In this note, you have an answer proposition for the following questions, as well as a terminology table below
Problem statement
- What is DIRAC supposed to do?
- What does ORBIT naturally compute?
- Why is there a gap between undirected sampling and directed causal inference?
- What exactly must be proven for active clamping to be credible?
- What hardware assumptions are required for the proposed compiler pipeline?
- Under what conditions might physical clamping be equivalent to intervention?
1- Purpose of DIRAC
Be able to generate/sample/infer an information from a logical chain of reasoning given an intervention on variables (clamping) using stochastic energy exploration and preventing combinatorial explosion. DIRAC should be able to instantly shift the embedded joint distribution into the conditional distribution required for causal models.
2- ORBIT Computation
Given a well-defined optimisation (QUBO-like for eg) problem where the purpose is to minimise an energy-based landscape of variables interacting, ORBIT allows the computation of ground states in a least costing manner (REF).
3- Gap between undirected sampling and directed causal inference
Interpretability of the links between nodes doesn’t go both ways anymore once we establish a cause-to-effect relationship between two variables. See difference between causal and anti-causal factorisation
4- What must be proven
To guarantee that active clamping is really working, the must is to prove that the constrained distribution/the energy function used/obtained by that clamping represents the distribution we actually want to sample from and infer information.
5- Hardware constraints
Constraints for now rather than requirements.
QUBO/Ising/Boltzmann Energy based model problem solving with static and preprocessed parameters OR updated outside in the CPU with a delay.
Rescaling importance with resolution, max energy, and temperature limit.
6- Equivalence between physical clamping and intervention
Discussed in Phase 6
The purpose is to understand whether the structural changes that are needed in causal theory can be implemented through clamping variables via a penalty on energy.
Glossary
tags: [glossary, graphical-models, ising, qubo, causal-inference, probabilistic-computing]
Graphical Model Fundamentals
| Term | Definition |
|---|---|
| DAG (Directed Acyclic Graph) | A directed graph containing no directed cycles — following edges in their direction can never lead back to a starting node. |
| Bayesian Network | A DAG whose nodes are random variables, where each node’s distribution depends only on its parents; the joint distribution factorizes as the product of these local conditionals. |
| Conditional Probability Table (CPT) | The table attached to a node in a Bayesian Network giving the probability of each of its states for every combination of its parents’ states. |
| Factor Graph | A bipartite graph of variable nodes and factor nodes, where each factor node connects to the variables it depends on, showing how a global function factorizes into local pieces. |
| Markov Random Field (MRF) or Markov Network | An undirected graphical model whose joint distribution factorizes over the graph’s cliques; each variable depends on the rest only through its graph neighbours. |
Optimisation Formulations
| Term | Definition |
|---|---|
| Ising Model | An energy-based model of binary spin variables (±1) with local fields and pairwise couplings; low-energy configurations correspond to high-probability or low-cost solutions. |
| QUBO (Quadratic Unconstrained Binary Optimization) | A binary ({0,1}) optimisation problem with a quadratic, constraint-free objective; mathematically equivalent to the Ising model under a linear variable change. |
| Higher-order Factor | A term in an energy function or factor graph involving three or more variables at once, which cannot be losslessly split into pairwise terms. |
| Quadratization | The process of rewriting a higher-order energy function as an equivalent quadratic (pairwise) one, typically by introducing auxiliary variables. |
| Auxiliary Variable | An extra variable, with no independent meaning in the original problem, introduced (e.g. during quadratization) to enforce a relationship among the true variables via its own energy terms. |
| 3 last used in VCPC paper |
Causal Inference Operations
| Term | Definition |
|---|---|
| Conditioning | Updating a distribution to reflect observed evidence via Bayes’ rule; changes beliefs about unobserved variables without altering the graph’s causal structure. |
| Hard Intervention | Pearl’s do(X=x) operator: externally forcing a variable to a fixed value, overriding its normal mechanism and severing its dependence on its parents. |
| Soft Intervention | An intervention that shifts or reweights a variable’s conditional distribution (e.g. modifies its CPT or adds a bias) without deterministically fixing its value or fully removing parental influence. |
| Graph Mutilation | The graph operation corresponding to a hard intervention: deleting all incoming edges to the intervened node, producing a “mutilated” graph for computing post-intervention distributions. |
Probabilistic (p-bit) Computing Implementation
Personal note : clamping excluded, these are not the most relevant
| Term | Definition |
|---|---|
| Clamping | Forcing a physical p-bit’s state to a fixed value throughout the sampling dynamics — the hardware-level analogue of a hard intervention. |
| Clamp Penalty Function | The bias/energy term added to a clamped unit that penalises it for deviating from its desired fixed state, setting how strongly the unit is held. |
| Hard Clamp | A clamp with an effectively infinite penalty (or a direct state override), fully decoupling the unit from the rest of the network — the physical equivalent of full graph mutilation. |
| Finite-bias Clamp | A clamp implemented with a large but finite bias, making the desired state highly probable without absolute certainty and preserving some residual coupling and stochasticity. |
| Dynamic Range | The span between the smallest and largest representable weight/bias magnitudes in a given hardware or numerical implementation; limits how strong a clamp can be made relative to other terms. |
| Virtual Mutilation | Reproducing the effect of graph mutilation on a probabilistic computer by applying a strong (finite-bias) clamp to a node, rather than physically removing edges — emulating a hard intervention without changing the network’s topology. |
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