Asking the Right Questions: AI’s Confidence Problem

Author: Denis Avetisyan

New research explores how quantifying uncertainty in neural networks can build more reliable and ethically sound question-answering systems.

The study demonstrates a probabilistic approach to question answering, where posterior predictive distributions-characterized by mean values and $ \pm 1\sigma $ uncertainty-effectively represent the model’s confidence in its predictions, with the predicted class indicated by a blue dot and the true label confirmed by a red star.

Bayesian inference and techniques like Laplace approximation enable better calibration and selective prediction in neural question answering models.

Despite advances in neural question answering, quantifying model confidence and enabling reliable abstention remain critical challenges for responsible AI deployment. This work, ‘Toward Ethical AI Through Bayesian Uncertainty in Neural Question Answering’, explores Bayesian inference-specifically Laplace approximation-to calibrate uncertainty estimates in transformer-based question answering systems. Demonstrating improved prediction calibration and selective response via techniques like LoRA adaptation, the study reveals that incorporating Bayesian methods allows models to abstain when lacking confidence. Could this approach pave the way for more transparent and ethically sound neural systems capable of acknowledging their limitations?

The Illusion of Certainty: Beyond Point Predictions

While neural networks, even advanced architectures like the Transformer, demonstrate remarkable proficiency in making predictions, a significant limitation lies in their inability to consistently quantify the uncertainty associated with those predictions. These models often output a single ‘best guess’ without indicating how confident they are in that answer, or the range of plausible alternatives. This is problematic because a highly accurate prediction accompanied by a low confidence score is as unhelpful as an inaccurate prediction with high confidence – especially in fields like medical diagnosis or autonomous driving where acknowledging a lack of knowledge is critical. The issue isn’t necessarily inaccurate predictions, but rather a disconnect between the predicted certainty and the actual probability of being correct, leaving users unable to reliably assess the trustworthiness of the model’s output and potentially leading to overreliance on flawed information.

The inability of many neural networks to reliably quantify their own uncertainty presents a significant obstacle to deployment in high-stakes applications. Fields like medical diagnosis, autonomous vehicle navigation, and financial modeling demand not only accurate predictions, but also a clear indication of the model’s confidence-or lack thereof-in those predictions. A misdiagnosis, an incorrect steering decision, or a flawed investment strategy carries substantial risk, and these risks are amplified when a system offers a confident, yet inaccurate, assessment. Knowing what a model doesn’t know allows for appropriate intervention, whether it be requesting human oversight, triggering a secondary verification process, or simply abstaining from a decision altogether. Consequently, the pursuit of well-calibrated models-those that accurately reflect their predictive accuracy with their stated confidence-is critical for building trustworthy and responsible artificial intelligence systems.

A significant challenge with contemporary neural networks lies in their frequent miscalibration – a disconnect between the confidence a model expresses in its predictions and the actual likelihood of those predictions being correct. While a model might assign a 95% probability to a specific answer, its accuracy on similar questions may, in reality, be far lower, perhaps only 70%. This disparity isn’t merely a statistical quirk; it fundamentally undermines the trustworthiness of the system, particularly in high-stakes applications like medical diagnosis or autonomous driving. A well-calibrated model, conversely, should exhibit a strong correlation between its predicted probabilities and observed frequencies of correctness, offering a more reliable indicator of its own limitations and prompting appropriate caution when facing uncertain scenarios. Addressing this calibration issue is therefore vital for deploying AI systems that can be genuinely trusted to operate safely and effectively.

Assessing how well a model’s predicted confidence aligns with its actual accuracy – a process known as calibration – is a vital, yet often overlooked, step in artificial intelligence development. Datasets like CommonsenseQA serve as crucial benchmarks for evaluating this aspect of performance, presenting questions demanding not just an answer, but also a reliable indication of the model’s certainty. Experiments utilizing CommonsenseQA have consistently demonstrated that achieving good calibration remains a significant challenge; models frequently exhibit overconfidence in incorrect answers or underconfidence in correct ones. This discrepancy underscores that reliable AI isn’t simply about achieving high accuracy, but about providing trustworthy estimates of that accuracy, allowing for informed decision-making and responsible deployment in real-world applications.

Laplace regularization improves the calibration of BERT-based models on CommonsenseQA, demonstrated by both enhanced accuracy at lower coverage levels and a closer alignment between predicted confidence and empirical accuracy.

