shape:
             Inputs:
@@ -729,23 +1217,35 @@ class RelPositionMultiheadAttention(nn.Module):
                 key_padding_mask.size(1), src_len
             )
 
-        q = q.permute(1, 2, 0, 3)  # (batch, head, time1, d_k)
+        q = q.transpose(0, 1)  # (batch, time1, head, d_k)
 
         pos_emb_bsz = pos_emb.size(0)
         assert pos_emb_bsz in (1, bsz)  # actually it is 1
+        p = self.linear_pos(pos_emb).view(pos_emb_bsz, -1, num_heads, head_dim)
+        # (batch, 2*time1, head, d_k) --> (batch, head, d_k, 2*time -1)
+        p = p.permute(0, 2, 3, 1)
+
+        q_with_bias_u = (q + self._pos_bias_u()).transpose(
+            1, 2
+        )  # (batch, head, time1, d_k)
+
+        q_with_bias_v = (q + self._pos_bias_v()).transpose(
+            1, 2
+        )  # (batch, head, time1, d_k)
 
         # compute attention score
         # first compute matrix a and matrix c
         # as described in "Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context" Section 3.3
         k = k.permute(1, 2, 3, 0)  # (batch, head, d_k, time2)
-        matrix_ac = torch.matmul(q, k)  # (batch, head, time1, time2)
+        matrix_ac = torch.matmul(
+            q_with_bias_u, k
+        )  # (batch, head, time1, time2)
 
         # compute matrix b and matrix d
-        pos_emb = self.linear_pos(pos_emb)  # (1, 2*time1-1, head)
-        matrix_bd = (
-            pos_emb.transpose(1, 2).unsqueeze(2).repeat(1, 1, tgt_len, 1)
-        )  # (1, head, time1, 2*time1-1)
-        matrix_bd = self.rel_shift(matrix_bd)  # (1, head, time1, time2)
+        matrix_bd = torch.matmul(
+            q_with_bias_v, p
+        )  # (batch, head, time1, 2*time1-1)
+        matrix_bd = self.rel_shift(matrix_bd, left_context)
 
         attn_output_weights = (
             matrix_ac + matrix_bd
@@ -780,6 +1280,39 @@ class RelPositionMultiheadAttention(nn.Module):
             )
 
         attn_output_weights = nn.functional.softmax(attn_output_weights, dim=-1)
+
+        # If we are using dynamic_chunk_training and setting a limited
+        # num_left_chunks, the attention may only see the padding values which
+        # will also be masked out by `key_padding_mask`, at this circumstances,
+        # the whole column of `attn_output_weights` will be `-inf`
+        # (i.e. be `nan` after softmax), so, we fill `0.0` at the masking
+        # positions to avoid invalid loss value below.
+        if (
+            attn_mask is not None
+            and attn_mask.dtype == torch.bool
+            and key_padding_mask is not None
+        ):
+            if attn_mask.size(0) != 1:
+                attn_mask = attn_mask.view(bsz, num_heads, tgt_len, src_len)
+                combined_mask = attn_mask | key_padding_mask.unsqueeze(
+                    1
+                ).unsqueeze(2)
+            else:
+                # attn_mask.shape == (1, tgt_len, src_len)
+                combined_mask = attn_mask.unsqueeze(
+                    0
+                ) | key_padding_mask.unsqueeze(1).unsqueeze(2)
+
+            attn_output_weights = attn_output_weights.view(
+                bsz, num_heads, tgt_len, src_len
+            )
+            attn_output_weights = attn_output_weights.masked_fill(
+                combined_mask, 0.0
+            )
+            attn_output_weights = attn_output_weights.view(
+                bsz * num_heads, tgt_len, src_len
+            )
+
         attn_output_weights = nn.functional.dropout(
             attn_output_weights, p=dropout_p, training=training
         )
@@ -813,16 +1346,21 @@ class ConvolutionModule(nn.Module):
         channels (int): The number of channels of conv layers.
         kernel_size (int): Kernerl size of conv layers.
         bias (bool): Whether to use bias in conv layers (default=True).
-
+        causal (bool): Whether to use causal convolution.
     """
 
     def __init__(
-        self, channels: int, kernel_size: int, bias: bool = True
+        self,
+        channels: int,
+        kernel_size: int,
+        bias: bool = True,
+        causal: bool = False,
     ) -> None:
         """Construct an ConvolutionModule object."""
         super(ConvolutionModule, self).__init__()
         # kernerl_size should be a odd number for 'SAME' padding
         assert (kernel_size - 1) % 2 == 0
+        self.causal = causal
 
         self.pointwise_conv1 = ScaledConv1d(
             channels,
@@ -850,12 +1388,17 @@ class ConvolutionModule(nn.Module):
             channel_dim=1, max_abs=10.0, min_positive=0.05, max_positive=1.0
         )
 
