DeepSeek V4.1

Size
552B + 196B Engram
Published
DeepSeek · Sep 2026
Line
New parts in the block · after DeepSeek-V3.2-Exp
Source

deepseek‑ai/DeepSeek‑V4.1‑Flash @ 2cba9e4 · parameter count checked against the checkpoint’s tensor headers · text model onlyHow to read

Indexer, re-scored

40 layers › 4 groups of 4 layers › Re-indexing layer › Compressed sparse attention › Indexer, re-scored

Index keys

×

supplied · no parametersshared_attn.index_k

Borrowed from layer 20: one 128-feature key per compressed position.

shape
KIK^{I} [B batch, T compressed positions, 128 index width]
Sources

Contextual evidence from Token group

One object hands compressed keys and values, index keys, selected positions and candidates from a source layer to the layers after it.

shared · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 1166–1180

Read code excerpt
class SharedAttentionRuntime:
    """What attention layers hand down the stack instead of recomputing. Layers run in order and
    every source writes before its consumers read, so one slot each is enough and nothing needs
    resetting between forwards. Sources: compress_kv and index_k from kv_source_layers, topk_idxs
    from index_source_layers, candidates from candidate_source_layer."""

    def __init__(self):
        self.compress_kv: torch.Tensor | None = None
        self.index_k: torch.Tensor | None = None
        self.topk_idxs: torch.Tensor | None = None
        self.candidates: torch.Tensor | None = None


# Only ever one model per process, same as world_size / rank / default_dtype above.
shared_attn = SharedAttentionRuntime()

Contextual evidence from Token group

A key–value source compresses its own input and writes the shared cache; an index source runs its indexer before the latent is rotated; every other layer reads what the nearest earlier source published.

attention-compress · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 722–763

Read code excerpt
    def _compress_topk_idxs(self, x, qr, latent, start_pos, offset, compress_len):
        """Which compressed positions each query attends to. Index sources run their own indexer;
        the layers in between reuse the result their source published."""
        if not self.is_index_source:
            return shared_attn.topk_idxs

        bsz, seqlen, _ = x.size()
        if compress_len == 0:
            idxs = torch.empty(bsz, seqlen, 0, dtype=torch.int32, device=x.device)
        else:
            assert self.indexer is not None
            if self.indexer.freqs_cis is None:
                self.indexer.freqs_cis = self.freqs_cis
            idxs = self.indexer(x, qr, latent, start_pos, offset)
        shared_attn.topk_idxs = idxs
        return idxs

    def _compress_kv(self, x, qr, start_pos, offset):
        """The shared compressed KV and the compressed positions every query may attend to. This
        layer compresses its own KV only when it is a source; otherwise it just reads the cache."""
        bsz, seqlen, _ = x.size()
        ratio = self.compress_ratio
        compress_len = (start_pos + seqlen) // ratio
        latent = None
        if self.is_kv_source:
            latent = self.compressor(x, start_pos)
            shared_attn.compress_kv = self.compress_kv_cache
        # the indexer needs the latent before RoPE, so it runs before the cache is written
        idxs = self._compress_topk_idxs(x, qr, latent, start_pos, offset, compress_len)
        if latent is not None:
            # a latent stands for the first token of its group, so group j takes position j * ratio
            freqs = (
                self.freqs_cis[: seqlen - seqlen % ratio : ratio]
                if start_pos == 0
                else self.freqs_cis[start_pos + 1 - ratio].unsqueeze(0)
            )
            apply_rotary_emb(latent[..., -self.rope_head_dim :], freqs)
            # Compressed KV uses groups of 16 with E4M3 scales; the indexer uses 32 with E8M0.
            fp4_act_quant(latent, 16, True, scale_dtype=torch.float8_e4m3fn)
            self.compress_kv_cache[:bsz, start_pos // ratio : start_pos // ratio + latent.size(1)] = latent
        # read after the write, so this does not depend on the slice aliasing the cache
        return shared_attn.compress_kv[:bsz, :compress_len], idxs

Contextual evidence from Token group

The reference configuration: 40 layers of width 5,120, 64 heads of 512 features with a 64-feature rotary part, a 1,280-feature query latent, a grouped output of 8 groups at rank 1,024, a window of 128, the per-layer compression ratios and the two source lists, the indexer and its candidate stage, hyper-connections of 4 streams, 384 routed experts of which 6 are used with 1 shared, Engram before layers 1 and 14, and three DSpark blocks.

config · deepseek-ai/DeepSeek-V4.1-Flash / inference/config.json
Pinned revision 2cba9e42aa02 ↗ · lines 1–66

Read code excerpt
{
    "vocab_size": 129280,
    "dim": 5120,
    "moe_inter_dim": 2304,
    "n_layers": 40,
    "n_mtp_layers": 3,
    "dspark_block_size": 5,
    "dspark_noise_token_id": 128799,
    "dspark_target_layer_ids": [37, 38, 39],
    "dspark_markov_rank": 256,
    "dspark_n_routed_experts": 128,
    "dspark_n_activated_experts": 3,
    "n_heads": 64,
    "n_routed_experts": 384,
    "n_shared_experts": 1,
    "n_activated_experts": 6,
    "score_func": "sqrtsoftplus",
    "route_scale": 1.5,
    "swiglu_limit": 10.0,
    "q_lora_rank": 1280,
    "head_dim": 512,
    "rope_head_dim": 64,
    "norm_eps": 1e-20,
    "o_groups": 8,
    "o_lora_rank": 1024,
    "window_size": 128,
    "kv_source_layers": [2, 8, 14, 20],
    "index_source_layers": [2, 8, 14, 20, 24, 28, 32, 36],
    "original_seq_len": 65536,
    "rope_theta": 10000,
    "rope_factor": 16,
    "beta_fast": 32,
    "beta_slow": 1,
    "index_n_heads": 32,
    "index_head_dim": 128,
    "index_topk": 512,
    "candidate_source_layer": 20,
    "candidate_topk_blocks": 2048,
    "candidate_block_size": 8,
    "hc_mult": 4,
    "hc_sinkhorn_iters": 20,
    "hc_eps": 1e-06,
    "engram_layer_ids": [1, 14],
    "engram_vocab_size": 16000000,
    "engram_num_embeddings": [384006168, 384016682],
    "engram_max_ngram_size": 4,
    "engram_pad_id": 2,
    "engram_compressed_vocab_size": 99092,
    "dtype": "fp8",
    "expert_dtype": "fp4",
    "compress_rope_theta": 160000,
    "compress_ratios": [0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
    "vision_n_layers": 32,
    "vision_dim": 1024,
    "vision_n_heads": 16,
    "vision_inter_dim": 2816,
    "vision_patch_size": 14,
    "vision_downsample_ratio": 3,
    "vision_max_n_token": 1024,
    "vision_min_pixels": 295936,
    "vision_max_wh_ratio": null,
    "image_token_id": 129264,
    "engram_n_heads": 8,
    "engram_head_dim": 256,
    "vision_rope_theta": 10000
}

Contextual evidence from Re-indexing layer

A block owns its attention and mixture, two RMSNorms, and for each sublayer a projection of the flattened streams to 24 mix numbers with 24 offsets and 3 scales.

block-init · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 907–946

Read code excerpt
class Block(nn.Module):
    """A block whose residual stream is `hc_mult` parallel copies (Hyper-Connections).

    Attention and FFN each sit between `hc_pre` (collapse the copies into one sublayer input) and
    `hc_post` (expand back out, mixing the residual in through `comb`). `hc_mixes` derives all three
    coefficient sets from the stream itself, `comb` made doubly stochastic by Sinkhorn.

    The coefficients a sublayer computes are used by the *next* one -- see `forward`.
    """

    attention_cls = Attention

    def __init__(
        self,
        layer_id: int,
        args: ModelArgs,
        engram_layout: EngramLayout | None = None,
    ):
        super().__init__()
        self.layer_id = layer_id
        self.norm_eps = args.norm_eps
        self.attn = self.attention_cls(layer_id, args)
        self.ffn = MoE(layer_id, args)
        self.engram = None
        if engram_layout is not None and layer_id in engram_layout.layer_ids:
            self.engram = Engram(args, layer_id, engram_layout)
        self.attn_norm = RMSNorm(args.dim, self.norm_eps)
        self.ffn_norm = RMSNorm(args.dim, self.norm_eps)
        self.hc_mult = hc_mult = args.hc_mult
        self.hc_sinkhorn_iters = args.hc_sinkhorn_iters
        self.hc_eps = args.hc_eps
        mix_hc = (2 + hc_mult) * hc_mult
        hc_dim = hc_mult * args.dim
        with set_dtype(torch.float32):
            self.hc_attn_fn = nn.Parameter(torch.empty(mix_hc, hc_dim))
            self.hc_ffn_fn = nn.Parameter(torch.empty(mix_hc, hc_dim))
            self.hc_attn_base = nn.Parameter(torch.empty(mix_hc))
            self.hc_ffn_base = nn.Parameter(torch.empty(mix_hc))
            self.hc_attn_scale = nn.Parameter(torch.empty(3))
            self.hc_ffn_scale = nn.Parameter(torch.empty(3))

