Thesis & projects proposals

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Here you will find some project and thesis proposals for students

The topics are available (in different declensions) both for projects, undergraduate final project (Laurea) and master thesis (Laurea Magistrale)

COLOR MEANING (just from a pure scientific perspective): 

• HOT PROJECT (high risk, high reward, probably publishable)

• Standard project (medium risk, medium reward, probably just developmental)

• Easy project (low risk, low reward, probably little more than compilative)

MANIFOLD TRANSFORM & MODELING

[SIT01] Adaptive Geodesic Convolutions with Learned Transport
Design a convolutional layer that learns how to combine features defined in different tangent spaces. The layer will separate the effect of geodesic distance from the transformation used to bring neighbouring features into a common frame. The student will derive conditions under which the output transforms consistently when local coordinate frames change, and test whether learned transport captures patterns that fixed parallel transport misses.

[SIT02] Invertible Multiscale Transforms on Manifolds
Develop a learnable lifting transform that splits manifold-valued signals into coarse and detail components. The architecture will use geometric prediction and update steps with an explicit inverse. The project will establish conditions for exact reconstruction and study how curvature affects numerical stability, the distribution of information across scales, and reconstruction when fine-scale coefficients are discarded.

[SIT03] Neural Networks with a Learned Atlas
A single coordinate chart can distort different parts of a manifold by different amounts. This project develops a network that learns several local charts and routes each input to the charts that best represent its neighbourhood. The student will design trainable transition maps, impose consistency where charts overlap, and test whether the learned atlas preserves local geometry and recovers structure that a single global representation distorts.

[SIT04] Transformers That Respect Changes of Basis in Covariance Data
Develop an attention layer for sequences of symmetric positive definite matrices. Attention scores will depend on geometric relations between matrices, and the layer will combine values through a geometric mean. The central question is which components of the architecture can preserve equivariance under invertible changes of basis. The student will prove the property for a simplified layer and measure the error introduced by faster approximations.

[SIT05] Generative Flows with Exact Matrix Constraints
Design a conditional flow that generates positive definite matrices while preserving a specified block exactly. The architecture will learn separate transformations for the cross-block terms and for the Schur complement, which controls positive definiteness once the fixed block is given. The student will establish which matrices the parameterization can represent and test how well the learned flow captures dependencies between observed and unobserved entries.

[SIT06] Unrolled Sparse Coding with Geometric Dictionaries
Build a neural architecture that unrolls a small number of sparse coding steps on a manifold. Each layer will update the contribution of learned dictionary atoms, and a geometric decoder will combine them into a valid manifold-valued representation. Starting from positive definite matrices, the project will study when the architecture can recover the active atoms and how the result changes when the matrices fail to commute.

[SIT07] Self-Supervised Architectures That Separate Content from Coordinate Changes
Develop an encoder with two outputs: a representation that stays stable under a specified family of transformations and a representation that tracks how the input was transformed. Training on paired views will test whether the architecture can learn both properties without collapsing to a constant representation. Controlled experiments will identify what information is lost when the model is made invariant to transformations that also change meaningful structure.

[SIT08] Learning the Metric Inside a Neural Network
Design an architecture that learns a smooth Riemannian metric and uses it to define neighbourhoods and distances inside the network. The metric will be constrained to keep distances from collapsing or growing without bound. The student will test whether the model can recover geometric properties from partial observations and study how changes in the learned metric affect the stability of subsequent layers.

[SIT09] Stable Recurrent Networks for Manifold-Valued Sequences
Develop a recurrent unit whose hidden state lies on a manifold. The unit will express each update as a tangent vector and map the result back to the manifold. The project will derive conditions under which small state errors stay bounded across repeated updates, then test how those conditions affect memory and long-horizon prediction on sequences with known dynamics.

[SIT10] Neural Operators That Transfer Across Manifold Discretizations
Design a neural operator that learns how a signal evolves on a surface and can be evaluated on different meshes of that surface. The architecture will combine a geometric diffusion operator with learned local mixing. Using surfaces with known diffusion dynamics, the student will test whether predictions converge as the mesh is refined and how much the output changes when the same surface is discretized in a different way.

GRAPH & HYPERGRAPH NEURAL NETWORKS

[HGR01] What Is Lost When a Hypergraph Becomes a Graph?
Different group structures can produce exactly the same pairwise graph. This project builds controlled examples in which the correct prediction depends on those hidden differences. The student will derive conditions under which a graph-based model cannot distinguish the examples and test whether hypergraph neural networks can recover the missing information.