+        self.lorder = kernel_size - 1
+        padding = (kernel_size - 1) // 2
+        if self.causal:
+            padding = 0
+
         self.depthwise_conv = ScaledConv1d(
             channels,
             channels,
             kernel_size,
             stride=1,
-            padding=(kernel_size - 1) // 2,
+            padding=padding,
             groups=channels,
             bias=bias,
         )
@@ -876,14 +1419,28 @@ class ConvolutionModule(nn.Module):
             initial_scale=0.25,
         )
 
-    def forward(self, x: Tensor) -> Tensor:
+    def forward(
+        self,
+        x: Tensor,
+        cache: Optional[Tensor] = None,
+        right_context: int = 0,
+    ) -> Tuple[Tensor, Tensor]:
         """Compute convolution module.
 
         Args:
             x: Input tensor (#time, batch, channels).
+            cache: The cache of depthwise_conv, only used in real streaming
+                decoding.
+            right_context:
+              How many future frames the attention can see in current chunk.
+              Note: It's not that each individual frame has `right_context` frames
+              of right context, some have more.
 
         Returns:
-            Tensor: Output tensor (#time, batch, channels).
+            If cache is None return the output tensor (#time, batch, channels).
+            If cache is not None, return a tuple of Tensor, the first one is
+            the output tensor (#time, batch, channels), the second one is the
+            new cache for next chunk (#kernel_size - 1, batch, channels).
 
         """
         # exchange the temporal dimension and the feature dimension
@@ -896,6 +1453,26 @@ class ConvolutionModule(nn.Module):
         x = nn.functional.glu(x, dim=1)  # (batch, channels, time)
 
         # 1D Depthwise Conv
+        if self.causal and self.lorder > 0:
+            if cache is None:
+                # Make depthwise_conv causal by
+                # manualy padding self.lorder zeros to the left
+                x = nn.functional.pad(x, (self.lorder, 0), "constant", 0.0)
+            else:
+                assert (
+                    not self.training
+                ), "Cache should be None in training time"
+                assert cache.size(0) == self.lorder
+                x = torch.cat([cache.permute(1, 2, 0), x], dim=2)
+                if right_context > 0:
+                    cache = x.permute(2, 0, 1)[
+                        -(self.lorder + right_context) : (  # noqa
+                            -right_context
+                        ),
+                        ...,
+                    ]
+                else:
+                    cache = x.permute(2, 0, 1)[-self.lorder :, ...]  # noqa
         x = self.depthwise_conv(x)
 
         x = self.deriv_balancer2(x)
@@ -903,7 +1480,11 @@ class ConvolutionModule(nn.Module):
 
         x = self.pointwise_conv2(x)  # (batch, channel, time)
 
-        return x.permute(2, 0, 1)
+        # torch.jit.script requires return types be the same as annotated above
+        if cache is None:
+            cache = torch.empty(0)
+
+        return x.permute(2, 0, 1), cache
 
 
 class Conv2dSubsampling(nn.Module):
diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/decode.py b/egs/librispeech/ASR/pruned_transducer_stateless7/decode.py
index 70afc3ea3..d8ae8e026 100755
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/decode.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/decode.py
@@ -44,21 +44,74 @@ Usage:
     --decoding-method modified_beam_search \
     --beam-size 4
 
