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arxiv: 2502.05935 · v8 · pith:HZRORPQLnew · submitted 2025-02-09 · 💻 cs.HC · cs.IT· math.IT

Interactive Inference: A Neuromorphic Theory of Human-Computer Interaction

Roel Vertegaal , Timothy Merritt , Saul Greenberg , Aneesh P. Tarun , Zhen Li , Zafeirios Fountas This is my paper

Pith reviewed 2026-05-23 03:21 UTC · model grok-4.3

classification 💻 cs.HC cs.ITmath.IT
keywords Interactive Inferenceneuromorphic HCIActive InferenceBayesian surprisesignal-to-noise ratiomental loadHick's LawFitts' Law
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The pith

Interactive Inference models user processing capacity as a logarithmic function of task signal-to-noise ratio.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces Interactive Inference as a neuromorphic theory for human-computer interaction based on Active Inference. It models user behavior as Bayesian inference where the surprise between predicted goal and observed progress is the mean square error of the task's signal-to-noise ratio, and processing capacity is the logarithm of that ratio. The approach unifies several established HCI laws and was validated in a car-following experiment showing the logarithmic relationship. If true, it would allow designers to calculate mental load in real time to reduce errors.

Core claim

Interactive Inference treats user behavior as Bayesian inference on progress and goal distributions. The error, or Bayesian surprise, is modeled as mean square error of the signal-to-noise ratio of a task, and user capacity to process this surprise follows the logarithm of the SNR. This allows expression of Hick's Law, Fitts' Law, and the Power Law within one framework for analyzing performance and error, with initial validation in a car-following task showing logarithmic capacity dependence on distance SNR.

What carries the argument

Bayesian surprise modeled as mean square error of task SNR, with processing capacity as the logarithm of that SNR.

If this is right

  • Hick's Law, Fitts' Law and the Power Law can be expressed using the model.
  • Quantitative analysis of performance and error is possible in one framework.
  • Real-time estimates of the mental load in users can be provided.
  • Errors rise quickly once average capacity is exceeded.
  • The model predicts human performance in tasks such as car following.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to predict load in other interactive tasks like touch interfaces or virtual environments.
  • Design tools might incorporate the model to simulate user capacity before building prototypes.
  • Neuromorphic systems for HCI could be engineered to operate within the same logarithmic capacity bounds.

Load-bearing premise

That the user's capacity to process Bayesian surprise follows the logarithm of the mean square error of the task's signal-to-noise ratio.

What would settle it

An experiment measuring human performance in a controlled task that fails to show processing capacity as a logarithmic function of SNR or where error rates do not rise as predicted beyond average capacity.

Figures

Figures reproduced from arXiv: 2502.05935 by Aneesh P. Tarun, Roel Vertegaal, Saul Greenberg, Timothy Merritt, Zafeirios Fountas, Zhen Li.

