Tesla interview questions

RNNs carry one hidden state step by step: cheap per step, but sequential, and gradients vanish over long spans. LSTMs add gates and a cell state so information survives longer. Transformers attend over all steps in parallel, train faster and capture long range, at cost quadratic in length; for streaming prediction I'd pick a causal decoder.

MPC is different: it uses a dynamics model to optimise actions over a short horizon, applies the first and replans. A learned sequence model can be that dynamics model or forecaster, while MPC enforces constraints.

Have the forward pass cache what the backward pass needs: the softmax probabilities P.

def attn_fwd(Q, K, V):              # (T, d) each
    S = Q @ K.T / np.sqrt(Q.shape[-1])
    S = S - S.max(-1, keepdims=True)
    P = np.exp(S)
    P /= P.sum(-1, keepdims=True)
    return P @ V, P

def attn_bwd(dO, Q, K, V, P):
    dV = P.T @ dO
    dP = dO @ V.T
    dS = P * (dP - (dP * P).sum(-1, keepdims=True))
    dS /= np.sqrt(Q.shape[-1])
    return dS @ K, dS.T @ Q, dV     # dQ, dK, dV

The key line is the softmax backward: each row's gradient is P times dP minus its P-weighted mean. Multi-head attention reshapes into heads around this, and a block adds residuals, LayerNorm and an MLP, each with its own backward. Prove it with a finite-difference gradient check.

Each output channel has one kernel spanning all input channels, so weights are in-channels times out-channels times kernel height times width. Bias adds one per output channel.

Example: 3 in, 64 out, 3 by 3 kernel gives 1,728 weights, 1,792 with bias. Groups divide the weight count.

PPO is stable and simple on-policy; SAC is off-policy and more sample-efficient, which matters when simulation is expensive.

Reward progress along the route, penalise speed above the limit with a penalty that grows with the excess, and add small penalties for jerk and harsh braking. Make collisions and red lights terminations or hard constraints, for example via a Lagrangian method, not weights the agent can trade away. Against exploits: reward route progress, not raw speed, so circling earns nothing; bound per-step rewards; and inspect rollouts for reward hacking in adversarial simulated scenarios.