Elucidating the rationale behind neural models' outputs has been challenging in the machine learning field, which is indeed applicable in this age of large language models (LLMs) and in-context learning (ICL). When it comes to estimating input attributions (IA), ICL poses a new issue of interpreting which example in the prompt, consisting of a set of examples, contributed to identifying the task/rule to be solved. To this end, in this paper, we introduce synthetic diagnostic tasks inspired by the poverty of the stimulus design in inductive reasoning; here, most in-context examples are ambiguous w.r.t. their underlying rule, and one critical example disambiguates the task demonstrated. The question is whether conventional IA methods can identify such an example in interpreting the inductive reasoning process in ICL. Our experiments provide several practical findings; for example, a certain simple IA method works the best, and the larger the model, the generally harder it is to interpret the ICL with gradient-based IA methods.

Language Models (LMs) acquire parametric knowledge from their training process, embedding it within their weights. The increasing scalability of LMs, however, poses significant challenges for understanding a model's inner workings and further for updating or correcting this embedded knowledge without the significant cost of retraining. This underscores the importance of unveiling exactly what knowledge is stored and its association with specific model components. Instance Attribution (IA) and Neuron Attribution (NA) offer insights into this training-acquired knowledge, though they have not been compared systematically. Our study introduces a novel evaluation framework to quantify and compare the knowledge revealed by IA and NA. To align the results of the methods we introduce the attribution method NA-Instances to apply NA for retrieving influential training instances, and IA-Neurons to discover important neurons of influential instances discovered by IA. We further propose a comprehensive list of faithfulness tests to evaluate the comprehensiveness and sufficiency of the explanations provided by both methods. Through extensive experiments and analysis, we demonstrate that NA generally reveals more diverse and comprehensive information regarding the LM's parametric knowledge compared to IA. Nevertheless, IA provides unique and valuable insights into the LM's parametric knowledge, which are not revealed by NA. Our findings further suggest the potential of a synergistic approach of combining the diverse findings of IA and NA for a more holistic understanding of an LM's parametric knowledge.

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency bands. Motivated by many applications in which this differentiation is pivotal, we overcome this limitation by learning a block-sparse, frequency-dependent, partial correlation graph, in which layers correspond to different frequency bands, and partial correlations can occur over just a few layers. To this aim, we formulate and solve two nonconvex learning problems: the first has a closed-form solution and is suitable when there is prior knowledge about the number of partial correlations; the second hinges on an iterative solution based on successive convex approximation, and is effective for the general case where no prior knowledge is available. Numerical results on synthetic data show that the proposed methods outperform the current state of the art. Finally, the analysis of financial time series confirms that partial correlations exist only within a few frequency bands, underscoring how our methods enable the gaining of valuable insights that would be undetected without discriminating along the frequency domain.