DeepSeek V4.1 · Split heads, rotate

40 layers › 2 groups of 6 layers › 5 reusing layers › Compressed sparse attention › Query heads

Split heads, rotate

no parametersq.unflatten(…); apply_rotary_emb(q[..., -rd:], freqs_cis) · 771–772

Split into 64 heads and rotate each head’s last 64 features by its position.

[B,\,T,\,32768]\;\to\;[B,\,64,\,T,\,512]

{\htmlClass{vl-stream-q}{Q_{\ldots,448:}}}\leftarrow {\htmlClass{vl-stream-context}{R_t}}\,{\htmlClass{vl-stream-q}{Q_{\ldots,448:}}}

in: $q$ [B batch, T positions, 32768 heads × d_h]
out: $Q$ [B batch, 64 heads, T positions, 512 d_h]

Rotate the last 64 features of each head by position, in pairs (model.py 392–406), with base 160,000 and YaRN scaling. The reference keeps positions before heads, [B, T, 64, 512] (model.py 771); the atlas writes the head axis first, here and in the states after it.

Codemodel.py 369–406, 765–789

model.py 765–789

    def forward(self, x: torch.Tensor, start_pos: int):
        bsz, seqlen, _ = x.size()
        freqs_cis = self.freqs_cis[start_pos : start_pos + seqlen]
        rd = self.rope_head_dim

        qr = self.q_norm(self.wq_a(x))
        q = self.wq_b(qr).unflatten(-1, (self.n_local_heads, self.head_dim))
        apply_rotary_emb(q[..., -rd:], freqs_cis)

        kv, topk_idxs = self._window_kv(x, freqs_cis, start_pos)
        if self.compress_ratio:
            compress_kv, compress_idxs = self._compress_kv(x, qr, start_pos, kv.size(1))
            kv = torch.cat([kv, compress_kv], dim=1)
            topk_idxs = torch.cat([topk_idxs, compress_idxs], dim=-1)

        o = sparse_attn(q, kv, self.attn_sink, topk_idxs, self.softmax_scale)
        apply_rotary_emb(o[..., -rd:], freqs_cis, True)

        # wo_a is block-diagonal over groups (each projects only its own heads), hence einsum not
        # Linear. convert.py dequantizes it to bf16; an fp8 grouped GEMM would halve the memory.
        o = o.view(bsz, seqlen, self.n_local_groups, -1)
        wo_a = self.wo_a.weight.view(self.n_local_groups, self.o_lora_rank, -1)
        o = torch.einsum("bsgd,grd->bsgr", o, wo_a)
        x = self.wo_b(o.flatten(2))
        return x

model.py 369–406

def precompute_freqs_cis(dim, seqlen, original_seq_len, base, factor, beta_fast, beta_slow) -> torch.Tensor:
    """Rotary frequencies as complex exponentials, one row per position.

    With original_seq_len > 0 this applies YaRN: dimensions whose wavelength already fits inside the
    training context keep their frequency, those far beyond it are divided by `factor`, and the
    `beta_fast`..`beta_slow` band in between is faded across with a linear ramp.
    """
    freqs = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32) / dim))
    if original_seq_len > 0:
        # the dim whose wavelength completes `rotations` turns over the training context
        def corrected_dim(rotations):
            return dim * math.log(original_seq_len / (rotations * 2 * math.pi)) / (2 * math.log(base))

        low = max(math.floor(corrected_dim(beta_fast)), 0)
        high = min(math.ceil(corrected_dim(beta_slow)), dim - 1)
        ramp = ((torch.arange(dim // 2, dtype=torch.float32) - low) / max(high - low, 1e-3)).clamp(0, 1)
        smooth = 1 - ramp
        freqs = freqs / factor * (1 - smooth) + freqs * smooth

    freqs = torch.outer(torch.arange(seqlen), freqs)
    return torch.polar(torch.ones_like(freqs), freqs)


def apply_rotary_emb(x: torch.Tensor, freqs_cis: torch.Tensor, inverse: bool = False) -> torch.Tensor:
    """Rotate `x` in place, taking adjacent element pairs as complex numbers. Accepts [b, s, d] and
    [b, s, h, d]; `inverse` conjugates the rotation, which is how the attention output gets the
    query's rotation removed again so the cache can stay in one shared rotated form."""
    y = x
    x = torch.view_as_complex(x.float().unflatten(-1, (-1, 2)))
    if inverse:
        freqs_cis = freqs_cis.conj()
    if x.ndim == 3:
        freqs_cis = freqs_cis.view(1, x.size(1), x.size(-1))
    else:
        freqs_cis = freqs_cis.view(1, x.size(1), 1, x.size(-1))
    x = torch.view_as_real(x * freqs_cis).flatten(-2)
    y.copy_(x)
    return y

