University of Bristol Team Develops Stochastic Tsetlin Machine for Interpretable Learning

A new classifier constructed using thermodynamic neutrons, autonomous quantum thermal machines, performs computation via heat flow without external control. Sparrow Suderman and Giulia Rubino, at University of Bristol, built the system as a stochastic analogue of the Tsetlin machine, an interpretable rule-based learning architecture. The resulting classification accuracy is statistically comparable to standard Tsetlin machines, despite the use of noisy components. These findings demonstrate that thermodynamic computation is a promising framework for physical machine learning, highlighting the potential of using physical effects like noise and dissipation as computational resources.

Thermodynamic machine learning rivals conventional approaches through stochastic dynamics

A new thermodynamic machine performs statistically comparably to the standard Tsetlin machine. Reliability arises from architectural mechanisms such as thresholding and redundancy, rather than exact logical operations. These results stress that accurate and interpretable learning can emerge from autonomous stochastic dynamics, establishing thermodynamic computation as a viable framework for physical machine learning. Conventional machine learning typically abstracts computation away from its physical implementation, assuming arithmetic operations are exact, and logic gates are reliable.

Randomness is generally attributed to the data, not the hardware. This abstraction is effective for digital hardware, where the underlying physical implementation can often be neglected, but obscures the fact that information processing is ultimately a physical process subject to thermodynamic constraints. This becomes less natural in emerging computing platforms like thermodynamic, neuromorphic and quantum devices, where information processing is inherently noisy, with switching events being probabilistic and device states fluctuating due to thermal or quantum effects.

Indeed, variability can even be part of the computational mechanism itself. Consequently, computation must be understood as a process taking place within a noisy physical substrate, rather than as an ideal deterministic procedure corrupted by noise. This perspective connects to broader efforts to understand the thermodynamic cost of computation, to develop thermodynamically consistent models of information processing, and to explore thermodynamic computing as an alternative model for computation and AI. The central challenge now shifts from suppressing noise in individual operations to ensuring reliable computation and learning can emerge from inherently stochastic dynamics.

Architectural principles such as redundancy, integration, thresholding and irreversibility become important for managing the trade-off between energetic efficiency and computational reliability. This challenge is addressed in this work by combining two main ingredients. The first is the thermodynamic neutron introduced in a previous publication, a quantum thermal machine that operates autonomously. Once the thermal inputs are fixed, it relaxes without externally timed control, producing an output interpreted as a logical gate.

The quantum description provides a microscopic account of the stochastic logic primitives, while network computation remains classical and Boolean. The second ingredient is the Tsetlin machine, a rule-based learning architecture operating on Boolean data and producing explicit logical clauses for classification. This framework has shown promising results across healthcare, regression and pattern recognition. Its discrete logical structure is naturally compatible with thermodynamic gates, while its interpretability, low-memory usage and energy-efficient character make it attractive for physical implementations.

These ingredients are combined to construct a thermodynamic rule-evaluation engine: an autonomous network of thermodynamic AND, NOT and OR gates implementing the rule-evaluation stage of the Tsetlin machine. Operation is stochastic, as both the individual gates and signal propagation between them are governed by probabilistic thermal transitions. Learning does not occur through externally timed operations, but unfolds through noisy physical transitions within the network.

Information is propagated between neurons by a probabilistic coupling mechanism, meaning stochasticity enters directly at the level of computation. The resulting architecture provides a concrete setting to study learning on a genuinely noisy physical substrate. A key challenge in such a network is reliability, as communication of outputs between successive neurons is mediated by the excitation of a signal qubit coupled to a finite output bath, making the transmission of logical values inherently probabilistic.

Individual gates can therefore fail with non-negligible probability, and such errors may accumulate across the network. However, simple architectural features overcome this challenge. By introducing a finite thermalisation interval and a redundancy scheme at the gate level, stochastic errors can be strongly suppressed without eliminating noise at the component level. Across a range of benchmark datasets, the resulting thermodynamic implementation achieves classification accuracy comparable, within statistical uncertainty, to that of the standard Tsetlin machine, with modest improvements in mean accuracy for some datasets.

Accurate and interpretable learning need not rely on deterministic logic or externally imposed control. Instead, it can emerge from an autonomous architecture governed by stochastic, dissipative dynamics. The remainder of this paper is organised as follows. We introduce the Tsetlin machine and the thermodynamic neuron as the framework’s building blocks. Then, we analyse the irreversible operation of an individual thermodynamic neuron through its entropy production.