Bayesian Reasoning: A Foundation for Quantified Uncertainty

Bayesian reasoning fundamentally differs from frequentist approaches by explicitly modeling parameters as random variables. Instead of assigning a single, fixed value to each parameter within a model, Bayesian methods define a probability distribution over the possible values. This distribution, known as the prior, encapsulates existing knowledge or beliefs about the parameter before any data is observed. The shape of this distribution – whether it’s normal, uniform, or another form – reflects the strength and nature of that prior belief. By treating parameters as random variables with associated distributions, Bayesian reasoning provides a mathematically rigorous framework for quantifying and propagating uncertainty throughout the modeling process, ultimately allowing for a more nuanced understanding of model results and predictions. The parameter $ \theta $ is not a fixed value, but a random variable with a probability distribution $p(\theta)$.

Prior distributions in Bayesian reasoning articulate pre-existing knowledge or assumptions about model parameters before any data is observed; they are probability distributions reflecting the plausibility of different parameter values. These priors are then combined with the likelihood function, which quantifies the compatibility of observed data with different parameter values. Specifically, the likelihood, denoted as $P(data|\theta)$, represents the probability of observing the given data, assuming a specific value $\theta$ for the parameter. A higher likelihood indicates that the observed data is more probable given that particular parameter value, effectively measuring the evidence the data provides for different parameter settings.

Posterior distributions are calculated using Bayes’ Theorem, which mathematically combines the prior distribution, $P(\theta)$, representing initial beliefs about a parameter $\theta$, with the likelihood function, $P(D|\theta)$, quantifying the support for $\theta$ given observed data $D$. The resulting posterior distribution, $P(\theta|D)$, is proportional to the product of the prior and likelihood: $P(\theta|D) \propto P(D|\theta)P(\theta)$. This distribution represents the updated beliefs about the parameter $\theta$ after considering the observed data, effectively refining the initial prior based on the evidence provided by the likelihood. The posterior can then be used for statistical inference, prediction, and decision-making, providing a complete probabilistic representation of the parameter given the data.

Bayesian Neural Networks (BNNs) apply Bayesian inference to the weights of a neural network, treating them as probability distributions rather than single point estimates. This allows for the quantification of predictive uncertainty; instead of a single prediction, a BNN outputs a distribution over possible predictions. This distribution, derived from the posterior distribution over the network’s weights, reflects both the model’s epistemic uncertainty (uncertainty due to lack of knowledge about the best model) and aleatoric uncertainty (inherent noise in the data). Specifically, given an input $x$, the predictive distribution $p(y|x,D)$ is obtained by integrating over the posterior distribution of the weights $p(w|D)$, where $D$ represents the observed data: $p(y|x,D) = \int p(y|x,w)p(w|D) dw$. This approach provides not only a prediction but also a measure of confidence, enabling more robust and reliable decision-making in applications where uncertainty is critical.

Bayesian updating concentrates and shifts probability distributions from initial priors (gray) to refined posteriors (black) as data informs parameter beliefs.

Sampling the Posterior: Approximating the Intractable

Monte Carlo sampling techniques are employed to approximate posterior probability distributions, particularly when analytical solutions are intractable. These methods operate by drawing random samples from the posterior, with the frequency of samples in a given region proportional to the posterior probability in that region. Markov Chain Monte Carlo (MCMC) methods refine this process by constructing a Markov chain whose stationary distribution is the posterior of interest; samples from this chain then represent approximations of the posterior. Hamiltonian Monte Carlo (HMC) is a specific MCMC algorithm that utilizes concepts from Hamiltonian dynamics to efficiently explore the posterior space, often exhibiting faster convergence and reduced autocorrelation compared to simpler MCMC approaches. The resulting set of samples allows for the estimation of various posterior properties, such as the mean, variance, and credible intervals, providing a means of quantifying uncertainty in Bayesian inference.

Sampling from the posterior distribution is a core technique in Bayesian inference for characterizing model uncertainty. By generating a set of samples – typically denoted as {$x_1, x_2, …, x_N$} – from the posterior $p(\theta|D)$, where $\theta$ represents the model parameters and $D$ is the observed data, we can approximate various statistical properties. The sample mean, calculated as $\frac{1}{N}\sum_{i=1}^{N}x_i$, provides an estimate of the posterior mean. Similarly, the sample variance, $\frac{1}{N-1}\sum_{i=1}^{N}(x_i – \bar{x})^2$, estimates the posterior variance. Crucially, these samples enable the construction of credible intervals, which define a range within which the true parameter value is likely to lie with a specified probability, offering a quantifiable measure of uncertainty beyond simple point estimates.

Laplace Approximation provides a computationally efficient method for approximating Bayesian posterior distributions, especially within the context of neural networks where exact Bayesian inference is often intractable. This technique utilizes a Gaussian distribution to represent the posterior, defined by the posterior mode (often approximated using Maximum A Posteriori or MAP estimation) and the inverse of the Hessian matrix of the negative log-posterior evaluated at that mode. Empirical evaluation, such as experiments performed on benchmark datasets, indicates that Laplace Approximation consistently achieves a superior accuracy-coverage trade-off compared to MAP estimation; it provides a more realistic estimate of uncertainty, resulting in broader credible intervals while maintaining comparable predictive performance. This improved calibration is particularly valuable in risk-sensitive applications where accurate uncertainty quantification is critical.

The Iris dataset, a standard benchmark in machine learning, was utilized to demonstrate the practical application of Bayesian inference techniques with a Multilayer Perceptron (MLP). This involved training the MLP and subsequently employing methods like Monte Carlo sampling and Laplace approximation to estimate the posterior distribution over the network’s weights. By analyzing this posterior, we can move beyond point estimates of model parameters and quantify the uncertainty associated with predictions. The Iris dataset’s low dimensionality and well-defined classes facilitate the visualization and validation of these methods, providing a concrete example of how Bayesian approaches can be implemented and assessed in a classification task. The results illustrate the ability to obtain not only predictions, but also a measure of confidence in those predictions, which is crucial for reliable decision-making.

Posterior predictive distributions accurately reflect predicted class probabilities (blue) around the true labels (red star) with error bars representing one standard deviation.

Parameter Efficiency: Scaling Bayesian Inference

Parameter efficiency has emerged as a crucial factor in advancing large language models, and techniques like Low-Rank Adaptation (LoRA) directly address this need. LoRA operates on the principle that pre-trained models possess an inherent low-rank structure; instead of retraining all parameters for a new task, it introduces trainable low-rank matrices that approximate the weight updates. This drastically reduces the number of trainable parameters – often by orders of magnitude – while maintaining comparable performance to full fine-tuning. Consequently, LoRA enables scaling to significantly larger models and datasets that would otherwise be computationally prohibitive. The approach not only conserves memory and storage but also accelerates the training process, fostering more efficient experimentation and deployment of sophisticated language technologies. By focusing adaptation on a smaller parameter space, LoRA paves the way for more accessible and sustainable machine learning practices.

The integration of parameter-efficient techniques with Bayesian inference addresses a critical computational challenge. Bayesian methods rely on sampling from the posterior distribution to quantify uncertainty and obtain well-calibrated predictions, but this sampling process can become prohibitively expensive as model size increases. Reducing the number of trainable parameters – through methods like low-rank adaptation – directly lessens the dimensionality of the parameter space that needs to be explored during sampling. This translates to fewer computations per sample and, crucially, faster convergence to a reliable estimate of the posterior. Consequently, researchers can apply robust Bayesian analysis to larger, more complex models than previously feasible, achieving both accuracy and a meaningful understanding of predictive uncertainty without incurring excessive computational costs. This is particularly impactful in scenarios where quantifying confidence in predictions is as important as the predictions themselves.

DistilBERT provides a compelling illustration of the inherent trade-off between model size and performance in natural language processing. Developed as a smaller, faster, and lighter version of the widely-used BERT model, DistilBERT achieves approximately 97% of BERT’s language understanding capabilities while being 40% smaller and 60% faster. This reduction in size is accomplished through a process called knowledge distillation, where a smaller “student” model – DistilBERT – learns to mimic the behavior of a larger, pre-trained “teacher” model – BERT. Consequently, DistilBERT retains a substantial degree of accuracy, making it an effective alternative when computational resources or latency are critical concerns, and demonstrating that significant performance can be maintained even with a reduced parameter count.

Recent advancements in machine learning demonstrate a pathway to models that are not only highly accurate but also provide well-calibrated predictions-meaning the confidence a model expresses in its predictions reliably reflects actual correctness-all while significantly lowering computational demands. This is achieved through parameter-efficient techniques that intelligently reduce the number of trainable variables without substantial performance loss. The result is a compelling trade-off: models can be scaled to handle increasingly complex datasets and tasks without requiring prohibitive computational resources. This optimization is particularly impactful for Bayesian inference, where numerous samples are needed to achieve robust uncertainty estimates; reducing the computational burden per sample allows for more comprehensive exploration of the parameter space, ultimately leading to more reliable and trustworthy predictive models.

Calibration plots from Experiment 2 demonstrate that abstaining on low-confidence answers improves accuracy and that predicted confidence generally aligns with empirical accuracy across confidence bins.

Predictive Power: Towards Honest Artificial Intelligence

Predictive accuracy is only one piece of the puzzle when it comes to reliable artificial intelligence; understanding the inherent uncertainty in those predictions is equally crucial. Researchers are moving beyond simple point predictions by leveraging posterior predictive distributions. These distributions aren’t single guesses, but rather a range of likely outcomes generated by integrating across multiple plausible parameter settings of a model – essentially, considering what the model ‘thinks’ is possible, given its learned knowledge. Obtaining these distributions can be computationally intensive, which is why the Sequential Monte Carlo algorithm, specifically its variant denoted SMC≡30, proved vital in this work. SMC≡30 efficiently samples from the posterior, enabling the creation of these predictive distributions and providing a more complete picture of potential future observations, rather than a single, potentially misleading, estimate. This approach allows for quantifying confidence in predictions, ultimately fostering more trustworthy AI systems.

Robustness in artificial intelligence is significantly improved through a technique called selective prediction, wherein a model strategically chooses to abstain from providing an answer when its internal confidence falls below a predetermined threshold. Rather than forcing a potentially inaccurate prediction, the system effectively acknowledges its limitations, thus avoiding errors that could arise from extrapolating beyond reliable data. This approach isn’t merely about avoiding incorrect answers; it’s about building trust by demonstrating awareness of uncertainty. By refraining from prediction under conditions of high ambiguity, the model minimizes risk and maximizes the reliability of its affirmative responses, ultimately leading to more dependable and trustworthy AI systems capable of functioning effectively in real-world scenarios where imperfect information is the norm.

The convergence of probabilistic modeling and selective prediction strategies represents a significant advancement in the pursuit of dependable artificial intelligence. By quantifying uncertainty inherent in predictions – rather than offering single-point estimates – probabilistic models provide a more complete picture of potential outcomes. This is further strengthened by selective prediction, a technique wherein the system consciously refrains from making a prediction when its confidence falls below a defined threshold. This deliberate abstention avoids potentially erroneous outputs, fostering greater trust in the system’s reliability. The resulting AI exhibits not only predictive capability, but also a crucial element of self-awareness regarding the limits of its knowledge, ultimately leading to more robust and trustworthy performance in real-world applications.

The trajectory of artificial intelligence is shifting towards systems capable of acknowledging what they don’t know. Beyond simply maximizing predictive accuracy, the next generation of AI will prioritize transparency regarding its own limitations; a model’s ability to confidently state “I am unsure” is becoming as valuable as a correct prediction. This isn’t merely about avoiding errors, but about fostering trust and enabling responsible deployment in critical applications. Such models, grounded in probabilistic reasoning, can quantify uncertainty and communicate it effectively, allowing human users to make informed decisions, even when the AI’s confidence is low. This move towards honest AI represents a fundamental shift, paving the way for more reliable, robust, and ultimately, more beneficial integration of artificial intelligence into everyday life.

The posterior predictive distribution, represented by mean values with one standard deviation error bars, accurately predicts the true class (red star) as indicated by the proximity of the predicted class (blue circle).

The pursuit of robust question answering systems, as detailed in the study, necessitates more than mere accuracy; it demands a quantifiable understanding of prediction confidence. This aligns perfectly with Andrey Kolmogorov’s assertion: “Probability theory is nothing but the science of logical consistency.” The application of Bayesian Neural Networks, particularly through Laplace approximation and LoRA, isn’t simply about achieving higher scores, but about establishing a logically consistent framework for evaluating those scores. By quantifying uncertainty, the research moves beyond empirical performance to a more principled approach, acknowledging that a well-calibrated system, one that knows what it doesn’t know, is fundamentally more trustworthy and reliable than a system that merely appears to function correctly.

What Remains to be Proven?

The pursuit of ‘ethical AI’ often begins with the illusion of solving an engineering problem. This work, while a step toward more honest model outputs via quantified uncertainty, merely reframes the core difficulty. A well-calibrated prediction of ignorance is still ignorance. The Laplace approximation, despite its elegance, remains an approximation. A truly rigorous solution demands a departure from variational inference, perhaps toward exact Bayesian computation – a path fraught with intractability, yet essential if one desires solutions, not merely heuristics.

Future efforts must address the limitations inherent in selective prediction. Abstaining from answering is a useful safety measure, but a complete system cannot simply avoid difficult questions. The challenge lies in constructing algorithms that actively seek to reduce their own uncertainty – systems capable of identifying knowledge gaps and formulating targeted inquiries. This requires a formal definition of ‘information gain’ within the context of neural networks, a definition currently obscured by empirical observation.

LoRA, as employed here, is a pragmatic optimization. However, the underlying assumption – that low-rank adaptation preserves the epistemic landscape – requires formal justification. The question is not whether it works on benchmark datasets, but whether it demonstrably improves the provable accuracy of uncertainty estimates. Until such proofs are established, the field remains, at best, a sophisticated form of applied statistics.

Original article: https://arxiv.org/pdf/2512.17677.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/