-(4) fast beam search
+(4) fast beam search (one best)
 ./pruned_transducer_stateless4/decode.py \
     --epoch 30 \
     --avg 15 \
     --exp-dir ./pruned_transducer_stateless4/exp \
     --max-duration 600 \
     --decoding-method fast_beam_search \
-    --beam 4 \
-    --max-contexts 4 \
-    --max-states 8
+    --beam 20.0 \
+    --max-contexts 8 \
+    --max-states 64
+
+(5) fast beam search (nbest)
+./pruned_transducer_stateless4/decode.py \
+    --epoch 30 \
+    --avg 15 \
+    --exp-dir ./pruned_transducer_stateless3/exp \
+    --max-duration 600 \
+    --decoding-method fast_beam_search_nbest \
+    --beam 20.0 \
+    --max-contexts 8 \
+    --max-states 64 \
+    --num-paths 200 \
+    --nbest-scale 0.5
+
+(6) fast beam search (nbest oracle WER)
+./pruned_transducer_stateless4/decode.py \
+    --epoch 30 \
+    --avg 15 \
+    --exp-dir ./pruned_transducer_stateless4/exp \
+    --max-duration 600 \
+    --decoding-method fast_beam_search_nbest_oracle \
+    --beam 20.0 \
+    --max-contexts 8 \
+    --max-states 64 \
+    --num-paths 200 \
+    --nbest-scale 0.5
+
+(7) fast beam search (with LG)
+./pruned_transducer_stateless4/decode.py \
+    --epoch 28 \
+    --avg 15 \
+    --exp-dir ./pruned_transducer_stateless4/exp \
+    --max-duration 600 \
+    --decoding-method fast_beam_search_nbest_LG \
+    --beam 20.0 \
+    --max-contexts 8 \
+    --max-states 64
+
+(8) decode in streaming mode (take greedy search as an example)
+./pruned_transducer_stateless4/decode.py \
+    --epoch 30 \
+    --avg 15 \
+    --simulate-streaming 1 \
+    --causal-convolution 1 \
+    --decode-chunk-size 16 \
+    --left-context 64 \
+    --exp-dir ./pruned_transducer_stateless4/exp \
+    --max-duration 600 \
+    --decoding-method greedy_search
+    --beam 20.0 \
+    --max-contexts 8 \
+    --max-states 64
 """
 
 
 import argparse
 import logging
+import math
 from collections import defaultdict
 from pathlib import Path
 from typing import Dict, List, Optional, Tuple
@@ -70,12 +123,15 @@ import torch.nn as nn
 from asr_datamodule import LibriSpeechAsrDataModule
 from beam_search import (
     beam_search,
+    fast_beam_search_nbest,
+    fast_beam_search_nbest_LG,
+    fast_beam_search_nbest_oracle,
     fast_beam_search_one_best,
     greedy_search,
     greedy_search_batch,
     modified_beam_search,
 )
-from train import get_params, get_transducer_model
+from train import add_model_arguments, get_params, get_transducer_model
 
 from icefall.checkpoint import (
     average_checkpoints,
@@ -83,6 +139,7 @@ from icefall.checkpoint import (
     find_checkpoints,
     load_checkpoint,
 )
+from icefall.lexicon import Lexicon
 from icefall.utils import (
     AttributeDict,
     setup_logger,
@@ -91,6 +148,8 @@ from icefall.utils import (
     write_error_stats,
 )
 
+LOG_EPS = math.log(1e-10)
+
 
 def get_parser():
     parser = argparse.ArgumentParser(
@@ -150,6 +209,13 @@ def get_parser():
         help="Path to the BPE model",
     )
 
+    parser.add_argument(
+        "--lang-dir",
+        type=Path,
+        default="data/lang_bpe_500",
+        help="The lang dir containing word table and LG graph",
+    )
+
     parser.add_argument(
         "--decoding-method",
         type=str,
@@ -159,6 +225,11 @@ def get_parser():
           - beam_search
           - modified_beam_search
           - fast_beam_search
+          - fast_beam_search_nbest
+          - fast_beam_search_nbest_oracle
+          - fast_beam_search_nbest_LG
+        If you use fast_beam_search_nbest_LG, you have to specify
+        `--lang-dir`, which should contain `LG.pt`.
         """,
     )
 