Next, the team develop the coupling mechanism for the autonomous network, analyse the role of redundancy in ensuring reliable operation, and show how the resulting network carries out rule evaluation for the Tsetlin machine and its resource requirements. Finally, the classification performance of the thermodynamic implementation is evaluated across a range of datasets. The Tsetlin machine, first introduced by M. L. Tsetlin in the 1960s, is a method for learning logical patterns from Boolean data and using them for classification tasks.

For example, given a dataset describing animals, the task may be to distinguish cats from birds based on properties such as having fur or being able to fly. The aim is to learn patterns such that a given input can be correctly assigned to a category. Each data point is described by True/False properties called features, and for each feature, both the feature and its negation are considered as literals. Memory can be represented by states 1 to 2N, with states 1 to N selecting exclusion of the corresponding literal from the rule, and states N + 1 to 2N selecting inclusion.

The precise number of states is not fixed by the model, but controls how easily the automaton changes action under feedback. States close to the boundary between the two regions correspond to a less stable decision, while states deep within either region correspond to a more stable decision to exclude or include the literal. A rule is therefore the conjunction of all included literals and evaluates to True only when all of them are satisfied. For example, the rule Has Fur ∧¬ Can Fly ∧¬ Lays Eggs would evaluate to True for an animal that has fur, cannot fly, and does not lay eggs, and can therefore be used to identify a cat as opposed to a bird.

Learning proceeds by iteratively updating these memory states based on observed data. The machine is initialised with all literals at state N = 5, namely at the edge of the exclusion region, adjacent to the inclusion region. During training, each input is provided together with its correct class label. The type of feedback applied is then determined by comparing this label with the evaluation of the rule on that input. When the label indicates that the input belongs to the target class, ‘Type I’ feedback is applied.

This feedback has two cases, depending on whether the rule evaluates to True or False. If the rule evaluates to True, it has correctly identified the input, reinforcing the literals that supported this classification. If instead the rule evaluates to False, this indicates that the rule does not capture the relevant features of the target class, effectively erasing the rule. Over time, some literals obtain high memory states, solidifying their presence in the rule, corresponding to the common traits that are True for all objects in the target class.

Literals which obtain memory states close to 1 correspond to traits that are unimportant. However, this is not the same as a property being systematically absent from the target class; in that case, the corresponding negated literal is included in the rule. When the input does not belong to the target class, ‘Type II’ feedback is used, applied only when the rule evaluates to True. In this case, literals that are True for the input are weakened, while those that are False are reinforced.

If instead the rule evaluates to False, no feedback is applied, as the rule correctly rejects the input. Overall, these feedback mechanisms update the memory states of the literals, reinforcing useful patterns and suppressing incorrect ones. ‘Type I’ feedback is applied stochastically, whereas ‘Type II’ feedback is typically deterministic. Stochasticity prevents the system from overfitting to specific examples by controlling how literals are updated.

Dependable machine learning can arise from the inherent randomness of physical systems, rather than precise calculations. The system combines thermodynamic AND, NOT and OR gates with an autonomous mechanism, realising a learning process that does not require external timing. Despite noisy components, classification accuracy is statistically comparable to a standard Tsetlin machine, with reliability stemming from architectural features like thresholding and redundancy.

However, the current implementation achieves accuracy merely comparable to the established Tsetlin machine, a rule-based learning system already known for its interpretability. This raises a critical question: is the complexity of harnessing thermodynamic principles justified by a negligible gain in performance, at least with this initial architecture. Still, acknowledging that this initial thermodynamic classifier matches the performance of existing Tsetlin machines is not dismissing its potential. Researchers have built a functioning computer using only heat and autonomous components. This proof-of-concept demonstrates that reliable computation can emerge from noisy, physical systems, potentially paving the way for new, energy-efficient computing paradigms to begin.

The research demonstrated that a classifier could be built using ‘thermodynamic neurons’ and achieve classification accuracy statistically comparable to a standard Tsetlin machine. This is significant because it shows learning systems do not necessarily require precise logical operations, and can instead function with inherent noise and randomness. The system utilises thermodynamic AND, NOT and OR gates, operating autonomously without external control. Researchers suggest this establishes thermodynamic computation as a viable framework for physical machine learning, and have created a functioning computer powered by heat.