[HGR02] Learning Hyperedges from Multivariate Time Series
In many systems, we observe signals from individual entities and must infer which groups interact. This project learns a hypergraph jointly with a model of the observed dynamics. Using simulations with known group interactions, the student will test whether good predictions imply that the model has recovered the correct hyperedges, and how this depends on noise and the amount of data.

[HGR03] Neural Sheaves for Different Roles Within a Group
Members of the same group can play different roles. A sender, a receiver, and a relay, for example, contribute different information to the same communication event. This project uses neural sheaves to learn how each member contributes to a shared group representation. Controlled experiments will test whether the model recovers these roles and generalizes to new combinations of members.

[HGR04] When Do High-Pass Sheaflets Help?
High-pass sheaflet filters can highlight local differences within a hypergraph, including both meaningful changes and noise. This project studies how those two effects can be separated. The student will vary the location and scale of informative changes and noise, then test whether a model that selects spectral bands adaptively improves on fixed low-pass and high-pass filters.

[HGR05] How Stable Are Sheaflet Representations?
A single error in a hypergraph can change which nodes belong to a group. This project studies how missing memberships and changes to learned sheaf maps affect representations at different scales. The student will derive perturbation bounds for a simplified sheaflet model and test whether those bounds explain the behavior of deeper networks.

[HGR06] Can Hyperedges Relieve Oversquashing?
Graph neural networks can struggle when information from many distant nodes must pass through a narrow part of the network. This project tests whether meaningful group connections help distant information reach its destination. Controlled experiments will compare hypergraph message passing with pairwise shortcuts at similar computational cost and measure how much information reaches a target node.

[HGR07] Learning Directional Interactions with Hypergraph Sheaves
Many processes have several inputs and several outputs. This project studies how directed hyperedges and learned sheaf maps represent such interactions. Ussimulations with known input and output groups, the student will test whether the model can predict what happens when the direction of an interaction changes or when a member moves from one group to the other.

[HGR08] Hypergraph World Models for Multi-Agent Systems
The outcome of an action can depend on which agents act together. This project builds a world model with time-varying hyperedges to represent teams that form, act, and split. The evaluation compares pairwise and higher-order models on their ability to predict the consequences of joint actions by teams that were absent from the training data.

[HGR09] Scaling Hypergraph Sheaf Networks with Local Computation
Sheaf-based models must transform and aggregate information across many node–hyperedge memberships. This project studies how to reduce that cost through local computation and low-rank approximations of the learned maps. The student will measure which approximations preserve predictive accuracy and how memory use and runtime change as the number and size of hyperedges grow.

[HGR10] Do Hypergraph Networks Generalize to Larger Groups?
A model trained on interactions among three or four entities may have to predict the behavior of much larger groups. This project studies which aggregation rules generalize across group sizes. Controlled tasks will separate properties that should stay constant as a group grows from properties that genuinely depend on its size, and test which models learn the appropriate rule.

WORLD MODELS

[SDR01] When World Models Imagine the Wrong Action
A world model can predict how an environment evolves and still rank two actions incorrectly. This project uses controlled simulations to compare the imagined and actual outcomes of alternative actions. The goal is to identify which prediction errors change the agent’s decision and measure how much performance is lost when they do.

[SDR02] Adaptive Imagination Horizons for Dreamer
How far ahead should an agent imagine? This project develops a method for adapting the length of Dreamer’s imagined trajectories during training based on uncertainty about the consequences of actions. Experiments compare adaptive and fixed horizons in terms of policy performance, computational cost, and sensitivity to errors that accumulate over time.

[SDR03] What Should a World Model Remember?
An agent sees a clue at the start of an episode and must use it much later to make a decision. This project compares Dreamer’s recurrent memory with a state-space model and a limited-window Transformer. Under comparable computational budgets, the experiments measure how long each model retains the information that matters for the choice.

[SDR04] Learning Decision-Relevant Latent States
In a visual task, the background may occupy most of the image while a small object determines whether the agent succeeds. This project studies how observation reconstruction and reward prediction shape the information that Dreamer retains in its latent state. The evaluation tests how the learned representation and policy respond to changes in irrelevant parts of the scene.

