The "black-box" nature of representations, combined with the known susceptibility of networks to learn spurious correlations [

Prolonged grief disorder affects around 1 in 20 people, and we're starting to understand the neuroscience behind it For most people, the intense sting of grief eases with time. For some, however, persistent and painful grief remains, developing into prolonged grief disorder. A new review of the condition, which affects around 5 per cent of bereaved people, sheds light on how it develops. This could help doctors predict which recently bereaved people will benefit from extra support. The decision to include prolonged grief disorder (PGD) in the American Psychiatric Association's diagnostic manual in 2022 sparked intense debate over whether it was pathologising a normal human response to loss and imposing an arbitrary timeline on what constitutes "normal" grief.

A long standing goal in neuroscience has been to elucidate the functional organization of the brain.

State-space models have gained popularity in sequence modelling due to their simple and efficient network structures. However, the absence of nonlinear activation along the temporal direction limits the model's capacity.

This paper focuses on the methods that explain what neurons learn during the training process.

Here, we include implementation details omitted from the main paper for brevity. Upon acceptance, a deanonymized repository will be released. The last layer's dimension depended upon the exact The feature extractors and decoders varied by domain. In particular, we found that if we did not apply this linear transformation (i.e., pass the raw encodings For VQ-based methods, use a large enough codebook to have at least one element per class. Other differences simply reflected differences in architecture (e.g., For iNat, we trained all models with batch size 256, using the hyperparameters specified in Table 3.

Lemma 3. Consider the ReLU activation The proof of Theorem 1 is given below. The inequality 3 uses strictly monotone property of p () . Code is available at this link. The neural networks are updated using Adam with learning rate initializes at 0.035 and All of them have no communication constraints. The training time is shown in Table 1.

We use induction to prove this statement. The penultimate step follows from the induction hypothesis completing the proof. Then, the fixed point of Eq.(5) is the value function of in f M . We focus on permanent value function in the next two theorems. The permanent value function is updated using Eq.