@@ -174,27 +245,42 @@ def get_parser():
     parser.add_argument(
         "--beam",
         type=float,
-        default=4,
+        default=20.0,
         help="""A floating point value to calculate the cutoff score during beam
         search (i.e., `cutoff = max-score - beam`), which is the same as the
         `beam` in Kaldi.
-        Used only when --decoding-method is fast_beam_search""",
+        Used only when --decoding-method is fast_beam_search,
+        fast_beam_search_nbest, fast_beam_search_nbest_LG,
+        and fast_beam_search_nbest_oracle
+        """,
+    )
+
+    parser.add_argument(
+        "--ngram-lm-scale",
+        type=float,
+        default=0.01,
+        help="""
+        Used only when --decoding_method is fast_beam_search_nbest_LG.
+        It specifies the scale for n-gram LM scores.
+        """,
     )
 
     parser.add_argument(
         "--max-contexts",
         type=int,
-        default=4,
+        default=8,
         help="""Used only when --decoding-method is
-        fast_beam_search""",
+        fast_beam_search, fast_beam_search_nbest, fast_beam_search_nbest_LG,
+        and fast_beam_search_nbest_oracle""",
     )
 
     parser.add_argument(
         "--max-states",
         type=int,
-        default=8,
+        default=64,
         help="""Used only when --decoding-method is
-        fast_beam_search""",
+        fast_beam_search, fast_beam_search_nbest, fast_beam_search_nbest_LG,
+        and fast_beam_search_nbest_oracle""",
     )
 
     parser.add_argument(
@@ -212,6 +298,48 @@ def get_parser():
         Used only when --decoding_method is greedy_search""",
     )
 
+    parser.add_argument(
+        "--simulate-streaming",
+        type=str2bool,
+        default=False,
+        help="""Whether to simulate streaming in decoding, this is a good way to
+        test a streaming model.
+        """,
+    )
+
+    parser.add_argument(
+        "--decode-chunk-size",
+        type=int,
+        default=16,
+        help="The chunk size for decoding (in frames after subsampling)",
+    )
+
+    parser.add_argument(
+        "--left-context",
+        type=int,
+        default=64,
+        help="left context can be seen during decoding (in frames after subsampling)",
+    )
+
+    parser.add_argument(
+        "--num-paths",
+        type=int,
+        default=200,
+        help="""Number of paths for nbest decoding.
+        Used only when the decoding method is fast_beam_search_nbest,
+        fast_beam_search_nbest_LG, and fast_beam_search_nbest_oracle""",
+    )
+
+    parser.add_argument(
+        "--nbest-scale",
+        type=float,
+        default=0.5,
+        help="""Scale applied to lattice scores when computing nbest paths.
+        Used only when the decoding method is fast_beam_search_nbest,
+        fast_beam_search_nbest_LG, and fast_beam_search_nbest_oracle""",
+    )
+    add_model_arguments(parser)
+
     return parser
 
 
@@ -220,6 +348,7 @@ def decode_one_batch(
     model: nn.Module,
     sp: spm.SentencePieceProcessor,
     batch: dict,
+    word_table: Optional[k2.SymbolTable] = None,
     decoding_graph: Optional[k2.Fsa] = None,
 ) -> Dict[str, List[List[str]]]:
     """Decode one batch and return the result in a dict. The dict has the
@@ -243,9 +372,12 @@ def decode_one_batch(
         It is the return value from iterating
         `lhotse.dataset.K2SpeechRecognitionDataset`. See its documentation
         for the format of the `batch`.
+      word_table:
+        The word symbol table.
       decoding_graph:
         The decoding graph. Can be either a `k2.trivial_graph` or HLG, Used
-        only when --decoding_method is fast_beam_search.
+        only when --decoding_method is fast_beam_search, fast_beam_search_nbest,
+        fast_beam_search_nbest_oracle, and fast_beam_search_nbest_LG.
     Returns:
       Return the decoding result. See above description for the format of
       the returned dict.
@@ -260,9 +392,26 @@ def decode_one_batch(
     supervisions = batch["supervisions"]
     feature_lens = supervisions["num_frames"].to(device)
 
-    encoder_out, encoder_out_lens = model.encoder(
-        x=feature, x_lens=feature_lens
+    feature_lens += params.left_context
+    feature = torch.nn.functional.pad(
+        feature,
+        pad=(0, 0, 0, params.left_context),
+        value=LOG_EPS,
     )
+
+    if params.simulate_streaming:
+        encoder_out, encoder_out_lens, _ = model.encoder.streaming_forward(
+            x=feature,
+            x_lens=feature_lens,
+            chunk_size=params.decode_chunk_size,
+            left_context=params.left_context,
+            simulate_streaming=True,
+        )
+    else:
+        encoder_out, encoder_out_lens = model.encoder(
+            x=feature, x_lens=feature_lens
+        )
+
     hyps = []
 