[SDR05] Learning Hidden Dynamics Through Intervention
Two environments can look identical until the agent takes an action that reveals how their dynamics differ. This project builds controlled environments of this kind and studies which experiences allow a world model to tell them apart. The evaluation tests whether the model can predict the effects of action sequences it did not encounter during training.

[SDR06] Adapting World Models to Changing Dynamics
An agent trained under one set of physical conditions may have to adapt when friction, mass, or response delay changes. This project compares updating a world model’s latent context with updating its network weights. Experiments in simulated control tasks measure how many interactions each method needs to recover performance and how well it handles conditions seen before.

[SDR07] World Models at Multiple Time Scales
An agent may need to correct a movement immediately while anticipating the effects of a decision much later. This project develops a world model with two latent states updated at different rates. Simulated control tasks are used to test whether this structure improves long-range predictions and reduces the cost of generating imagined trajectories.

[SDR08] Rare Failures in Imagined Trajectories
A policy with a high average return can still choose actions that occasionally lead to serious failures. This project tests whether a world model can represent rare outcomes and estimate their probability. In a simulator where failure rates can be controlled, the experiments compare policies that optimize average return with policies that also account for the worst outcomes.

[SDR09] When Should a Robot Ask for Help?
A robot navigating an ambiguous scene can continue using a lightweight world model or ask a vision-language model for clarification. This project studies when extra information is likely to change the robot’s next action enough to justify the cost of a request. The evaluation measures navigation success, response time, and the number of requests in simulation.

[SDR10] World Models for Active HF Spectrum Monitoring
An intermittent radio transmission can appear silent when it is masked by interference. This project uses a world model to track overlapping radio signals and decide when to run a neural source separator. On sequences of I/Q samples with known transmission activity, the experiments test whether planning reduces false alarms and missed detections under a fixed budget of separator calls.

NEUROCOMPUTING & NEURAL DYNAMICS

[ABR01] What Can a World Model Recover from EEG?
Different patterns of neural activity can produce very similar signals at the scalp. This project uses simulations with known sources to study which aspects of the underlying dynamics a world model can recover. By varying sensor coverage and the length of the observation history, the student will test when accurate prediction of EEG signals also implies accurate recovery of the dynamics that generated them.

[ABR02] Learning EEG Representations That Transfer Across Devices
EEG recordings can use different electrode positions, channel counts, and reference schemes. This project develops an encoder that uses electrode coordinates to build a shared representation across sensor layouts. Controlled changes to the layout will test whether the model preserves the same information about the signal and transfers to a configuration it has never seen.

[ABR03] When Do Brain Networks Need Hypergraphs?
Graphs describe pairwise relations between brain regions, while hypergraphs can represent interactions among several regions at once. This project builds simulated brain networks with similar pairwise statistics but different group interactions. The student will test which interactions graph and hypergraph neural networks can recover, and how much data each model needs to do so reliably.

[ABR04] From Brain Connectivity to Causal Predictions
A model can predict brain signals accurately while learning the wrong direction of influence between regions. This project studies whether an anatomical connectivity graph helps a model infer those directions. Experiments on simulated networks will compare predictions on ordinary recordings with predictions made after perturbing a region, where the true response is known.

[ABR05] Learning Shared Dynamics from EEG and fNIRS
EEG and fNIRS capture different aspects of brain activity at different time scales. This project develops a model with separate observation processes and a shared latent state. Using simulations with known delays and paired recordings where available, the student will test when combining the two signals improves recovery of the shared dynamics and when apparent agreement comes from features specific to one modality.

[ABR06] Detecting Changes in Neural Dynamics Before an Event
A change in EEG can reflect a change in neural dynamics, a change in signal power, or a recording artifact. This project tests whether multiscale features, including wavelet-based measures, can distinguish these possibilities. Simulations provide known transition times. An evaluation on held-out subjects then tests whether the most reliable features remain informative in recordings around seizure onset.

[ABR07] Memory and Stability in Spiking Neural Networks
A spiking network can retain information through the timing of spikes and the evolution of its internal state. This project studies how those mechanisms affect memory and stability when inputs are noisy or irregular. Controlled sequence tasks and EEG segments will be used to compare spiking and gated recurrent networks under comparable model sizes, with attention to memory span, robustness, and computational cost.

