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This paper formalises the Canadian Traveller problem as a positional two-player game on graphs. We consider two variants depending on whether an edge is blocked. In the locally-informed variant, the traveller learns if an edge is blocked upon reaching one of its endpoints, while in the uninformed variant, they discover this only when the edge is supposed to appear. We provide a polynomial algorithm for each shortest path variant in the uninformed case. This algorithm also solves the case of directed acyclic non-temporal graphs. In the locally-informed case, we prove that finding a winning strategy is PSPACE-complete. Moreover, we establish that the problem is polynomial-time solvable when $k=1$ but NP-hard for $k\geq 2$. Additionally, we show that the standard (non-temporal) Canadian Traveller Problem is NP-hard when there are $k\geq 4$ blocked edges, which is, to the best of our knowledge, the first hardness result for CTP for a constant number of blocked edges.

We present DiffExplainer, a novel framework that, leveraging language-vision models, enables multimodal global explainability. DiffExplainer employs diffusion models conditioned on optimized text prompts, synthesizing images that maximize class outputs and hidden features of a classifier, thus providing a visual tool for explaining decisions. Moreover, the analysis of generated visual descriptions allows for automatic identification of biases and spurious features, as opposed to traditional methods that often rely on manual intervention. The cross-modal transferability of language-vision models also enables the possibility to describe decisions in a more human-interpretable way, i.e., through text. We conduct comprehensive experiments, which include an extensive user study, demonstrating the effectiveness of DiffExplainer on 1) the generation of high-quality images explaining model decisions, surpassing existing activation maximization methods, and 2) the automated identification of biases and spurious features.

We present SAM, a biologically-plausible selective attention-driven modulation approach to enhance classification models in a continual learning setting. Inspired by neurophysiological evidence that the primary visual cortex does not contribute to object manifold untangling for categorization and that primordial attention biases are still embedded in the modern brain, we propose to employ auxiliary saliency prediction features as a modulation signal to drive and stabilize the learning of a sequence of non-i.i.d. classification tasks. Experimental results confirm that SAM effectively enhances the performance (in some cases up to about twenty percent points) of state-of-the-art continual learning methods, both in class-incremental and task-incremental settings. Moreover, we show that attention-based modulation successfully encourages the learning of features that are more robust to the presence of spurious features and to adversarial attacks than baseline methods. Code is available at: https://github.com/perceivelab/SAM.

Generative Adversarial Networks (GANs) have demonstrated their ability to generate synthetic samples that match a target distribution. However, from a privacy perspective, using GANs as a proxy for data sharing is not a safe solution, as they tend to embed near-duplicates of real samples in the latent space. Recent works, inspired by k-anonymity principles, address this issue through sample aggregation in the latent space, with the drawback of reducing the dataset by a factor of k. Our work aims to mitigate this problem by proposing a latent space navigation strategy able to generate diverse synthetic samples that may support effective training of deep models, while addressing privacy concerns in a principled way. Our approach leverages an auxiliary identity classifier as a guide to non-linearly walk between points in the latent space, minimizing the risk of collision with near-duplicates of real samples. We empirically demonstrate that, given any random pair of points in the latent space, our walking strategy is safer than linear interpolation. We then test our path-finding strategy combined to k-same methods and demonstrate, on two benchmarks for tuberculosis and diabetic retinopathy classification, that training a model using samples generated by our approach mitigate drops in performance, while keeping privacy preservation., Comment: Accepted at MICCAI 2023

Humans can learn incrementally, whereas neural networks forget previously acquired information catastrophically. Continual Learning (CL) approaches seek to bridge this gap by facilitating the transfer of knowledge to both previous tasks (backward transfer) and future ones (forward transfer) during training. Recent research has shown that self-supervision can produce versatile models that can generalize well to diverse downstream tasks. However, contrastive self-supervised learning (CSSL), a popular self-supervision technique, has limited effectiveness in online CL (OCL). OCL only permits one iteration of the input dataset, and CSSL's low sample efficiency hinders its use on the input data-stream. In this work, we propose Continual Learning via Equivariant Regularization (CLER), an OCL approach that leverages equivariant tasks for self-supervision, avoiding CSSL's limitations. Our method represents the first attempt at combining equivariant knowledge with CL and can be easily integrated with existing OCL methods. Extensive ablations shed light on how equivariant pretext tasks affect the network's information flow and its impact on CL dynamics., Comment: 10 pages, 4 figures

Video saliency prediction has recently attracted attention of the research community, as it is an upstream task for several practical applications. However, current solutions are particularly computationally demanding, especially due to the wide usage of spatio-temporal 3D convolutions. We observe that, while different model architectures achieve similar performance on benchmarks, visual variations between predicted saliency maps are still significant. Inspired by this intuition, we propose a lightweight model that employs multiple simple heterogeneous decoders and adopts several practical approaches to improve accuracy while keeping computational costs low, such as hierarchical multi-map knowledge distillation, multi-output saliency prediction, unlabeled auxiliary datasets and channel reduction with teacher assistant supervision. Our approach achieves saliency prediction accuracy on par or better than state-of-the-art methods on DFH1K, UCF-Sports and Hollywood2 benchmarks, while enhancing significantly the efficiency of the model. Code is on https://github.com/feiyanhu/tinyHD, Comment: WACV2023

A coloring of a digraph is a partition of its vertex set such that each class induces a digraph with no directed cycles. A digraph is $k$-chromatic if $k$ is the minimum number of classes in such partition, and a digraph is oriented if there is at most one arc between each pair of vertices. Clearly, the smallest $k$-chromatic digraph is the complete digraph on $k$ vertices, but determining the order of the smallest $k$-chromatic oriented graphs is a challenging problem. It is known that the smallest $2$-, $3$- and $4$-chromatic oriented graphs have $3$, $7$ and $11$ vertices, respectively. In 1994, Neumann-Lara conjectured that a smallest $5$-chromatic oriented graph has $17$ vertices. We solve this conjecture and show that the correct order is $19$.

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.

The dichromatic number $\dic(D)$ of a digraph $D$ is the least integer $k$ such that $D$ can be partitioned into $k$ directed acyclic digraphs. A digraph is $k$-dicritical if $\dic(D) = k$ and each proper subgraph $D'$ of $D$ satisfies $\dic(D') \leq k-1$. An oriented graph is a digraph with no directed cycle of length $2$. For integers $k$ and $n$, we denote by $o_k(n)$ the minimum number of edges of a $k$-critical oriented graph on $n$ vertices (with the convention $o_k(n)=+\infty$ if there is no $k$-dicritical oriented graph of order $n$). The main result of this paper is a proof that $o_3(n) \geq \frac{7n+2}{3}$ together with a construction witnessing that $o_3(n) \leq \left \lceil \frac{5n}{2} \right \rceil$ for all $n \geq 12$. We also give a construction showing that for all sufficiently large $n$ and all $k\geq 3$, $o_k(n) < (2k-3)n$, disproving a conjecture of Hoshino and Kawarabayashi. Finally, we prove that, for all $k\geq 2$, $o_k(n) \geq \pth{ k - \frac{3}{4}-\frac{1}{4k-6}} n + \frac{3}{4(2k-3)}$, improving the previous best known lower bound of Bang-Jensen, Bellitto, Schweser and Stiebitz.

Early detection of precancerous cysts or neoplasms, i.e., Intraductal Papillary Mucosal Neoplasms (IPMN), in pancreas is a challenging and complex task, and it may lead to a more favourable outcome. Once detected, grading IPMNs accurately is also necessary, since low-risk IPMNs can be under surveillance program, while high-risk IPMNs have to be surgically resected before they turn into cancer. Current standards (Fukuoka and others) for IPMN classification show significant intra- and inter-operator variability, beside being error-prone, making a proper diagnosis unreliable. The established progress in artificial intelligence, through the deep learning paradigm, may provide a key tool for an effective support to medical decision for pancreatic cancer. In this work, we follow this trend, by proposing a novel AI-based IPMN classifier that leverages the recent success of transformer networks in generalizing across a wide variety of tasks, including vision ones. We specifically show that our transformer-based model exploits pre-training better than standard convolutional neural networks, thus supporting the sought architectural universalism of transformers in vision, including the medical image domain and it allows for a better interpretation of the obtained results.