Sources2

Direct evidence

Queries through the latent with their rotary part rotated; window and compressed keys and values joined; sparse attention over the listed positions; the output rotated back, projected per group of heads and then to the model width.

attention-forward · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 765–789

Read code excerpt

    def forward(self, x: torch.Tensor, start_pos: int):
        bsz, seqlen, _ = x.size()
        freqs_cis = self.freqs_cis[start_pos : start_pos + seqlen]
        rd = self.rope_head_dim

        qr = self.q_norm(self.wq_a(x))
        q = self.wq_b(qr).unflatten(-1, (self.n_local_heads, self.head_dim))
        apply_rotary_emb(q[..., -rd:], freqs_cis)

        kv, topk_idxs = self._window_kv(x, freqs_cis, start_pos)
        if self.compress_ratio:
            compress_kv, compress_idxs = self._compress_kv(x, qr, start_pos, kv.size(1))
            kv = torch.cat([kv, compress_kv], dim=1)
            topk_idxs = torch.cat([topk_idxs, compress_idxs], dim=-1)

        o = sparse_attn(q, kv, self.attn_sink, topk_idxs, self.softmax_scale)
        apply_rotary_emb(o[..., -rd:], freqs_cis, True)

        # wo_a is block-diagonal over groups (each projects only its own heads), hence einsum not
        # Linear. convert.py dequantizes it to bf16; an fp8 grouped GEMM would halve the memory.
        o = o.view(bsz, seqlen, self.n_local_groups, -1)
        wo_a = self.wo_a.weight.view(self.n_local_groups, self.o_lora_rank, -1)
        o = torch.einsum("bsgd,grd->bsgr", o, wo_a)
        x = self.wo_b(o.flatten(2))
        return x

Direct evidence

Rotary frequencies with the YaRN scaling above the original context, and the rotation of adjacent feature pairs, with an inverse.

rope · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 369–406

Read code excerpt

def precompute_freqs_cis(dim, seqlen, original_seq_len, base, factor, beta_fast, beta_slow) -> torch.Tensor:
    """Rotary frequencies as complex exponentials, one row per position.

    With original_seq_len > 0 this applies YaRN: dimensions whose wavelength already fits inside the
    training context keep their frequency, those far beyond it are divided by `factor`, and the
    `beta_fast`..`beta_slow` band in between is faded across with a linear ramp.
    """
    freqs = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32) / dim))
    if original_seq_len > 0:
        # the dim whose wavelength completes `rotations` turns over the training context
        def corrected_dim(rotations):
            return dim * math.log(original_seq_len / (rotations * 2 * math.pi)) / (2 * math.log(base))

        low = max(math.floor(corrected_dim(beta_fast)), 0)
        high = min(math.ceil(corrected_dim(beta_slow)), dim - 1)
        ramp = ((torch.arange(dim // 2, dtype=torch.float32) - low) / max(high - low, 1e-3)).clamp(0, 1)
        smooth = 1 - ramp
        freqs = freqs / factor * (1 - smooth) + freqs * smooth

    freqs = torch.outer(torch.arange(seqlen), freqs)
    return torch.polar(torch.ones_like(freqs), freqs)


def apply_rotary_emb(x: torch.Tensor, freqs_cis: torch.Tensor, inverse: bool = False) -> torch.Tensor:
    """Rotate `x` in place, taking adjacent element pairs as complex numbers. Accepts [b, s, d] and
    [b, s, h, d]; `inverse` conjugates the rotation, which is how the attention output gets the
    query's rotation removed again so the cache can stay in one shared rotated form."""
    y = x
    x = torch.view_as_complex(x.float().unflatten(-1, (-1, 2)))
    if inverse:
        freqs_cis = freqs_cis.conj()
    if x.ndim == 3:
        freqs_cis = freqs_cis.view(1, x.size(1), x.size(-1))
    else:
        freqs_cis = freqs_cis.view(1, x.size(1), 1, x.size(-1))
    x = torch.view_as_real(x * freqs_cis).flatten(-2)
    y.copy_(x)
    return y