[ABR08] Do Explanations of Brain Network Models Survive Intervention?
A graph neural network can highlight a connection as important even when its prediction changes little after that connection is modified. This project tests explanations using controlled interventions on simulated brain networks. The student will distinguish connections that influence the model’s output from connections that drive the simulated process, and measure how often explanation methods recover each type.

[ABR09] World Models for Active EEG Sensing
If an EEG system can read only a few channels at a time, which channels should it read next? This project uses a world model to estimate what each measurement could reveal about a hidden neural state. Under a fixed measurement budget, the experiments compare fixed channel sets, selection based on immediate information gain, and planning over several future measurements.

[ABR10] Learning Anatomy That Transfers Across MRI Scanners
A model trained on brain MRI can use scanner-specific image patterns as shortcuts. This project tests whether anatomical constraints help a model preserve its representation when image contrast or acquisition style changes. Using controlled image transformations and held-out scanners where available, the student will measure whether the model stays consistent for the same anatomy while remaining sensitive to genuine structural changes.

TRAINING REGIMES AND EXPLAINABILITY

[PMK01] Learning to Identify Training Regimes in Deep Networks
This project develops a model that learns to detect regime changes across layers and training steps. Starting with shallow MLPs and progressing to deep MLPs and residual networks, the student will test whether the model can distinguish a network-wide transition from a change confined to one block, and whether the regimes transfer across depths and optimizers.

[PMK02] Training Diagnostics That Survive Reparameterization
Two ReLU networks can represent the same function while having different layer-wise gradient norms. This project develops diagnostics that distinguish changes in the network’s predictions from changes in how its parameters are expressed. The student will derive the effect of function-preserving rescaling on gradient–loss coupling, then test whether diagnostics based on the effect of individual layer updates on predictions yield more consistent explanations across equivalent parameterizations.

[PMK03] From Gradient-Loss Coupling to Feature Learning
A change in gradient–loss coupling may signal that a network is learning new features, or it may reflect changes in gradient scale as the loss decreases. This project starts with deep linear networks, where the evolution of individual learning modes can be analysed, and then moves to nonlinear networks with matched linearized baselines. The student will test which coupling patterns reliably mark the point at which a network begins to depart from the behaviour predicted by its initialization.

[PMK04] Which Layers Actually Drove Learning?
A layer with large gradients may contribute little to what the network ultimately learns. This project develops a method that explains a training phase by identifying which blocks, updated during that phase, affected the acquisition of specific features. Starting from the same checkpoint, the student will replay short segments of training while suppressing selected updates. A deep encoder with a probabilistic head that learns class- and feature-specific bandwidths can serve as a controlled test bed for separating changes in the representation from changes in the decision rule.

[PMK05] Learning When to Update Each Layer
This project develops a training controller that learns when to change a block’s learning rate or pause its updates. The controller observes signals such as gradient–loss coupling and changes in layer representations. Each action is logged with the training signal that triggered it. The student will compare the learned controller with fixed schedules at a matched training budget and use checkpoint replays to test whether the stated reasons predict the actual effect of each intervention.

[PMK06] Concept Bottlenecks That Support Reliable Corrections
If a user corrects a concept predicted by a neural network, does the final prediction change for the expected reason? This project designs a concept bottleneck that limits how much extra information can pass through the concept representations. On datasets with known factors, the student will test whether the network relies on the stated concepts and whether correcting one concept changes the prediction as intended.

[PMK07] Counterfactual Explanations with Feasible Changes
A counterfactual explanation describes what would need to change for a model to make a different decision. This project develops a generator that proposes changes to meaningful input factors and accounts for how those changes affect other variables. Using simulated data with known dependencies, the student will compare methods on three criteria: whether the decision changes, whether the proposed change is feasible, and whether the explanation identifies the factor that produced the change.

[PMK08] Detecting Shortcut Learning Before Accuracy Drops
A neural network may keep the same accuracy across two environments while changing which features it uses. This project constructs controlled environments in which useful features and shortcuts can be varied independently. The student will develop a diagnostic based on targeted feature interventions and test whether it detects changes in the model’s reliance on shortcuts earlier than standard performance metrics.

[PMK09] Finding the Smallest Circuit That Explains a Prediction
Which components of a deep network carry out a specific computation? This project learns a sparse set of connections between neurons or blocks and tests whether that set explains how the model solves a controlled reasoning task. The student will replace selected activations with those from matched inputs and test both whether the proposed circuit can reproduce the behaviour and whether disrupting it removes that behaviour on unseen examples.