Figure 1
Figure 1. Figure 1: Bayes Theorem. Distributions of the Likelihood P(o|s) of observations, in green, given a Prior P(s) that describes the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Bayesian Fitts’ Law. Distribution of the Posterior probability P(s|o) of the cursor being within the Goal, from top [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Two cars with normal distributions 𝐺(𝑥) and 𝑃 (𝑥) representing uncertainty in their position. The percentage of overlap between distributions equals the probability of a collision. The negative logarithm of this probability gives the number of bits of difference. logarithm by measuring the amount of information 𝐻 using Equa￾tion 32 and by performing a regression on the result (we discuss how we operational… view at source ↗
Figure 4
Figure 4. Figure 4: Participant’s experimental setup. The white bar [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Driver information capacity plotted against noise-to-signal ratio ( [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Error (non-surprise, in bits) plotted against noise-to-signal ratio ( [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Perceived task difficulty for each condition: participants’ responses to the question “This driving task was difficult” [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Neuromorphic Human-Computer Interaction (HCI) is a theoretical approach to designing better user experiences (UX) motivated by advances in the understanding of the neurophysiology of the brain. Inspired by the neuroscientific theory of Active Inference, Interactive Inference is a first example of such an approach. It offers a simplified interpretation of Active Inference that allows designers to more readily apply this theory to design and evaluation. The basic premise in Interactive Inference is that the user predicts a result prior to performing a task. User behaviour is modeled as Bayesian inference on progress and goal distributions that predicts the next action. The difference between the observed result and the prediction is what is processed by the brain. This error between goal and progress distributions, or Bayesian surprise, can be modeled as a simple mean square error of the signal-to-noise ratio (SNR) of a task. The problem is that the user's capacity to process Bayesian surprise follows the logarithm of this SNR. This means errors rise quickly once average capacity is exceeded. Our model allows the quantitative analysis of performance and error using one framework that can provide real-time estimates of the mental load in users that needs to be minimized by design. We show how three basic laws of HCI, Hick's Law, Fitts' Law and the Power Law can be expressed using our model. We then test the validity of the model by empirically measuring how well it predicts human performance and error in a car following task. Results suggest that driver processing capacity indeed is a logarithmic function of the SNR of the distance to a lead car. This result provides initial evidence that Interactive Inference can be useful as a new theoretical design tool.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes Interactive Inference, a simplified neuromorphic HCI framework derived from Active Inference. Users are modeled as performing Bayesian inference over goal and progress distributions; Bayesian surprise is equated to mean-square error on task SNR, and processing capacity is taken to be the logarithm of that SNR. The framework is shown to recover Hick's Law, Fitts' Law and the Power Law, and is tested in a car-following experiment whose results are interpreted as confirming that driver capacity is logarithmic in the SNR of lead-car distance.

Significance. If the modeling steps linking Active Inference to the SNR-log-capacity equation can be rigorously derived and the empirical result replicated with full methodological detail, the work would supply a single quantitative, real-time mental-load metric applicable across HCI tasks. The explicit unification of three classical laws under one functional form would be a substantive contribution to theoretical HCI.

major comments (3)
  1. [Abstract] Abstract (paragraph beginning 'This error between goal and progress distributions...'): the identification of Bayesian surprise with 'a simple mean square error of the signal-to-noise ratio (SNR) of a task' and the subsequent claim that capacity 'follows the logarithm of this SNR' are introduced without derivation from the Bayesian update on the two distributions or from the Active Inference formalism. These two modeling choices are load-bearing for every subsequent claim.
  2. [Abstract] Abstract (final two sentences): the headline empirical result ('driver processing capacity indeed is a logarithmic function of the SNR') is obtained only after imposing the MSE(SNR) and log(SNR) parametrizations; the car-following experiment therefore tests a specific functional form rather than the Interactive Inference framework itself.
  3. [Abstract] Abstract (sentence 'We show how three basic laws...'): the derivations of Hick's, Fitts' and Power laws from the single SNR-log-capacity equation must be shown to be independent rather than recovered by construction; otherwise the unification does not constitute a novel prediction of the theory.
minor comments (1)
  1. [Abstract] The phrasing 'The problem is that the user's capacity...' is ambiguous; clarify whether the logarithmic relation is an additional modeling assumption or an empirical claim to be tested.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which identify key areas where the theoretical links and empirical claims require clarification. We address each major comment below, indicating revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph beginning 'This error between goal and progress distributions...'): the identification of Bayesian surprise with 'a simple mean square error of the signal-to-noise ratio (SNR) of a task' and the subsequent claim that capacity 'follows the logarithm of this SNR' are introduced without derivation from the Bayesian update on the two distributions or from the Active Inference formalism. These two modeling choices are load-bearing for every subsequent claim.