In the medical field, multi-center collaborations are often sought to yield more generalizable findings by leveraging the heterogeneity of patient and clinical data. However, recent privacy regulations hinder the possibility to share data, and consequently, to come up with machine learning-based solutions that support diagnosis and prognosis. Federated learning (FL) aims at sidestepping this limitation by bringing AI-based solutions to data owners and only sharing local AI models, or parts thereof, that need then to be aggregated. However, most of the existing federated learning solutions are still at their infancy and show several shortcomings, from the lack of a reliable and effective aggregation scheme able to retain the knowledge learned locally to weak privacy preservation as real data may be reconstructed from model updates. Furthermore, the majority of these approaches, especially those dealing with medical data, relies on a centralized distributed learning strategy that poses robustness, scalability and trust issues. In this paper we present a federated and decentralized learning strategy, FedER, that, exploiting experience replay and generative adversarial concepts, effectively integrates features from local nodes, providing models able to generalize across multiple datasets while maintaining privacy. FedER is tested on two tasks -- tuberculosis and melanoma classification -- using multiple datasets in order to simulate realistic non-i.i.d. medical data scenarios. Results show that our approach achieves performance comparable to standard (non-federated) learning and significantly outperforms state-of-the-art federated methods in their centralized (thus, more favourable) formulation. Code is available at https://github.com/perceivelab/FedER

In Continual Learning (CL), a neural network is trained on a stream of data whose distribution changes over time. In this context, the main problem is how to learn new information without forgetting old knowledge (i.e., Catastrophic Forgetting). Most existing CL approaches focus on finding solutions to preserve acquired knowledge, so working on the past of the model. However, we argue that as the model has to continually learn new tasks, it is also important to put focus on the present knowledge that could improve following tasks learning. In this paper we propose a new, simple, CL algorithm that focuses on solving the current task in a way that might facilitate the learning of the next ones. More specifically, our approach combines the main data stream with a secondary, diverse and uncorrelated stream, from which the network can draw auxiliary knowledge. This helps the model from different perspectives, since auxiliary data may contain useful features for the current and the next tasks and incoming task classes can be mapped onto auxiliary classes. Furthermore, the addition of data to the current task is implicitly making the classifier more robust as we are forcing the extraction of more discriminative features. Our method can outperform existing state-of-the-art models on the most common CL Image Classification benchmarks.

This work investigates the entanglement between Continual Learning (CL) and Transfer Learning (TL). In particular, we shed light on the widespread application of network pretraining, highlighting that it is itself subject to catastrophic forgetting. Unfortunately, this issue leads to the under-exploitation of knowledge transfer during later tasks. On this ground, we propose Transfer without Forgetting (TwF), a hybrid approach building upon a fixed pretrained sibling network, which continuously propagates the knowledge inherent in the source domain through a layer-wise loss term. Our experiments indicate that TwF steadily outperforms other CL methods across a variety of settings, averaging a 4.81% gain in Class-Incremental accuracy over a variety of datasets and different buffer sizes., Comment: 22 pages, 3 Figures. Accepted at 17th European Conference on Computer Vision (ECCV 2022), Tel Aviv, Israel

A dominating set in a directed graph is a set of vertices $S$ such that all the vertices that do not belong to $S$ have an in-neighbour in $S$. A locating set $S$ is a set of vertices such that all the vertices that do not belong to $S$ are characterized uniquely by the in-neighbours they have in $S$, i.e. for every two vertices $u$ and $v$ that are not in $S$, there exists a vertex $s\in S$ that dominates exactly one of them. The size of a smallest set of a directed graph $D$ which is both locating and dominating is denoted by $\gamma^{LD}(D)$. Foucaud, Heydarshahi and Parreau proved that any twin-free digraph $D$ satisfies $\gamma^{LD}(D)\leq \frac{4n} 5 +1$ but conjectured that this bound can be lowered to $\frac{2n} 3$. The conjecture is still open. They also proved that if $D$ is a tournament, i.e. a directed graph where there is one arc between every pair of vertices, then $\gamma^{LD}(D)\leq \lceil \frac{n}{2}\rceil$. The main result of this paper is the generalization of this bound to connected local tournaments, i.e. connected digraphs where the in- and out-neighbourhoods of every vertex induce a tournament. We also prove $\gamma^{LD}(D)\leq \frac{2n} 3$ for all quasi-twin-free digraphs $D$ that admit a supervising vertex (a vertex from which any vertex is reachable). This class of digraphs generalizes twin-free acyclic graphs, the most general class for which this bound was known.

We propose a novel 3D fully convolutional deep network for automated pancreas segmentation from both MRI and CT scans. More specifically, the proposed model consists of a 3D encoder that learns to extract volume features at different scales; features taken at different points of the encoder hierarchy are then sent to multiple 3D decoders that individually predict intermediate segmentation maps. Finally, all segmentation maps are combined to obtain a unique detailed segmentation mask. We test our model on both CT and MRI imaging data: the publicly available NIH Pancreas-CT dataset (consisting of 82 contrast-enhanced CTs) and a private MRI dataset (consisting of 40 MRI scans). Experimental results show that our model outperforms existing methods on CT pancreas segmentation, obtaining an average Dice score of about 88%, and yields promising segmentation performance on a very challenging MRI data set (average Dice score is about 77%). Additional control experiments demonstrate that the achieved performance is due to the combination of our 3D fully-convolutional deep network and the hierarchical representation decoding, thus substantiating our architectural design.

