Paper:
We propose Deep Asymmetric Multitask Feature Learning (Deep-AMTFL) which can learn deep representations shared across multiple tasks while effectively preventing negative transfer that may happen in the feature sharing process. Specifically, we introduce an asymmetric autoencoder term that allows reliable predictors for the easy tasks to have high contribution to the feature learning while suppressing the influences of unreliable predictors for more difficult tasks. This allows the learning of less noisy representations, and enables unreliable predictors to exploit knowledge from the reliable predictors via the shared latent features. Such asymmetric knowledge transfer through shared features is also more scalable and efficient than inter-task asymmetric transfer. We validate our Deep-AMTFL model on multiple benchmark datasets for multitask learning and image classification, on which it significantly outperforms existing symmetric and asymmetric multitask learning models, by effectively preventing negative transfer in deep feature learning.

Review:
Summary: The paper proposes a multi-task feature learning framework with a focus on avoiding negative transfer. The objective has two kinds of terms to minimise: (1) The reweighed per-task loss, and (2) Regularisation. The new contribution is an asymmetric reconstruction error in the regularisation term, and one parameter matrix in the regulariser influences the reweighing of the pre-task loss. 
Strength: 
The method has some contribution in dealing with negative transfer. The experimental results are positive.
Weakness:
Several issues in terms of concept, methodology, experiments and analysis.
Details:
1. Overall conceptual issues.
1.1. Unclear motivation re prior work. The proposed approach is motivated by the claim that GO-MTL style models assumes symmetric transfer where bad tasks can hurt good tasks. This assertion seems flawed. The point of grouping/overlap in “GO”-MTL is that a “noisy”, “hard”, or “unrelated" task can just take its own latent predictor that is disjoint from the pool of predictors shared by the good/related tasks. 
Correspondingly, Fig 2 seems over-contrived. A good GO-MTL solution would assign the noisy task $w_3$ its own latent basis, and let the two good tasks share the other two latent bases. 
1.2  Very unclear intuition of the algorithm. In the AMTFL, task asymmetry is driven by the per-task loss. The paper claims this is because transfer must go from easy=>hard to avoid negative transfer. But this logic relies on several questionable assumptions surrounding conflating the distinct issues of difficulty and relatedness: (i) There could be several easy tasks that are totally un-related. One could construct synthetic examples with data that are trivially separable (easy) but require unrelated or orthogonal classifiers. (ii) A task could appear to be “easy" just by severe overfitting, and therefore still be detrimental to transfer despite low loss. (iii) A task could be very "difficult" in the sense of high loss, but it could still be perfectly learned in the sense of finding the ideal "ground-truth” classifier, but for a dataset that is highly non-separable in the provided feature-space. Such a perfectly learned classifier may still be useful to transfer despite high loss. (iv) Analogous to point (i), there could be several “difficult” tasks that are indeed related and should share knowledge. (Since difficult/high loss != badly learned as mentioned before). Overall there are lots of holes in the intuitive justification of the algorithm.
2. Somewhat incremental method. 
3.1 It’s a combination of AMTL (Lee 2016) and vanilla auto encoder. 
3. Methodology issues: 
3.1 Most of the explanation (Sec 3-3.1) is given re: Matrix B in Eq.(4) (AMTL method’s objective function). However the final proposed model uses matrix A in Eq.(6) for the same purpose of measuring the amount of outgoing transfers from task $t$ to all other tasks. However in the reconstruction loss, they work in very different ways: matrix B is for the reconstruction of model parameters, while matrix A is for the reconstruction of latent features. This is a big change of paradigm without adequate explanation. Why is it still a valid approach?
3.2 Matrix B in the original paper of AMTL (Eq.(1) of Lee et al., 2016) has a constraint $B \geq 0$, should matrix A have the same constraint? If not, why?
3.3 Question Re: the |W-WB| type assumption for task relatedness. A bad task could learn an all-zero vector of outgoing related ness $b^0_t$ so it doesn’t directly influence other tasks in feed-forward sense. But hat about during training? Does training one task’s weights endup influencing other tasks’s weights via backprop? If a bad task is defined in terms of incoming relatedness from good tasks, then tuning the bad task with backprop will eventually also update the good tasks? (presumably detrimentally).
4. Experimental Results not very strong.
4.1 Tab 1: Neural Network NN and MT-NN beat the conventional shallow MTL approaches decisively for AWA and MNIST.  The difference between MT-NN and AMTFL is not significant. The performance boost is more likely due to using NNs rather than the proposed MTL module. For School, there is not significant difference between the methods. For ImageNet-Room AMTL and AMTFL have overlapping errors. Also, a variant of AMTL (AMTL-imbalance) was reported in Lee’2016, but not here where the number is $40\pm1.71$. 
4.2 Tab 2: The “real” experiments are missing state of the art competitors. Besides a deep GO-MTL alternative, which should be a minimum,  there are lots of deep MTL state of the art: Misra CVPR’16 , Yang ICLR’17, Long arXiv/NIPS’17 Multilinear Relationship Nets,  Ruder arXiv’17 Sluice Nets, etc.
5. Analysis
5.1 The proposed method revolves around the notion of “noisy”/“unrelated”/“difficult” tasks. Although the paper conflates them, it may still be a useful algorithm in practice. But it in this case it should devise much better analysis to provide insight and convince us that this is not a fatal oversimplification: What is the discovered relatedness matrix in some benchmarks? Does the discovered relatedness reflect expert knowledge where this is available? Is there a statistically significant correlation between relatedness and task difficulty in practice? Or between relatedness and degree of benefit from transfer, etc? But this is hard to do cleanly as even if the results show a correlation between difficulty and relatedness, it may just be because that’s how relatedness is defined in the proposed algorithm.