    Authors: We agree that the manuscript introduces these equivalences as modeling simplifications without a full derivation from the Active Inference update rules. Interactive Inference is explicitly positioned as a reduced form to improve accessibility for HCI practitioners. In revision we will insert a dedicated subsection deriving the MSE approximation to Bayesian surprise from the KL divergence between goal and progress distributions, and the logarithmic capacity from rate-distortion considerations in neuromorphic systems. This will make the load-bearing steps explicit. revision: yes

  2. Referee: [Abstract] Abstract (final two sentences): the headline empirical result ('driver processing capacity indeed is a logarithmic function of the SNR') is obtained only after imposing the MSE(SNR) and log(SNR) parametrizations; the car-following experiment therefore tests a specific functional form rather than the Interactive Inference framework itself.

    Authors: The referee correctly notes that the experiment evaluates the combined functional form rather than the Bayesian-inference core in isolation. We will revise the abstract, methods, and discussion to state that the car-following data provide initial support for the logarithmic capacity assumption within the Interactive Inference model, and we will add a sentence clarifying that future work could test alternative capacity functions. The result remains informative because it links the proposed real-time mental-load metric to observable performance. revision: yes

  3. Referee: [Abstract] Abstract (sentence 'We show how three basic laws...'): the derivations of Hick's, Fitts' and Power laws from the single SNR-log-capacity equation must be shown to be independent rather than recovered by construction; otherwise the unification does not constitute a novel prediction of the theory.

    Authors: We will expand the main-text derivations to demonstrate that each law arises from distinct task-parameter mappings (choice entropy for Hick's, precision-distance trade-off for Fitts', and cumulative error accumulation for the Power Law) under the same capacity equation. If the current presentation makes the recoveries appear tautological, we will rephrase to emphasize the independent predictions that follow once the SNR-log form is fixed. We view this as a clarification rather than a fundamental change. revision: partial

Circularity Check

2 steps flagged

Central empirical claim depends on un-derived modeling step that sets Bayesian surprise = MSE(SNR) and capacity = log(SNR)

specific steps
  1. self definitional [Abstract]
    "This error between goal and progress distributions, or Bayesian surprise, can be modeled as a simple mean square error of the signal-to-noise ratio (SNR) of a task. The problem is that the user's capacity to process Bayesian surprise follows the logarithm of this SNR."

    The paper defines capacity as following the logarithm of SNR, then reports an empirical result that capacity 'indeed is a logarithmic function of the SNR'. The result is the modeling premise restated as a finding.

  2. fitted input called prediction [Abstract]
    "We show how three basic laws of HCI, Hick's Law, Fitts' Law and the Power Law can be expressed using our model. ... Results suggest that driver processing capacity indeed is a logarithmic function of the SNR of the distance to a lead car."

    The model is constructed with the log(SNR) capacity rule; the laws and the car-following result are then recovered inside that same rule. The 'predictions' are therefore forced by the initial functional choice rather than derived from the Bayesian inference premise.

full rationale

The paper's derivation begins by stipulating two functional forms without derivation from Active Inference or Bayesian updating: surprise is replaced by MSE on task SNR, and capacity is stipulated to equal log(SNR). The three HCI laws are then shown to be expressible inside this same equation, and the car-following experiment is presented as confirming that capacity 'indeed is' logarithmic in SNR. Because the functional form was imposed at the outset, both the law recoveries and the empirical confirmation reduce to the modeling choice rather than independent predictions from the framework. This matches the 'fitted_input_called_prediction' pattern at the level of the core claim.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the untested mapping of Bayesian surprise to MSE of SNR and on the assumption that capacity is strictly logarithmic in that quantity; both are introduced without independent derivation or external benchmark in the abstract.

free parameters (1)
  • logarithmic capacity constant
    The slope relating processing capacity to log(SNR) is required for quantitative predictions but its value is not derived from first principles.
axioms (2)
  • domain assumption Active Inference theory supplies the correct generative model for user prediction and error processing
    Invoked in the opening sentence as the neuroscientific foundation.
  • ad hoc to paper Bayesian surprise equals mean-square error of SNR
    Stated directly as the modeling choice that enables the log-capacity claim.

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