At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k \log k)} \cdot n^{\mathcal{O}(1)}$-time algorithm on graphs of treewidth at most $k$, assuming the Exponential Time Hypothesis. This contrasts with the $3^{k} \cdot k^{\mathcal{O}(1)} \cdot n$-time algorithm for FVS using the Cut&Count technique. During their live talk at IPEC 2020, Bergougnoux et al.~posed a number of open questions, which we answer in this work. - Subset Even Cycle Transversal, Subset Odd Cycle Transversal, Subset Feedback Vertex Set can be solved in time $2^{\mathcal{O}(k \log k)} \cdot n$ in graphs of treewidth at most $k$. This matches a lower bound for Even Cycle Transversal of Bergougnoux et al.~and improves the polynomial factor in some of their upper bounds. - Subset Feedback Vertex Set and Node Multiway Cut can be solved in time $2^{\mathcal{O}(k \log k)} \cdot n$, if the input graph is given as a clique-width expression of size $n$ and width $k$. - Odd Cycle Transversal can be solved in time $4^k \cdot k^{\mathcal{O}(1)} \cdot n$ if the input graph is given as a clique-width expression of size $n$ and width $k$. Furthermore, the existence of a constant $\varepsilon > 0$ and an algorithm performing this task in time $(4-\varepsilon)^k \cdot n^{\mathcal{O}(1)}$ would contradict the Strong Exponential Time Hypothesis., Comment: 32 pages, 4 figures

In this work, we propose a 3D fully convolutional architecture for video saliency prediction that employs hierarchical supervision on intermediate maps (referred to as conspicuity maps) generated using features extracted at different abstraction levels. We provide the base hierarchical learning mechanism with two techniques for domain adaptation and domain-specific learning. For the former, we encourage the model to unsupervisedly learn hierarchical general features using gradient reversal at multiple scales, to enhance generalization capabilities on datasets for which no annotations are provided during training. As for domain specialization, we employ domain-specific operations (namely, priors, smoothing and batch normalization) by specializing the learned features on individual datasets in order to maximize performance. The results of our experiments show that the proposed model yields state-of-the-art accuracy on supervised saliency prediction. When the base hierarchical model is empowered with domain-specific modules, performance improves, outperforming state-of-the-art models on three out of five metrics on the DHF1K benchmark and reaching the second-best results on the other two. When, instead, we test it in an unsupervised domain adaptation setting, by enabling hierarchical gradient reversal layers, we obtain performance comparable to supervised state-of-the-art.

The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbidden-transition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bio-informatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an in-depth study of tractability with regards to various graph-width parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbidden-transition graph is W[1]-hard when parameterized by the vertex-deletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edge-colored graph; properly colored walks in edge-colored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs.

A 2-edge-coloured graph $G$ is {\bf supereulerian} if $G$ contains a spanning closed trail in which the edges alternate in colours. An {\bf eulerian factor} of a 2-edge-coloured graph is a collection of vertex disjoint induced subgraphs which cover all the vertices of $G$ such that each of these subgraphs is supereulerian. We give a polynomial algorithm to test if a 2-edge-coloured graph has an eulerian factor and to produce one when it exists. A 2-edge-coloured graph is {\bf (trail-)colour-connected} if it contains a pair of alternating $(u,v)$-paths ($(u,v)$-trails) whose union is an alternating closed walk for every pair of distinct vertices $u,v$. A 2-edge-coloured graph is {\bf M-closed} if $xz$ is an edge of $G$ whenever some vertex $u$ is joined to both $x$ and $z$ by edges of the same colour. M-closed 2-edge-coloured graphs, introduced in \cite{balbuenaDMTCS21}, form a rich generalization of 2-edge-coloured complete graphs. We show that if $G$ is an extension of an M-closed 2-edge-coloured complete graph, then $G$ is supereulerian if and only if $G$ is trail-colour-connected and has an eulerian factor. We also show that for general 2-edge-coloured graphs it is NP-complete to decide whether the graph is supereulerian. Finally we pose a number of open problems.