Inductive bias

Overview

An inductive bias is any preference a learner has over functions beyond the training data. The paper's starting point is that some such preference is needed to generalize at all, and that test data drawn from the training distribution cannot reveal a bias toward that distribution 2011.15091 §2. Without assumptions about how training and test distributions relate, nothing can be said about a changed distribution 2011.15091 §1.1.

The paper argues that data, compute and architecture alone are not enough, and that deep learning needs extra biases to generalize out of distribution and systematically 2011.15091 §1 2011.15091 tab. 2. The biases it proposes are taken from high-level, conscious cognition: variables that can be put into words, that change sparsely, and that combine through a sparse structure. It presents these as hypotheses and as an open research direction, not as a tested method 2011.15091 §1.

Variants

Here "variant" means one of the paper's proposed biases. They are design arguments that can be combined, and the paper does not test any of them alone or together.

Verbalisable causal variables

Representations should be built from high-level variables, which the paper says are generally verbalizable and often causal 2011.15091 §3.4 2011.15091 §3.5. Attention is read as a soft form of variable binding, but the paper says discrete typed arguments and hard choices are missing 2011.15091 §3.2. See attention mechanism.

Sparse, local changes

Most distribution shifts come from one or a few variables or mechanisms, and interventions start at one or a few nodes of the causal graph 2011.15091 §3.6. A model that assumes this should adapt by changing only the parts that moved.

Stable and fast knowledge

Stable knowledge is learned slowly and shared, and volatile knowledge is learned fast and is the only part that needs adapting. The paper says this needs at least two learning speeds, like the outer and inner loops of meta-learning 2011.15091 §3.7 2011.15091 §2.

Sparse factor graph

The joint distribution over high-level variables should be a sparse factor graph, not a set of independent marginals. The paper ties this sparsity to the small capacity of a global-workspace bottleneck 2011.15091 §3.8 2011.15091 §3.3.

Reusable schemas

Knowledge is written as schemas whose argument variables are bound to instances, so one rule covers many objects and is not stored per instance 2011.15091 §3.9.

Short causal chains

Learning and inference chains should be short in depth, even when the events they link are far apart in time 2011.15091 §3.10. The authors say earlier work they cite found this the strongest remedy for vanishing gradients over long dependencies 2011.15091 §3.10.

Top-down and bottom-up combination

Top-down context should combine with bottom-up sensory signals dynamically, at every level of the hierarchy 2011.15091 §3.11.

Independent mechanisms

Intervening on one mechanism should not change the others, and knowing one mechanism should say nothing about another 2011.15091 §4.1. The paper states the structural causal model behind this in 2011.15091 §4 eq. 1 and 2011.15091 §4 eq. 2.

Use non-stationarity

Data should not be shuffled into an i.i.d. sample, because changes between sources carry causal information 2011.15091 §4.2.

When to use which

The paper reports no experiments, so none of these rows is backed by a measured comparison. The rows follow the paper's own conditions for each bias.

Implementation sketch

The paper gives no training algorithm. The sketch below only shows how one of its formal objects, the structural causal model, can be sampled. Its order is a standard topological order, not the paper's procedure 2011.15091 §4 eq. 2.

# Sample one joint draw from a structural causal model
# Input:  parents[i] for each of M variables, from the DAG
#         functions[i], noise_samplers[i]
# Output: values of X_1..X_M for one draw

def sample_scm(parents, functions, noise_samplers):
    # One independent noise per variable  [arxiv:2011.15091 §4 eq. 2]
    noises = [draw(noise_samplers[i]) for i in range(M)]
    values = [None] * M
    # Visit variables so each parent is set before its children
    for i in topological_order(parents):
        # X_i := f_i(parents of i, N_i)  [arxiv:2011.15091 §4 eq. 2]
        values[i] = functions[i](values[parents[i]], noises[i])
    return values

Contradictions

Only one paper card covers this concept, so there is no conflict between cards. The paper does argue against an assumption that is common in disentangling work: it rejects treating high-level variables as marginally independent and asks for a sparse joint structure instead 2011.15091 §3.8. See disentangled representation. The paper also says its compositional biases may be worth "even possibly exponentially more data", without a derivation 2011.15091 §2. The paper does not resolve these points.

Papers

• Inductive Biases for Deep Learning of Higher-Level Cognition: position paper that proposes nine inductive biases from conscious, causal processing for out-of-distribution and systematic generalization. No experiments.