CALIBRATING AI MODELS FOR FEW-SHOT DEMODULATION VIA CONFORMAL PREDICTION Kﬁr M. Cohen1 Sangwoo Park1 Osvaldo Simeone1Shlomo Shamai Shitz2

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CALIBRATING AI MODELS FOR FEW-SHOT DEMODULATION

VIA CONFORMAL PREDICTION

Kﬁr M. Cohen1, Sangwoo Park1, Osvaldo Simeone1Shlomo Shamai (Shitz)2

1KCLIP Lab, Department of Engineering, King’s College London, UK.

2Viterbi Faculty of Electrical and Computing Engineering, The Technion, Haifa, Israel.

ABSTRACT

AI tools can be useful to address model deﬁcits in the design

of communication systems. However, conventional learning-

based AI algorithms yield poorly calibrated decisions, un-

abling to quantify their outputs uncertainty. While Bayesian

learning can enhance calibration by capturing epistemic un-

certainty caused by limited data availability, formal calibra-

tion guarantees only hold under strong assumptions about the

ground-truth, unknown, data generation mechanism. We pro-

pose to leverage the conformal prediction framework to ob-

tain data-driven set predictions whose calibration properties

hold irrespective of the data distribution. Speciﬁcally, we in-

vestigate the design of baseband demodulators in the pres-

ence of hard-to-model nonlinearities such as hardware imper-

fections, and propose set-based demodulators based on con-

formal prediction. Numerical results conﬁrm the theoretical

validity of the proposed demodulators, and bring insights into

their average prediction set size efﬁciency.

Index Terms—Calibration, Conformal Prediction, De-

modulation

1. INTRODUCTION

Artiﬁcial intelligence (AI) models typically report a conﬁ-

dence measure associated with each prediction, which reﬂects

the model’s self-evaluation of the accuracy of a decision. No-

tably, neural networks implement probabilistic predictors that

produce a probability distribution across all possible values of

the output variable. As an example, Fig. 1 illustrates the oper-

ation of a neural network-based demodulator [1, 2, 3], which

outputs a probability distribution on the constellation points

given the corresponding received baseband sample. The self-

reported model conﬁdence, however, may not be a reliable

The work of K. M. Cohen, S. Park and O. Simeone has been supported by

the European Research Council (ERC) under the European Union’s Horizon

2020 research and innovation programme, grant agreement No. 725731. The

work of O. Simeone has also been supported by an Open Fellowship of the

EPSRC.

The work of S. Shamai has been supported by the European Union’s

Horizon 2020 Research And Innovation Programme, grant agreement No.

694630.

The authors acknowledge use of the research computing facility at

King’s College London, Rosalind (https://rosalind.kcl.ac.uk).

(b)

(a) x1

{,,,}{ ,}

set predictor:

inaccurate

well-calibrated

inaccurate

poorly-calibrated

accurate

well-calibrated

accurate

poorly-calibrated

(c)

probability probability probability probability

{, , }{ }

probabilistic

predictor:

input space

Fig. 1. QPSK demodulation with a demodulator trained using

a limited number of pilots (gray symbols): (a) Constellation

symbols (colored markers), optimal hard prediction (dashed

lines), and model trained using the few pilots (solid lines).

Accuracy and calibration of the trained predictor depend on

the test input (gray square). (b) Probabilistic predictors ob-

tained from the trained model (solid bars) and optimal pre-

dictive probabilities (dashed bars), with thick line indicating

the hard prediction. (c) Set predictors output a subset of the

constellation symbols for each input.

measure of the true, unknown, accuracy of the prediction, in

which case we say that the AI model is poorly calibrated.

Poor calibration may be a substantial problem when AI-based

decisions are processed within a larger system such as a com-

munication network.

Deep learning models tend to produce either overconﬁ-

dent decisions when designed following a frequentist frame-

work [4]; or else calibration levels that rely on strong as-

sumptions about the ground-truth, unknown, data generation

mechanism when Bayesian learning is applied [5, 6, 7, 8, 9,

10]. This paper investigates the adoption of conformal pre-

diction (CP) [11, 12, 13] as a framework to design provably

well-calibrated AI predictors, with distribution-free calibra-

tion guarantees that do not require making any assumption

about the ground-truth data generation mechanism.

Consider again the example in Fig. 1, which corresponds

to the problem of designing a demodulator for a QPSK con-

stellation in the presence of an I/Q imbalance that rotates and

distorts the constellation. The hard decision regions of an op-

arXiv:2210.04621v1 [eess.SP] 10 Oct 2022

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CALIBRATINGAIMODELSFORFEW-SHOTDEMODULATIONVIACONFORMALPREDICTIONKrM.Cohen1,SangwooPark1,OsvaldoSimeone1ShlomoShamai(Shitz)21KCLIPLab,DepartmentofEngineering,King'sCollegeLondon,UK.2ViterbiFacultyofElectricalandComputingEngineering,TheTechnion,Haifa,Israel.ABSTRACTAItoolscanbeusefultoaddressmodelde...

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CALIBRATING AI MODELS FOR FEW-SHOT DEMODULATION VIA CONFORMAL PREDICTION Kﬁr M. Cohen1 Sangwoo Park1 Osvaldo Simeone1Shlomo Shamai Shitz2

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