Contextual evidence from Re-indexing layer

Attention reads the streams with the mix the previous sublayer computed and writes with its own; the mixture reads with the mix attention computed and writes with its own, and hands its reading mix to the next layer.

block-forward · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 968–994

Read code excerpt
    def forward(
        self,
        x: torch.Tensor,
        start_pos: int,
        pre_mix: torch.Tensor,
        image_mask: torch.Tensor | None,
        *attn_args,
    ) -> tuple[torch.Tensor, torch.Tensor]:
        """`pre_mix` collapses the hc_mult copies down to one input for this block's attention. Each
        sub-block's own `hc_mixes` produces the mix for the *next* one, so attention uses what the
        previous layer's FFN produced and the FFN uses what this attention produced.

        image_mask: [b, s] bool, True inside image spans (selects the VL routing bias)."""
        residual = x
        attn_pre, attn_post, attn_comb = self.hc_mixes(x, self.hc_attn_fn, self.hc_attn_scale, self.hc_attn_base)
        x = self.hc_pre(x, pre_mix)
        x = self.attn_norm(x)
        x = self.attn(x, start_pos, *attn_args)
        x = self.hc_post(x, residual, attn_post, attn_comb)

        residual = x
        ffn_pre, ffn_post, ffn_comb = self.hc_mixes(x, self.hc_ffn_fn, self.hc_ffn_scale, self.hc_ffn_base)
        x = self.hc_pre(x, attn_pre)
        x = self.ffn_norm(x)
        x = self.ffn(x, image_mask)
        x = self.hc_post(x, residual, ffn_post, ffn_comb)
        return x, ffn_pre

Contextual evidence from Re-indexing layer

The mix numbers are a projection of the flattened streams divided by their root mean square; reading is a weighted sum of the streams; writing adds the sublayer output, weighted per stream, to a combination of the streams.

block-hc · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 948–966

Read code excerpt
    def hc_mixes(self, x: torch.Tensor, hc_fn: torch.Tensor, hc_scale: torch.Tensor, hc_base: torch.Tensor):
        """x: [b,s,hc,d], hc_fn: [mix_hc, hc*d], hc_scale: [3], hc_base: [mix_hc]. Returns the
        pre / post / comb coefficients, split out of one projection of the flattened stream."""
        # normalized over the whole flattened hc*d stream, one statistic per token
        x = x.flatten(2).float()
        rsqrt = torch.rsqrt(x.square().mean(-1, keepdim=True) + self.norm_eps)
        mixes = F.linear(x, hc_fn) * rsqrt
        return hc_split_sinkhorn(mixes, hc_scale, hc_base, self.hc_mult, self.hc_sinkhorn_iters, self.hc_eps)

    def hc_pre(self, x: torch.Tensor, pre_mix: torch.Tensor):
        """Collapse the hc copies into one, weighted by pre_mix. [b,s,hc,d] x [b,s,hc] -> [b,s,d]"""
        y = torch.sum(pre_mix.unsqueeze(-1) * x.float(), dim=2)
        return y.to(x.dtype)

    def hc_post(self, x: torch.Tensor, residual: torch.Tensor, post: torch.Tensor, comb: torch.Tensor):
        """Expand the sublayer output back to hc copies and mix the residual in through `comb`.
        x: [b,s,d], residual: [b,s,hc,d], post: [b,s,hc], comb: [b,s,hc,hc] -> [b,s,hc,d]"""
        y = post.unsqueeze(-1) * x.unsqueeze(-2) + torch.sum(comb.unsqueeze(-1) * residual.unsqueeze(-2), dim=2)
        return y.type_as(x)

Contextual evidence from Compressed sparse attention

Attention owns a low-rank query, one key–value projection, a learned sink per head, a grouped low-rank output, a ring buffer for the window, and, by the two source lists, a compressor and an indexer; layers that attend to compressed positions use the larger rotary base with YaRN.

attention-init · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 613–698

Read code excerpt
class Attention(nn.Module):
    """Latent attention over two KV sources at once, concatenated into one `sparse_attn` call: a
    sliding window of raw KV, plus -- when compress_ratio > 0 -- `index_topk` compressed positions
    reaching further back. Q and the output projection are both low-rank, the latter grouped.