     if params.decoding_method == "fast_beam_search":
@@ -277,6 +426,49 @@ def decode_one_batch(
         )
         for hyp in sp.decode(hyp_tokens):
             hyps.append(hyp.split())
+    elif params.decoding_method == "fast_beam_search_nbest_LG":
+        hyp_tokens = fast_beam_search_nbest_LG(
+            model=model,
+            decoding_graph=decoding_graph,
+            encoder_out=encoder_out,
+            encoder_out_lens=encoder_out_lens,
+            beam=params.beam,
+            max_contexts=params.max_contexts,
+            max_states=params.max_states,
+            num_paths=params.num_paths,
+            nbest_scale=params.nbest_scale,
+        )
+        for hyp in hyp_tokens:
+            hyps.append([word_table[i] for i in hyp])
+    elif params.decoding_method == "fast_beam_search_nbest":
+        hyp_tokens = fast_beam_search_nbest(
+            model=model,
+            decoding_graph=decoding_graph,
+            encoder_out=encoder_out,
+            encoder_out_lens=encoder_out_lens,
+            beam=params.beam,
+            max_contexts=params.max_contexts,
+            max_states=params.max_states,
+            num_paths=params.num_paths,
+            nbest_scale=params.nbest_scale,
+        )
+        for hyp in sp.decode(hyp_tokens):
+            hyps.append(hyp.split())
+    elif params.decoding_method == "fast_beam_search_nbest_oracle":
+        hyp_tokens = fast_beam_search_nbest_oracle(
+            model=model,
+            decoding_graph=decoding_graph,
+            encoder_out=encoder_out,
+            encoder_out_lens=encoder_out_lens,
+            beam=params.beam,
+            max_contexts=params.max_contexts,
+            max_states=params.max_states,
+            num_paths=params.num_paths,
+            ref_texts=sp.encode(supervisions["text"]),
+            nbest_scale=params.nbest_scale,
+        )
+        for hyp in sp.decode(hyp_tokens):
+            hyps.append(hyp.split())
     elif (
         params.decoding_method == "greedy_search"
         and params.max_sym_per_frame == 1
@@ -324,14 +516,17 @@ def decode_one_batch(
 
     if params.decoding_method == "greedy_search":
         return {"greedy_search": hyps}
-    elif params.decoding_method == "fast_beam_search":
-        return {
-            (
-                f"beam_{params.beam}_"
-                f"max_contexts_{params.max_contexts}_"
-                f"max_states_{params.max_states}"
-            ): hyps
-        }
+    elif "fast_beam_search" in params.decoding_method:
+        key = f"beam_{params.beam}_"
+        key += f"max_contexts_{params.max_contexts}_"
+        key += f"max_states_{params.max_states}"
+        if "nbest" in params.decoding_method:
+            key += f"_num_paths_{params.num_paths}_"
+            key += f"nbest_scale_{params.nbest_scale}"
+            if "LG" in params.decoding_method:
+                key += f"_ngram_lm_scale_{params.ngram_lm_scale}"
+
+        return {key: hyps}
     else:
         return {f"beam_size_{params.beam_size}": hyps}
 
@@ -341,6 +536,7 @@ def decode_dataset(
     params: AttributeDict,
     model: nn.Module,
     sp: spm.SentencePieceProcessor,
+    word_table: Optional[k2.SymbolTable] = None,
     decoding_graph: Optional[k2.Fsa] = None,
 ) -> Dict[str, List[Tuple[List[str], List[str]]]]:
     """Decode dataset.
@@ -354,9 +550,12 @@ def decode_dataset(
         The neural model.
       sp:
         The BPE model.
+      word_table:
+        The word symbol table.
       decoding_graph:
         The decoding graph. Can be either a `k2.trivial_graph` or HLG, Used
-        only when --decoding_method is fast_beam_search.
+        only when --decoding_method is fast_beam_search, fast_beam_search_nbest,
+        fast_beam_search_nbest_oracle, and fast_beam_search_nbest_LG.
     Returns:
       Return a dict, whose key may be "greedy_search" if greedy search
       is used, or it may be "beam_7" if beam size of 7 is used.
@@ -374,7 +573,7 @@ def decode_dataset(
     if params.decoding_method == "greedy_search":
         log_interval = 50
     else:
-        log_interval = 10
+        log_interval = 20
 
     results = defaultdict(list)
     for batch_idx, batch in enumerate(dl):
@@ -385,6 +584,7 @@ def decode_dataset(
             model=model,
             sp=sp,
             decoding_graph=decoding_graph,
+            word_table=word_table,
             batch=batch,
         )
 
