Skip to content

Exploring Quantum Mechanics Analogies in ILQL for NLP

Posted on:November 22, 2023 at 10:00 PM

In the realm of NLP, the paper “Offline RL for Natural Language Generation with Implicit Language Q Learning” presents a novel method, ILQL, with fascinating analogies to quantum mechanics.

Quantum Concepts in ILQL

The paper’s approach to NLP through ILQL finds striking parallels in quantum physics, particularly in how systems evolve and are measured.

  1. POMDP as Quantum Measurement:

    • In ILQL, POMDPs represent the environment’s partial observability, similar to how quantum measurements provide limited information due to the probabilistic nature of quantum states. This mirrors the uncertainty principle in quantum mechanics.
    • Quantum Measurement
  2. Bellman Equation and Schrödinger Equation:

    • The Bellman equation in ILQL, used for calculating the optimal policy, shares conceptual similarities with the Schrödinger equation. Both describe system evolution: the former for value functions over time, and the latter for wave functions.
    • Schrödinger Equation
  3. Expectile Regression and Quantum Superposition:

    • ILQL’s use of expectile regression to approximate Bellman optimality is akin to quantum superposition. It involves considering multiple potential outcomes, paralleling states in superposition in quantum theory.
    • Quantum Superposition
  4. Q-Function as Probability Amplitude:

    • The Q-function, predicting expected returns of actions, is analogous to the probability amplitude, predicting particle states in quantum mechanics.
    • Probability Amplitude

Hilbert Space and Decision-Making in ILQL

Some of the Decision-Making system made me think of exploring a Hilbert space.

Offline RL and Static Dataset Analysis

Learning from a static dataset in offline RL is compared to analyzing historical quantum data. This resembles the method of inferring the behavior of quantum systems from past experimental results.

Policy Extraction and Value Function

  1. Policy Extraction as Quantum State Collapse:

    • In ILQL, policy extraction influenced by value functions can be likened to the collapse of a quantum state during measurement.
    • Quantum State Collapse
  2. Value Function as Wave Function:

    • The RL value function, directing policy actions, is similar to a quantum wave function guiding particle probabilities.
    • Wave Function

Temporal Compositionality and Quantum Entanglement

ILQL’s emphasis on the interdependence of past, present, and future states in decision-making can be related to the phenomenon of quantum entanglement, where particles remain interconnected despite distances.


This paper is cool and does require some pretty deep math and ML knowlegde but I think once you have this foundation it can be rewarding to think and draw parallels to other fields. Such interdisciplinary connections open new avenues for innovation and understanding in both fields.

Read the full paper here for a comprehensive insight: Offline RL with ILQL.