    compress_ratio > 0 does not mean the layer compresses its own KV: only kv_source_layers do,
    the rest read that same cache.
    """

    def __init__(self, layer_id: int, args: ModelArgs):
        super().__init__()
        self.layer_id = layer_id
        self.dim = args.dim
        self.n_heads = args.n_heads
        self.n_local_heads = args.n_heads // world_size
        self.q_lora_rank = args.q_lora_rank
        self.o_lora_rank = args.o_lora_rank
        self.head_dim = args.head_dim
        self.rope_head_dim = args.rope_head_dim
        self.nope_head_dim = args.head_dim - args.rope_head_dim
        self.n_groups = args.o_groups
        self.n_local_groups = self.n_groups // world_size
        self.window_size = args.window_size
        self.compress_ratio = args.compress_ratios[layer_id]
        self.eps = args.norm_eps

        self.attn_sink = nn.Parameter(torch.empty(self.n_local_heads, dtype=torch.float32))
        self.wq_a = Linear(self.dim, self.q_lora_rank)
        self.q_norm = RMSNorm(self.q_lora_rank, self.eps)
        self.wq_b = ColumnParallelLinear(self.q_lora_rank, self.n_heads * self.head_dim)
        self.wkv = Linear(self.dim, self.head_dim)
        self.kv_norm = RMSNorm(self.head_dim, self.eps)
        self.wo_a = ColumnParallelLinear(
            self.n_heads * self.head_dim // self.n_groups,
            self.n_groups * args.o_lora_rank,
            dtype=torch.bfloat16,
        )
        self.wo_b = RowParallelLinear(self.n_groups * args.o_lora_rank, self.dim)
        self.softmax_scale = self.head_dim**-0.5

        is_backbone = layer_id < args.n_layers
        self.is_kv_source = is_backbone and layer_id in args.kv_source_layers
        self.is_index_source = is_backbone and layer_id in args.index_source_layers
        self.compressor: Compressor | None = None
        self.indexer: Indexer | None = None
        if self.is_kv_source:
            self.compressor = Compressor(args, layer_id)
        if self.is_index_source:
            self.indexer = Indexer(args, layer_id)

        self.window_kv_cache: torch.Tensor
        self.register_buffer(
            "window_kv_cache",
            torch.zeros(args.max_batch_size, args.window_size, self.head_dim),
            persistent=False,
        )
        if self.is_kv_source:
            self.compress_kv_cache: torch.Tensor
            self.register_buffer(
                "compress_kv_cache",
                torch.zeros(
                    args.max_batch_size,
                    args.max_seq_len // self.compress_ratio,
                    self.head_dim,
                ),
                persistent=False,
            )
        if self.compress_ratio:
            original_seq_len, rope_theta = (
                args.original_seq_len,
                args.compress_rope_theta,
            )
        else:
            # disable YaRN and use base rope_theta in pure sliding-window attention
            original_seq_len, rope_theta = 0, args.rope_theta
        freqs_cis = precompute_freqs_cis(
            self.rope_head_dim,
            args.max_seq_len,
            original_seq_len,
            rope_theta,
            args.rope_factor,
            args.beta_fast,
            args.beta_slow,
        )
        self.freqs_cis: torch.Tensor
        self.register_buffer("freqs_cis", freqs_cis, persistent=False)

Contextual evidence from Compressed sparse attention

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

Contextual evidence from Indexer, re-scored

The indexer scores every compressed position for every query with few small heads against one shared key, masks what the query may not see, and keeps the best 512; the candidate source also publishes its candidate blocks, and later indexers score inside them.

indexer · deepseek-ai/DeepSeek-V4.1-Flash / inference/model.py
Pinned revision 2cba9e42aa02 ↗ · lines 488–580

Read code excerpt
class Indexer(torch.nn.Module):
    """Keeps the `index_topk` best compressed positions per query.