[PMK10] When Equally Accurate Networks Give Different Explanations
Networks with similar test accuracy can rely on different evidence. This project trains a set of comparably performing models and compares their explanations on inputs with known informative and redundant features. The student will develop a method that reports which features the models consistently rely on, where they disagree, and how much of that disagreement comes from the models themselves or from the explanation method.

HUMAN-MACHINE & HUMAN-ROBOT INTERACTION

[PRS01] Can Llama Predict Where People Look in an Advertisement?
This project tests whether a multimodal Llama model can predict how viewers distribute their attention across a brand logo, product image, headline, and offer. Our gaze estimation and fixation detection algorithms will provide measures such as time to first fixation and total viewing time. The student will compare Llama’s predictions with dedicated saliency models and measured human gaze, and test whether they capture how viewing patterns change when people look for the brand or try to understand the offer.

[PRS02] From Eye Movements to Brand Recall
Does looking at a brand help predict whether someone will remember which product it was associated with? This project combines eye-tracking data, visual layout features, and attention estimates from Llama and saliency models to predict brand recall when viewers are later shown a product cue. The student will compare models that use the ad image alone, predicted attention, measured gaze, or a combination of these inputs. Testing on unseen ad families will show whether gaze adds information that generalizes beyond the original designs.

[PRS03] Redesigning Advertisements with Llama and Eye-Tracking Feedback
This project develops a system in which multimodal Llama proposes specific layout edits and our visual analysis algorithms help score the resulting designs. Edits may move or resize the logo, adjust contrast, or change spacing while preserving the wording, claims, prices, and offer conditions. An eye-tracking experiment will compare the original ads, versions edited using fixed design rules, and versions edited using AI. The main outcome is brand recall, with additional checks on readability and offer comprehension.

[PRS04] Predicting the Order in Which People Read an Advertisement
Two viewers can look at the same elements in a different order. This project uses computer vision to identify ad elements and fixation detection to reconstruct the sequence in which each viewer looks at them. The student will compare a sequence model with Llama-based predictions and test whether the order of fixations improves predictions of offer comprehension beyond total viewing time.

[PRS05] How Logo Size and Position Affect Attention and Memory
This project uses controlled versions of the same ads to vary logo size and position independently. Viewers will be randomly assigned to different versions, and eye tracking will show how each design change affects when and for how long they look at the brand. The student will test whether these changes also affect product-cued brand recall and whether visual saliency models predict the direction of the effect.

[PRS06] Do Llama’s Explanations Match the Evidence It Uses?
This project studies which parts of an advertisement influence Llama’s answers about the brand, product, or offer. The student will mask or replace selected regions and measure how the answers change. The results will be compared with the regions Llama names in its explanations and with human fixation maps. The evaluation will measure separately how well the explanations reflect the model’s own behaviour and how closely they align with human gaze.

[PRS07] Predicting Disagreement in Visual Attention
Some advertisements draw most viewers to the same element, while others produce very different viewing patterns. This project uses eye-tracking data to develop models that predict a distribution of attention across ad elements. The student will test whether image features and Llama’s descriptions help identify ads on which viewers are likely to disagree, and whether the model’s uncertainty matches the variation observed in new viewers.

[PRS08] How Reliable Is Webcam Eye Tracking for Advertising Research?
This project compares our camera-based gaze estimation and fixation detection algorithms with recordings from a reference eye tracker. The student will test which conclusions about attention to the brand, product, and offer remain reliable as lighting, head position, and the size of ad elements change. The evaluation will identify which advertising research questions can be studied with webcam data and which require more precise measurements.

[PRS09] Does Attention Prediction Transfer Across Languages?
This project compares versions of the same advertisements in different languages while controlling the layout and visual prominence of the text as closely as possible. Eye-tracking data will be used to test whether multimodal Llama and dedicated saliency models predict where attention shifts when the text changes. The student will evaluate how well each model transfers to an unseen language and separate changes associated with reading from those associated with the layout.

[PRS10] Modelling Attention to Ads in a Scrolling Feed
In a scrolling feed, viewers can pass an advertisement before they have time to examine it. This project combines eye tracking, scroll logs, and image features extracted with computer vision and Llama to model when an ad becomes visible, attracts a fixation, or is passed over. The student will compare a model based on the ad image alone with a sequential model that also uses the surrounding content and recent scrolling behaviour.