@@ -466,6 +666,9 @@ def main():
         "greedy_search",
         "beam_search",
         "fast_beam_search",
+        "fast_beam_search_nbest",
+        "fast_beam_search_nbest_LG",
+        "fast_beam_search_nbest_oracle",
         "modified_beam_search",
     )
     params.res_dir = params.exp_dir / params.decoding_method
@@ -475,10 +678,19 @@ def main():
     else:
         params.suffix = f"epoch-{params.epoch}-avg-{params.avg}"
 
+    if params.simulate_streaming:
+        params.suffix += f"-streaming-chunk-size-{params.decode_chunk_size}"
+        params.suffix += f"-left-context-{params.left_context}"
+
     if "fast_beam_search" in params.decoding_method:
         params.suffix += f"-beam-{params.beam}"
         params.suffix += f"-max-contexts-{params.max_contexts}"
         params.suffix += f"-max-states-{params.max_states}"
+        if "nbest" in params.decoding_method:
+            params.suffix += f"-nbest-scale-{params.nbest_scale}"
+            params.suffix += f"-num-paths-{params.num_paths}"
+            if "LG" in params.decoding_method:
+                params.suffix += f"-ngram-lm-scale-{params.ngram_lm_scale}"
     elif "beam_search" in params.decoding_method:
         params.suffix += (
             f"-{params.decoding_method}-beam-size-{params.beam_size}"
@@ -507,6 +719,11 @@ def main():
     params.unk_id = sp.piece_to_id("<unk>")
     params.vocab_size = sp.get_piece_size()
 
+    if params.simulate_streaming:
+        assert (
+            params.causal_convolution
+        ), "Decoding in streaming requires causal convolution"
+
     logging.info(params)
 
     logging.info("About to create model")
@@ -592,10 +809,24 @@ def main():
     model.to(device)
     model.eval()
 
-    if params.decoding_method == "fast_beam_search":
-        decoding_graph = k2.trivial_graph(params.vocab_size - 1, device=device)
+    if "fast_beam_search" in params.decoding_method:
+        if params.decoding_method == "fast_beam_search_nbest_LG":
+            lexicon = Lexicon(params.lang_dir)
+            word_table = lexicon.word_table
+            lg_filename = params.lang_dir / "LG.pt"
+            logging.info(f"Loading {lg_filename}")
+            decoding_graph = k2.Fsa.from_dict(
+                torch.load(lg_filename, map_location=device)
+            )
+            decoding_graph.scores *= params.ngram_lm_scale
+        else:
+            word_table = None
+            decoding_graph = k2.trivial_graph(
+                params.vocab_size - 1, device=device
+            )
     else:
         decoding_graph = None
+        word_table = None
 
     num_param = sum([p.numel() for p in model.parameters()])
     logging.info(f"Number of model parameters: {num_param}")
@@ -617,6 +848,7 @@ def main():
             params=params,
             model=model,
             sp=sp,
+            word_table=word_table,
             decoding_graph=decoding_graph,
         )
 
diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/train.py b/egs/librispeech/ASR/pruned_transducer_stateless7/train.py
index 48c0e683d..893a6a749 100755
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/train.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/train.py
@@ -41,8 +41,20 @@ export CUDA_VISIBLE_DEVICES="0,1,2,3"
   --full-libri 1 \
   --max-duration 550
 
-"""
+# train a streaming model
+./pruned_transducer_stateless4/train.py \
+  --world-size 4 \
+  --num-epochs 30 \
+  --start-epoch 1 \
+  --exp-dir pruned_transducer_stateless4/exp \
+  --full-libri 1 \
+  --dynamic-chunk-training 1 \
+  --causal-convolution 1 \
+  --short-chunk-size 25 \
+  --num-left-chunks 4 \
+  --max-duration 300
 
+"""
 
 import argparse
 import copy
@@ -88,6 +100,42 @@ LRSchedulerType = Union[
 ]
 
