# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang # This file is modified and supported by the Moonshot AI Team import torch import torch.nn.functional as F import triton import triton.language as tl from fla.ops.utils.index import prepare_chunk_indices from fla.ops.utils.op import exp from fla.ops.utils.softplus import softplus from fla.utils import IS_AMD, autocast_custom_bwd, autocast_custom_fwd, autotune_cache_kwargs, check_shared_mem, input_guard BS_LIST = [32, 64] if check_shared_mem() else [16, 32] BT_LIST_AUTOTUNE = [32, 64, 128] NUM_WARPS_AUTOTUNE = [2, 4, 8, 16] if IS_AMD else [4, 8, 16, 32] def naive_kda_gate( g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, output_dtype: torch.dtype = torch.float32, ) -> torch.Tensor: """ Torch reference implementation for KDA gate computation. Computes: g = -A_log.exp().unsqueeze(-1) * softplus(g + dt_bias.view(g.shape[-2:])) Args: g (torch.Tensor): Input tensor of shape `[..., H, K]`. A_log (torch.Tensor): Parameter tensor with `H` elements. dt_bias (torch.Tensor | None): Optional bias tensor added to `g` before activation, shape `[H * K]`. Returns: Output tensor of shape `[..., H, K]` . """ H, _ = g.shape[-2:] g = g.float() if dt_bias is not None: g = g + dt_bias.view(H, -1) g = (-A_log.view(H, 1).float().exp() * F.softplus(g.float())).to(output_dtype) return g def naive_kda_lowerbound_gate( g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, lower_bound: float = -5.0, output_dtype: torch.dtype = torch.float32, ) -> torch.Tensor: H, _ = g.shape[-2:] g = g.float() if dt_bias is not None: g = g + dt_bias.view(H, -1) g = lower_bound * F.sigmoid(A_log.view(H, 1).exp() * g) return g.to(output_dtype) @triton.heuristics({ "HAS_BIAS": lambda args: args["dt_bias"] is not None, "HAS_BETA": lambda args: args["beta"] is not None, 'USE_LOWER_BOUND': lambda args: args['lower_bound'] is not None, }) @triton.autotune( configs=[ triton.Config({"BT": BT}, num_warps=num_warps, num_stages=num_stages) for BT in BT_LIST_AUTOTUNE for num_warps in NUM_WARPS_AUTOTUNE for num_stages in [2, 3] ], key=["H", "D"], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['T']) def kda_gate_fwd_kernel( g, A_log, dt_bias, beta, yg, yb, lower_bound, T, H: tl.constexpr, D: tl.constexpr, BT: tl.constexpr, BD: tl.constexpr, HAS_BIAS: tl.constexpr, HAS_BETA: tl.constexpr, USE_LOWER_BOUND: tl.constexpr, ): i_t, i_h = tl.program_id(0), tl.program_id(1) b_A = tl.load(A_log + i_h).to(tl.float32) p_g = tl.make_block_ptr(g + i_h * D, (T, D), (H * D, 1), (i_t * BT, 0), (BT, BD), (1, 0)) p_yg = tl.make_block_ptr(yg + i_h * D, (T, D), (H * D, 1), (i_t * BT, 0), (BT, BD), (1, 0)) # [BT, BD] b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32) if HAS_BIAS: p_b = tl.make_block_ptr(dt_bias, (H * D,), (1,), (i_h * D,), (BD,), (0,)) b_g = b_g + tl.load(p_b, boundary_check=(0,)).to(tl.float32) if not USE_LOWER_BOUND: b_yg = -exp(b_A) * softplus(b_g) else: b_yg = lower_bound * tl.sigmoid(exp(b_A) * b_g) tl.store(p_yg, b_yg.to(p_yg.dtype.element_ty), boundary_check=(0, 1)) if HAS_BETA: p_b = tl.make_block_ptr(beta + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,)) p_yb = tl.make_block_ptr(yb + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,)) b_yb = tl.sigmoid(tl.load(p_b, boundary_check=(0,)).to(tl.float32)) tl.store(p_yb, b_yb.to(p_yb.dtype.element_ty), boundary_check=(0,)) @triton.heuristics({ "HAS_BIAS": lambda args: args["dt_bias"] is not None, "HAS_BETA": lambda args: args["beta"] is not None, 'USE_LOWER_BOUND': lambda args: args['lower_bound'] is not None, }) @triton.autotune( configs=[ triton.Config({}, num_warps=num_warps, num_stages=num_stages) for num_warps in NUM_WARPS_AUTOTUNE for num_stages in [2, 3] ], key=["H", "D"], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['T']) def