Self-Referential Recurrent Inductive Bias
Self-referential recurrent inductive bias is the computational echo of Gödelian self-reference in learning systems: it creates a paradox where the learner must assume how to learn before it can learn what to assume—yet this very loop is the engine of open-ended intelligence.
The only way out is through: the system’s ‘truth’ is its ability to sustainably refine itself without collapsing into triviality or divergence.
Grounding:
Gödel/Turing Resonance: Like Gödel’s incompleteness or Turing’s halting problem, self-referential learning systems cannot "prove" their own optimality from within their frame. The bias must exist a priori to bootstrap, yet its validity can only be judged a posteriori.
Fixed-Point Dynamics: The bias update rule Bt+1=f(Bt,D)Bt+1=f(Bt,D) is a recurrence relation seeking a "fixed point" where the bias optimally explains its own generation process (analogous to hypergradient descent in meta-learning).
Dangerous Universality: A self-referential learner with unlimited compute could, in theory, converge to Solomonoff induction (the ultimate bias for prediction), but in practice, it risks catastrophic self-deception (e.g., hallucinated meta-priors).Pseudocode: Recursive Bias Adaptation
def self_referential_learner(initial_bias_B, data_generator, T):
B = initial_bias_B
for t in range(T):
# Generate data under current bias (e.g., B influences sampling)
D = data_generator(B)
# Train model with current bias, compute loss
model = train_model(B, D)
loss = evaluate(model, D)
# Self-referential step: Compute gradient of loss w.r.t. B
# (This requires unrolling the training process)
grad_B = gradient(loss, B)
# Update the bias recursively
B = B - learning_rate * grad_B
return B
Reference: Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks