Contrary to common belief, we show that gradient ascent-based unconstrained optimization methods frequently fail to perform machine unlearning, a phenomenon we attribute to the inherent statistical dependence between the forget and retain data sets. This dependence, which can manifest itself even as simple correlations, undermines the misconception that these sets can be independently manipulated during unlearning. We provide empirical and theoretical evidence showing these methods often fail precisely due to this overlooked relationship. For random forget sets, this dependence means that degrading forget set metrics (which, for the oracle, should mirror test set metrics) inevitably harms overall test performance. Going beyond random sets, we consider logistic regression as an instructive example where a critical failure mode emerges: inter-set dependence causes gradient descentascent iterations to progressively diverge from the oracle. Strikingly, these methods can converge to solutions that are not only far from the oracle but are potentially even further from it than the original model itself, rendering the unlearning process actively detrimental. A toy example further illustrates how this dependence can trap models in inferior local minima, inescapable via finetuning. Our findings highlight that the presence of such statistical dependencies, even when manifest only as correlations, can be sufficient for ascent-based unlearning to fail. Our theoretical insights are corroborated by experiments on complex neural networks, demonstrating that these methods do not perform as expected in practice due to this unaddressed statistical interplay.

We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA).

Details regarding the datasets used in the experiments are included in Table 2. For Yang et al. [2020], we progressively doubled the number of regions searched which is the only adjustable hyperparameter. To make this figure, we run all the experiments (all attacks, datasets, and choices of hyperparameters)onaserverwith40coresofIntel(R)Xeon(R)Gold6230CPU@2.10GHz. This outcome is seemingly perplexing than the previous one. We explain it for different values ofm, namely the small-mandthelarge-mregions.

Four new books grapple with a global mental-health crisis and the dawn of algorithmic therapy. A technician adjusts the wiring inside the Mark I Perceptron. This early AI system was designed not by a mathematician but by a psychologist. More than a billion people worldwide suffer from a mental-health condition, according to the World Health Organization. The prevalence of anxiety and depression is growing in many demographics, particularly young people, and suicide is claiming hundreds of thousands of lives globally each year. Given the clear demand for accessible and affordable mental-health services, it's no wonder that people have looked to artificial intelligence for possible relief.

Decoding in large language models is often described as scoring tokens and normalizing with softmax. We give a minimal, self-contained account of this step as a constrained variational principle on the probability simplex. The discrete, normalization-respecting ascent is the classical multiplicative-weights (entropic mirror) update; its continuous-time limit is the replicator flow. From these ingredients we prove that, for a fixed context and temperature, the next-token distribution follows a smooth trajectory inside the simplex and converges to the softmax equilibrium. This formalizes the common ``manifold traversal'' intuition at the output-distribution level. The analysis yields precise, practice-facing consequences: temperature acts as an exact rescaling of time along the same trajectory, while top-k and nucleus sampling restrict the flow to a face with identical guarantees. We also outline a controlled account of path-dependent score adjustments and their connection to loop-like, hallucination-style behavior. We make no claims about training dynamics or internal representations; those are deferred to future work.

In the main text, many algorithmic details were omitted and only discussed briefly. A.1 Dataset Details We expand upon the seven datasets used for our experiments in this section. The task is multi-class classification with a heavy class imbalance. It has 8 features including price, day of the week and units transferred. We discard instances with missing values.

Machine Unlearning allows participants to remove their data from a trained machine learning model in order to preserve their privacy, and security. However, the machine unlearning literature for generative models is rather limited. The literature for image-to-image generative model (I2I model) considers minimizing the distance between Gaussian noise and the output of I2I model for forget samples as machine unlearning. However, we argue that the machine learning model performs fairly well on unseen data i.e., a retrained model will be able to catch generic patterns in the data and hence will not generate an output which is equivalent to Gaussian noise. In this paper, we consider that the model after unlearning should treat forget samples as out-of-distribution (OOD) data, i.e., the unlearned model should no longer recognize or encode the specific patterns found in the forget samples. To achieve this, we propose a framework which decouples the model parameters with gradient ascent, ensuring that forget samples are OOD for unlearned model with theoretical guarantee. We also provide $(\epsilon, \delta)$-unlearning guarantee for model updates with gradient ascent. The unlearned model is further fine-tuned on the remaining samples to maintain its performance. We also propose an attack model to ensure that the unlearned model has effectively removed the influence of forget samples. Extensive empirical evaluation on two large-scale datasets, ImageNet-1K and Places365 highlights the superiority of our approach. To show comparable performance with retrained model, we also show the comparison of a simple AutoEncoder on various baselines on CIFAR-10 dataset.