kda_gate_bwd_kernel( g, A_log, dt_bias, beta, dyg, dyb, dg, dA, dbeta, lower_bound, T, H: tl.constexpr, D: tl.constexpr, BT: tl.constexpr, BD: tl.constexpr, HAS_BIAS: tl.constexpr, HAS_BETA: tl.constexpr, USE_LOWER_BOUND: tl.constexpr, ): i_t, i_h = tl.program_id(0), tl.program_id(1) b_A = tl.load(A_log + i_h).to(tl.float32) p_g = tl.make_block_ptr(g + i_h * D, (T, D), (H * D, 1), (i_t * BT, 0), (BT, BD), (1, 0)) p_dg = tl.make_block_ptr(dg + i_h * D, (T, D), (H * D, 1), (i_t * BT, 0), (BT, BD), (1, 0)) p_dyg = tl.make_block_ptr(dyg + i_h * D, (T, D), (H * D, 1), (i_t * BT, 0), (BT, BD), (1, 0)) # [BT, BD] b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32) b_dyg = tl.load(p_dyg, boundary_check=(0, 1)).to(tl.float32) if HAS_BIAS: p_b = tl.make_block_ptr(dt_bias, (H * D,), (1,), (i_h * D,), (BD,), (0,)) b_g = b_g + tl.load(p_b, boundary_check=(0,)).to(tl.float32) # [BT, BD] if not USE_LOWER_BOUND: b_A = -exp(b_A) b_yg = b_A * softplus(b_g) b_dg = b_A * (b_dyg * tl.sigmoid(b_g)) b_dA = tl.sum(tl.sum(b_dyg * b_yg, 1), 0) else: b_A = exp(b_A) b_inner = b_A * b_g b_sig = tl.sigmoid(b_inner) b_dsig = b_sig * (1.0 - b_sig) # Common term: dy * (LB * dsig) b_d_inner_term = b_dyg * (lower_bound * b_dsig) # dg = d_inner_term * A b_dg = b_d_inner_term * b_A b_dA = tl.sum(tl.sum(b_dg * b_g, 1), 0) tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1)) tl.store(dA + i_t * H + i_h, b_dA) if HAS_BETA: p_b = tl.make_block_ptr(beta + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,)) p_db = tl.make_block_ptr(dbeta + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,)) p_dyb = tl.make_block_ptr(dyb + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,)) b_b = tl.load(p_b, boundary_check=(0,)).to(tl.float32) b_db = tl.load(p_dyb, boundary_check=(0,)).to(tl.float32) * b_b * (1.0 - b_b) tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,)) def kda_gate_fwd( g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, lower_bound: float | None = None, output_dtype: torch.dtype = torch.float32, ) -> torch.Tensor: H, K = g.shape[-2:] T = g.numel() // (H * K) yg = torch.empty_like(g, dtype=output_dtype) def grid(meta): return (triton.cdiv(T, meta["BT"]), H) kda_gate_fwd_kernel[grid]( g=g, A_log=A_log, dt_bias=dt_bias, beta=None, yg=yg, yb=None, T=T, H=H, D=K, BD=triton.next_power_of_2(K), lower_bound=lower_bound, ) return yg def kda_gate_bwd( g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, dyg: torch.Tensor | None = None, lower_bound: float | None = None, ) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor | None]: H, K = g.shape[-2:] T = g.numel() // (H * K) BT = 32 NT = triton.cdiv(T, BT) dg = torch.empty_like(g, dtype=torch.float32) dA = A_log.new_empty(NT, H, dtype=torch.float32) grid = (triton.cdiv(T, BT), H) kda_gate_bwd_kernel[grid]( g=g, A_log=A_log, dt_bias=dt_bias, beta=None, dyg=dyg, dyb=None, dg=dg, dA=dA, dbeta=None, T=T, H=H, D=K, BT=BT, BD=triton.next_power_of_2(K), lower_bound=lower_bound, ) dg = dg.view_as(g).type_as(g) dA = dA.sum(0).view_as(A_log).type_as(A_log) dbias = dg.view(-1, H * K).sum(0).to(dt_bias) if dt_bias is not None else None return dg, dA, dbias class KDAGateFunction(torch.autograd.Function): @staticmethod @input_guard @autocast_custom_fwd def forward( ctx, g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, lower_bound: float | None = None, output_dtype: torch.dtype = torch.float32, ) -> torch.Tensor: yg = kda_gate_fwd( g=g, A_log=A_log, dt_bias=dt_bias, lower_bound=lower_bound, output_dtype=output_dtype ) ctx.save_for_backward(g, A_log, dt_bias) ctx.lower_bound = lower_bound return yg @staticmethod @input_guard @autocast_custom_bwd def backward(ctx, dyg: torch.Tensor): g, A_log, dt_bias = ctx.saved_tensors dg, dA, dbias = kda_gate_bwd( g=g, A_log=A_log, dt_bias=dt_bias, dyg=dyg, lower_bound=ctx.lower_bound ) return dg, dA, dbias, None, None @torch.compiler.disable def fused_kda_gate( g: torch.Tensor, A_log: torch.Tensor, dt_bias: torch.Tensor | None = None, lower_bound: float | None = None, output_dtype: torch.dtype = torch.float32, ) -> torch.Tensor | tuple[torch.Tensor, torch.Tensor]: """ Fused KDA gate computation with autograd support. Computes: g = -A_log.exp().unsqueeze(-1) * softplus(g + dt_bias.view(g.shape[-2:])) Args: g (torch.Tensor): Input tensor of shape `[..., H, K]`. A_log (torch.Tensor): Parameter tensor with `H` elements. dt_bias (torch.Tensor | None): Optional bias tensor added to `g` before activation, shape `[H * K]`. Returns: Output tensor of shape `[..., H, K]`. """ return KDAGateFunction.apply(g, A_log, dt_bias, lower_bound, output_dtype) @triton.heuristics({ "HAS_BIAS": lambda args: args["dt_bias"] is not None, 'HAS_SCALE': lambda args: args['scale'] is not None, 'IS_VARLEN': lambda args: args['cu_seqlens'] is not None, 'USE_LOWER_BOUND': lambda args: args['lower_bound'] is not None, }) @triton.autotune( configs=[ triton.Config({'BS': BS}, num_warps=num_warps) for BS in BS_LIST for num_warps in [2, 4, 8] ], key=['H', 'S', 'BT', 'IS_VARLEN', 'REVERSE'], **autotune_cache_kwargs, ) @triton.jit(do_not_specialize=['T']) def kda_gate_chunk_cumsum_vector_kernel( s, A_log, dt_bias, o, scale, cu_seqlens, chunk_indices, lower_bound, T, H: tl.constexpr, S: tl.constexpr, BT: tl.constexpr, BS: tl.constexpr, REVERSE: tl.constexpr, HAS_BIAS: tl.constexpr, HAS_SCALE: tl.constexpr, IS_VARLEN: tl.constexpr, USE_LOWER_BOUND: tl.constexpr, ): i_s, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H if IS_VARLEN: i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32) T = eos - bos else: bos, eos = i_b * T, i_b * T + T p_s = tl.make_block_ptr(s + (bos * H + i_h) * S, (T, S), (H*S, 1), (i_t * BT, i_s * BS), (BT, BS), (1, 0)) p_o = tl.make_block_ptr(o + (bos * H + i_h) * S, (T, S), (H*S, 1), (i_t * BT, i_s * BS), (BT, BS), (1, 0)) # [BT, BS] b_s = tl.load(p_s, boundary_check=(0, 1)).to(tl.float32) # Apply dt_bias if exists if HAS_BIAS: p_b = tl.make_block_ptr(dt_bias + i_h * S, (S,), (1,), (i_s * BS,), (BS,), (0,)) b_bias = tl.load(p_b, boundary_check=(0,)).to(tl.float32) b_s = b_s + b_bias[None, :] b_A = tl.load(A_log + i_h).to(tl.float32) if not USE_LOWER_BOUND: # Apply gate: -exp(A_log) * softplus(g + bias) b_gate = -exp(b_A) * softplus(b_s) else: b_gate = lower_bound * tl.sigmoid(exp(b_A) * b_s) # Apply chunk local cumsum if REVERSE: b_o = tl.cumsum(b_gate, axis=0, reverse=True) else: b_o = tl.cumsum(b_gate, axis=0) if HAS_SCALE: b_o *= scale tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) @input_guard def kda_gate_chunk_cumsum( g: torch.Tensor, A_log: torch.Tensor, chunk_size: int, scale: float = None, dt_bias: torch.Tensor | None = None, cu_seqlens: torch.Tensor | None = None, output_dtype: torch.dtype | None = torch.float, chunk_indices: torch.LongTensor | None = None, lower_bound: float | None = None, **kwargs, ) -> torch.Tensor: if cu_seqlens is not None: assert g.shape[0] == 1, "Only batch size 1 is supported when cu_seqlens are provided" assert len(g.shape) == 4 B, T, H, S = g.shape BT = chunk_size if chunk_indices is None and cu_seqlens is not None: chunk_indices = prepare_chunk_indices(cu_seqlens, BT) NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices) assert chunk_size == 2**(chunk_size.bit_length()-1), "chunk_size must be a power of 2" g_org, g = g, torch.empty_like(g, dtype=output_dtype or g.dtype) def grid(meta): return (triton.cdiv(meta['S'], meta['BS']), NT, B * H) kda_gate_chunk_cumsum_vector_kernel[grid]( s=g_org, A_log=A_log, dt_bias=dt_bias, o=g, scale=scale, cu_seqlens=cu_seqlens, chunk_indices=chunk_indices, lower_bound=lower_bound, T=T, H=H, S=S, BT=BT, REVERSE=False, ) return g