TLDR; The authors propose a new Diverse Beam Search (DBS) decoding procedure that produces more diverse responses than standard Beam Search (BS). The authors divide the beam of size B into G groups of size B/G. At each step they perform beam search for each group with an added similarity penalty (with scaling factor lambda) that encourages groups to be pick different outputs. This procedure is done greedily, i.e. group 1 does regular BS, group 2 is conditioned on group 1, group 3 is conditioned on group 1 and 2, and so on. Similarity functions include Hamming distance, Cumulative Diversity, n-gram diversity and neural embedding diversity. Hamming Distance tends to perform best. The authors evaluate their model on Image Captioning (COCO, PASCAL-50S), Machine Translation (europarl) and Visual Question Generation. For Image Captioning the authors perform a human evaluation (1000 examples on Mechanical Turk) and find that DBS is preferred over BS 60% of the time.

https://www.youtube.com/watch?v=_S1lyQbbJM4

TLDR; The authors encourage exploration by adding a pseudo-reward of the form $\frac{\beta}{\sqrt{count(state)}}$ for infrequently visited states. State visits are counted using Locality Sensitive Hashing (LSH) based on an environment-specific feature representation like raw pixels or autoencoder representations. The authors show that this simple technique achieves gains in various classic RL control tasks and several games in the ATARI domain.

While the algorithm itself is simple there are now several more hyperaprameters to tune: The bonus coefficient `beta`, the LSH hashing granularity (how many bits to use for hashing) as well as the type of feature representation based on which the hash is computed, which itself may have more parameters. The experiments don't paint a consistent picture and different environments seem to need vastly different hyperparameter settings, which in my opinion will make this technique difficult to use in practice.

In proteomics, a popular method to identify peptides is mass spectrometry. An experimental tandem mass spectrum consists of mass peaks that stem from fragmenting a peptide to fragment ions. 
To identify the peptide, that produced the experimental spectrum, all peptides that could produce the seen fragment ions must be analysed. Unfortunately, the space of possible peptides to search against is large.  The paper simplifies this problem by searching against a peptide database.

The approach describes a 4-step method:

- Data reduction: only the 200 most abundant peaks of the experimental spectrum are kept
- Search: peptides with a mass similar to the experimental spectrum's precursor are selected
- Scoring: the score for each selected peptide is based on the number of predicted fragment ions seen in the experimental spectrum.
- Cross-correlation: For the top 500 scoring peptides, theoretical spectra is constructed. These spectra are are evaluated by cross-correlation with the experimental spectrum. The top scoring peptide is considered the identified peptide.

Since a database of known peptides is needed for this approach, it can not be used for de-novo peptide identification, meaning identifying peptides for species where no sequenced genome or proteome is available.

## Task

A neural network for classification typically has a **softmax** layer and outputs the class with the max probability. However, this probability does not represent the **confidence**. If the average confidence (average of max probs) for a dataset matches the accuracy, it is called **well-calibrated**. Old models like LeNet (1998) was well-calibrated, but modern networks like ResNet (2016) are no longer well-calibrated. This paper explains what caused this and compares various calibration methods.

## Figure - Confidence Histogram

https://i.imgur.com/dMtdWsL.png

The bottom row: group the samples by confidence (max probailities) into bins, and calculates the accuracy (# correct / # bin size) within each bin.

- ECE (Expected Calibration Error): average of |accuracy-confidence| of bins
- MCE (Maximum Calibration Error): max of |accuracy-confidence| of bins

## Analysis - What
The paper experiments how models are mis-calibrated with different factors: (1) model capacity, (2) batch norm, (3) weight decay, (4) NLL.

## Solution - Calibration Methods

Many calibration methods for binary classification and multi-class classification are evaluated. The method that performed the best is **temperature scailing**, which simply multiplies logits before the softmax by some constant. The paper used the validation set to choose the best constant.