    A small side attention: fp4 query heads against one shared key per compressed position, scores
    rectified then combined by `weights_proj`. With a candidate source this is the second of two
    levels; `select_candidate_blocks` is the first.
    """

    def __init__(self, args: ModelArgs, layer_id: int):
        super().__init__()
        # the index keys are derived from the compressor's latent, so only a layer that compresses
        # its own KV can produce them; every other indexer reads them from that layer's cache
        self.owns_k = layer_id in args.kv_source_layers
        self.compress_ratio = args.compress_ratios[layer_id]
        self.is_candidate_source = layer_id == args.candidate_source_layer
        self.uses_candidates = 0 <= args.candidate_source_layer < layer_id
        self.candidate_topk_blocks = args.candidate_topk_blocks
        self.candidate_block_size = args.candidate_block_size
        self.dim = args.dim
        self.n_heads = args.index_n_heads
        self.n_local_heads = args.index_n_heads // world_size
        self.index_head_dim = args.index_head_dim
        self.rope_head_dim = args.rope_head_dim
        self.index_topk = args.index_topk
        self.q_lora_rank = args.q_lora_rank
        self.softmax_scale = self.index_head_dim**-0.5
        self.wq_b = ColumnParallelLinear(self.q_lora_rank, self.n_heads * self.index_head_dim)
        self.weights_proj = ColumnParallelLinear(self.dim, self.n_heads, dtype=torch.bfloat16)
        self.freqs_cis: torch.Tensor | None = None
        if self.owns_k:
            self.wk = Linear(args.head_dim, self.index_head_dim, dtype=torch.bfloat16)
            self.k_norm = RMSNorm(self.index_head_dim, args.norm_eps)
            self.k_cache: torch.Tensor
            self.register_buffer(
                "k_cache",
                torch.zeros(args.max_batch_size, args.max_seq_len // self.compress_ratio, args.index_head_dim),
                persistent=False,
            )

    def forward(self, x: torch.Tensor, qr: torch.Tensor, latent: torch.Tensor, start_pos: int, offset: int):
        """`latent` is this layer's RoPE-free compressed latent, None when this layer does not
        compress or when its current group is still incomplete. An index-key owner turns it into
        index keys here, which has to happen before Attention overwrites that same storage with
        the RoPE'd, quantized values."""
        assert self.freqs_cis is not None
        bsz, seqlen, _ = x.size()
        ratio, rd, end_pos = self.compress_ratio, self.rope_head_dim, start_pos + seqlen

        # latent is None while a group is still filling up, so there is nothing to publish yet
        if self.owns_k and latent is not None:
            # a latent stands for the first token of its group, so group j takes position j * ratio
            freqs = (
                self.freqs_cis[: seqlen - seqlen % ratio : ratio]
                if start_pos == 0
                else self.freqs_cis[start_pos + 1 - ratio].unsqueeze(0)
            )
            k = self.k_norm(self.wk(latent))
            apply_rotary_emb(k[..., -rd:], freqs)
            fp4_act_quant(k, fp4_block_size, True)
            self.k_cache[:bsz, start_pos // ratio : start_pos // ratio + k.size(1)] = k
            shared_attn.index_k = self.k_cache

        q = self.wq_b(qr).unflatten(-1, (self.n_local_heads, self.index_head_dim))
        apply_rotary_emb(q[..., -rd:], self.freqs_cis[start_pos:end_pos])
        fp4_act_quant(q, fp4_block_size, True)

        index_k = shared_attn.index_k[:bsz, : end_pos // ratio]
        weights = self.weights_proj(x) * (self.softmax_scale * self.n_heads**-0.5)
        index_score = torch.einsum("bshd,btd->bsht", q, index_k)
        index_score = (index_score.relu_() * weights.unsqueeze(-1)).sum(dim=2)
        if world_size > 1:
            dist.all_reduce(index_score)

        # how many compressed positions each query can see: a block becomes visible once the query
        # has passed its last token. One query per decode step, so there it is just a number.
        if start_pos == 0:
            compress_lens = (torch.arange(1, seqlen + 1, device=x.device) // ratio).unsqueeze(-1)
            index_score.masked_fill_(torch.arange(seqlen // ratio, device=x.device) >= compress_lens, -torch.inf)
        else:
            compress_lens = end_pos // ratio

        if self.is_candidate_source:
            shared_attn.candidates = select_candidate_blocks(
                index_score, compress_lens, self.candidate_topk_blocks, self.candidate_block_size
            )
        elif self.uses_candidates:
            # level two: score with our own weights, but only inside the source's candidate blocks
            index_score = index_score.masked_fill(~shared_attn.candidates, -torch.inf)

        # top-k by score, re-sorted into position order; unreachable -> -1, rest shifted by offset
        topk = min(self.index_topk, end_pos // ratio)
        idxs = index_score.topk(topk, dim=-1, sorted=False).indices.sort(dim=-1).values
        return torch.where(idxs < compress_lens, idxs + offset, -1).int()

Contextual evidence from Indexer, re-scored

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