🧠 D: DOCUMENT — Problem & Opportunity

SKaiNET ships a Gru recurrent layer but no LSTM. Two concrete consumers are blocked:

1. Parakeet FastConformer-TDT ASR (SKaiNET-parakeet): the TDT prediction network is a
   2-layer LSTM (hidden 640). This blocks running nvidia/parakeet-tdt-0.6b-v3 and the German
   primeline/parakeet-primeline on the SKaiNET stack.
2. Silero VAD (coraldevboard PLAN item 4.1): "needs new LSTM layer upstream (GRU is the
   template)" — the last runtime-Python piece of the SL2610 demo.

Transducer-style decoding additionally needs a single-step form: one token at a time with
the recurrent state (h, c) carried by the caller — which is also exactly the shape that lowers
to a fixed-shape StableHLO graph (state as graph I/O, no loop construct needed).

Summary: Add Lstm to skainet-lang-core mirroring Gru (unrolled, primitive-ops-only),
plus an explicit-state step() API (LstmState) required by transducer decoders.

🔍 A: ASSESS — Feasibility & Impact

✔️ Feasibility

• Direct analog of Gru.kt: built from existing primitives (matmul/add/narrow/sigmoid/tanh/ multiply/reshape/unsqueeze/concat) — no new TensorOps op, no new converter; traces to
  StableHLO exactly like Gru.
• One extra state tensor (cell c) vs Gru; 4 gates vs 3.

✔️ Expected Impact

• Unblocks Parakeet-TDT and Silero VAD; completes the recurrent-layer pair (GRU+LSTM).
• The step()/LstmState pattern establishes the idiom for streaming/transducer models.

✔️ Risks / Constraints

• Gate order: PyTorch order i, f, g, o must be pinned in docs and tests, or imported
  weights silently produce garbage.
• Dual biases: PyTorch keeps b_ih and b_hh separately; keep both for weight-map fidelity
  (mathematically summable).
• API consistency: constructor/parameter naming mirrors Gru exactly (matmul-ready [in, 4H]
  / [H, 4H] weights).

✔️ Dependencies

• None beyond skainet-lang-core primitives. Autodiff via the standard tape (unrolled).

📚 R: RESEARCH — What Must Be Understood First?

• torch.nn.LSTM contract: gate order i,f,g,o; weight_ih_l{k} [4H, in], weight_hh_l{k} [4H, H], dual biases; recurrence
  c' = f⊙c + i⊙tanh(g), h' = o⊙tanh(c') — https://docs.pytorch.org/docs/stable/generated/torch.nn.LSTM.html
• Hochreiter & Schmidhuber (1997), Long Short-Term Memory, Neural Computation 9(8).
• Gru.kt as the in-repo design template (unroll-at-trace-time, matmul-ready weights).
• NeMo RNNT/TDT prediction network uses torch.nn.LSTM (stacked, batch-first) — weight
  import must be layer-by-layer single-layer cells to keep the step() API.
• Open question: also add a symmetric Gru.step()/GruState in the same PR? (proposed: yes,
  follow-up acceptable)

🛠️ C: CODE — Implementation Plan

Development Tasks

• skainet-lang-core/.../nn/Lstm.kt: Lstm<T, V> module — sequence forward
  [B,S,in] → [B,S,H] (unrolled, h0=c0=0) + step(xt, state, ctx): Pair<out, LstmState>
  + LstmState<T, V>(h, c) + initialState(batch, ctx)
• Numeric test vs independent scalar reference (mirrors GruTest in skainet-backend-cpu)
• step() consistency test: sequence forward == iterated step() outputs
• KDoc with gate math + PyTorch import notes (transpose to matmul-ready)
• .api dump sync (apiCheck)
• PR referencing this issue (Gitflow: feature/lstm-layer → develop)

Acceptance Criteria

• Parity vs torch.nn.LSTM golden ≤ 1e-5 (G2 gate of SKaiNET-parakeet)
• Traces to StableHLO with zero Unsupported ops (conformance row lstm-step planned)
• KtLint/Detekt/CI green; no regressions