 
+def add_model_arguments(parser: argparse.ArgumentParser):
+    parser.add_argument(
+        "--dynamic-chunk-training",
+        type=str2bool,
+        default=False,
+        help="""Whether to use dynamic_chunk_training, if you want a streaming
+        model, this requires to be True.
+        """,
+    )
+
+    parser.add_argument(
+        "--causal-convolution",
+        type=str2bool,
+        default=False,
+        help="""Whether to use causal convolution, this requires to be True when
+        using dynamic_chunk_training.
+        """,
+    )
+
+    parser.add_argument(
+        "--short-chunk-size",
+        type=int,
+        default=25,
+        help="""Chunk length of dynamic training, the chunk size would be either
+        max sequence length of current batch or uniformly sampled from (1, short_chunk_size).
+        """,
+    )
+
+    parser.add_argument(
+        "--num-left-chunks",
+        type=int,
+        default=4,
+        help="How many left context can be seen in chunks when calculating attention.",
+    )
+
+
 def get_parser():
     parser = argparse.ArgumentParser(
         formatter_class=argparse.ArgumentDefaultsHelpFormatter
@@ -281,6 +329,8 @@ def get_parser():
         help="Whether to use half precision training.",
     )
 
+    add_model_arguments(parser)
+
     return parser
 
 
@@ -367,6 +417,10 @@ def get_encoder_model(params: AttributeDict) -> nn.Module:
         nhead=params.nhead,
         dim_feedforward=params.dim_feedforward,
         num_encoder_layers=params.num_encoder_layers,
+        dynamic_chunk_training=params.dynamic_chunk_training,
+        short_chunk_size=params.short_chunk_size,
+        num_left_chunks=params.num_left_chunks,
+        causal=params.causal_convolution,
     )
     return encoder
 
@@ -603,6 +657,15 @@ def compute_loss(
             (feature_lens // params.subsampling_factor).sum().item()
         )
 
+    # `utt_duration` and `utt_pad_proportion` would be normalized by `utterances`  # noqa
+    info["utterances"] = feature.size(0)
+    # averaged input duration in frames over utterances
+    info["utt_duration"] = feature_lens.sum().item()
+    # averaged padding proportion over utterances
+    info["utt_pad_proportion"] = (
+        ((feature.size(1) - feature_lens) / feature.size(1)).sum().item()
+    )
+
     # Note: We use reduction=sum while computing the loss.
     info["loss"] = loss.detach().cpu().item()
     info["simple_loss"] = simple_loss.detach().cpu().item()
@@ -847,6 +910,11 @@ def run(rank, world_size, args):
     params.blank_id = sp.piece_to_id("<blk>")
     params.vocab_size = sp.get_piece_size()
 
+    if params.dynamic_chunk_training:
+        assert (
+            params.causal_convolution
+        ), "dynamic_chunk_training requires causal convolution"
+
     logging.info(params)
 
     logging.info("About to create model")
@@ -932,6 +1000,7 @@ def run(rank, world_size, args):
             optimizer=optimizer,
             sp=sp,
             params=params,
+            warmup=0.0 if params.start_epoch == 1 else 1.0,
         )
 
     scaler = GradScaler(enabled=params.use_fp16)
@@ -992,6 +1061,7 @@ def scan_pessimistic_batches_for_oom(
     optimizer: torch.optim.Optimizer,
     sp: spm.SentencePieceProcessor,
     params: AttributeDict,
+    warmup: float,
 ):
     from lhotse.dataset import find_pessimistic_batches
 
@@ -1002,9 +1072,6 @@ def scan_pessimistic_batches_for_oom(
     for criterion, cuts in batches.items():
         batch = train_dl.dataset[cuts]
         try:
-            # warmup = 0.0 is so that the derivs for the pruned loss stay zero
-            # (i.e. are not remembered by the decaying-average in adam), because
-            # we want to avoid these params being subject to shrinkage in adam.
             with torch.cuda.amp.autocast(enabled=params.use_fp16):
                 loss, _ = compute_loss(
                     params=params,
@@ -1012,7 +1079,7 @@ def scan_pessimistic_batches_for_oom(
                     sp=sp,
                     batch=batch,
                     is_training=True,
-                    warmup=0.0,
+                    warmup=warmup,
                 )
             loss.backward()
             optimizer.step()