Claudio Battiloro
@clabat9.bsky.social
Postdoc @Harvard | Topological Signal Processing ⋂ Deep Learning ⋂ AI for Health and Climate ⋂ Stochastic Optimization | Ex Visiting Associate @PennEngineers
🔗 cbattiloro.com
🔗 cbattiloro.com
🧵 7/7
Given our results, these tasks will hopefully also serve as proper benchmarks for the TDL and GeomDL communities.
💻 Code, data, and tutorial soon available!
@francescadomin8
Given our results, these tasks will hopefully also serve as proper benchmarks for the TDL and GeomDL communities.
💻 Code, data, and tutorial soon available!
@francescadomin8
May 28, 2025 at 2:56 PM
🧵 7/7
Given our results, these tasks will hopefully also serve as proper benchmarks for the TDL and GeomDL communities.
💻 Code, data, and tutorial soon available!
@francescadomin8
Given our results, these tasks will hopefully also serve as proper benchmarks for the TDL and GeomDL communities.
💻 Code, data, and tutorial soon available!
@francescadomin8
🧵 6/7
🧠 Based on these theoretical insights, we test SSNs on brain dynamics classification tasks, showing huge improvements upon existing methods by up to 50% over vanilla message-passing GNNs and by up to 27% over the second-best models.
🧠 Based on these theoretical insights, we test SSNs on brain dynamics classification tasks, showing huge improvements upon existing methods by up to 50% over vanilla message-passing GNNs and by up to 27% over the second-best models.
May 28, 2025 at 2:56 PM
🧵 6/7
🧠 Based on these theoretical insights, we test SSNs on brain dynamics classification tasks, showing huge improvements upon existing methods by up to 50% over vanilla message-passing GNNs and by up to 27% over the second-best models.
🧠 Based on these theoretical insights, we test SSNs on brain dynamics classification tasks, showing huge improvements upon existing methods by up to 50% over vanilla message-passing GNNs and by up to 27% over the second-best models.
🧵 5/7
✅ We utilize SSNs to bridge the gap between neurotopology and the deep learning world, marking a first-time connection. In particular, we prove that SSNs are able to recover several key topological invariants that are critical to characterize brain activity.
✅ We utilize SSNs to bridge the gap between neurotopology and the deep learning world, marking a first-time connection. In particular, we prove that SSNs are able to recover several key topological invariants that are critical to characterize brain activity.
May 28, 2025 at 2:56 PM
🧵 5/7
✅ We utilize SSNs to bridge the gap between neurotopology and the deep learning world, marking a first-time connection. In particular, we prove that SSNs are able to recover several key topological invariants that are critical to characterize brain activity.
✅ We utilize SSNs to bridge the gap between neurotopology and the deep learning world, marking a first-time connection. In particular, we prove that SSNs are able to recover several key topological invariants that are critical to characterize brain activity.
🧵 4/7
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
May 28, 2025 at 2:56 PM
🧵 4/7
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
🧵 3/7
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
May 28, 2025 at 2:56 PM
🧵 3/7
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🧵 2/7
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
May 28, 2025 at 2:56 PM
🧵 2/7
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
🧵 4/7
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
May 28, 2025 at 2:56 PM
🧵 4/7
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
✅ SSNs can be implemented following any differentiable approach, not only message-passing.
✅ We also introduce Routing-SSNs (R-SSNs), lightweight scalable variants that dynamically select the most relevant interactions in a learnable way.
🧵 3/7
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
May 28, 2025 at 2:56 PM
🧵 3/7
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🌟 Contribution:
✅ We present Semi-Simplicial Neural Networks (SSNs), models operating on semi-simplicial sets, representing the currently most comprehensive deep learning framework to capture topological higher-order directed interactions in data.
🧵 2/7
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
May 28, 2025 at 2:56 PM
🧵 2/7
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
Thank you all, especially
@manuel_lecha, who has been the incredibly talented, driving force behind this work. I will not forget our endless conversations at every time of day and night! 😅 🤣🫂
Reposted by Claudio Battiloro
Thank you Guillermo Bernárdez, @clabat9.bsky.social @ninamiolane.bsky.social
for making this work possible!
🏠 @geometric-intel.bsky.social @ucsb.bsky.social
for making this work possible!
🏠 @geometric-intel.bsky.social @ucsb.bsky.social
May 19, 2025 at 6:04 PM
Thank you Guillermo Bernárdez, @clabat9.bsky.social @ninamiolane.bsky.social
for making this work possible!
🏠 @geometric-intel.bsky.social @ucsb.bsky.social
for making this work possible!
🏠 @geometric-intel.bsky.social @ucsb.bsky.social
Reposted by Claudio Battiloro
🍩TopoTune takes any neural network as input and builds the most general TDL model to date, complete with permutation equivariance and unparalleled expressivity.
⚙️ Thanks to its implementation in TopoBench, defining and training these models only requires a few lines of code.
⚙️ Thanks to its implementation in TopoBench, defining and training these models only requires a few lines of code.
May 19, 2025 at 6:04 PM
🍩TopoTune takes any neural network as input and builds the most general TDL model to date, complete with permutation equivariance and unparalleled expressivity.
⚙️ Thanks to its implementation in TopoBench, defining and training these models only requires a few lines of code.
⚙️ Thanks to its implementation in TopoBench, defining and training these models only requires a few lines of code.
When we view causality subjectively, it turns into relative causal knowledge—much like a fact can seem like an opinion when seen subjectively. Still, causality is causality and a fact remains a fact, but it becomes understandable only when viewed within the entire network.🧵 9/9
March 18, 2025 at 1:34 PM
When we view causality subjectively, it turns into relative causal knowledge—much like a fact can seem like an opinion when seen subjectively. Still, causality is causality and a fact remains a fact, but it becomes understandable only when viewed within the entire network.🧵 9/9
Each subject in a network of relations has then its subjective Causal Knowledge, BUT it can be be accessed by the other subjects of the network only trough their own perspective. Imagine how important is this in an agent AI network (or in any human network).
🧵 8/9
🧵 8/9
March 18, 2025 at 1:34 PM
Each subject in a network of relations has then its subjective Causal Knowledge, BUT it can be be accessed by the other subjects of the network only trough their own perspective. Imagine how important is this in an agent AI network (or in any human network).
🧵 8/9
🧵 8/9
Overall, what we did was using these tools to go beyond Structural Causal Models as we usually intend them and define a broad notion of Causal Knowledge.
🧵 7/9
🧵 7/9
March 18, 2025 at 1:34 PM
Overall, what we did was using these tools to go beyond Structural Causal Models as we usually intend them and define a broad notion of Causal Knowledge.
🧵 7/9
🧵 7/9
Although they are sophisticated mathematical frameworks, we invite any ML practitioner to read this work, it is self-contained and has immediate methodological and practical implications.
🧵 6/9
🧵 6/9
March 18, 2025 at 1:34 PM
Although they are sophisticated mathematical frameworks, we invite any ML practitioner to read this work, it is self-contained and has immediate methodological and practical implications.
🧵 6/9
🧵 6/9
We believe this was a necessary step toward a better understanding of causality and will have significant implications on AI.
The moment our conceptual goal was clear, we found the technical tools needed to implement it: Network sheaves and category theory.
🧵 5/9
The moment our conceptual goal was clear, we found the technical tools needed to implement it: Network sheaves and category theory.
🧵 5/9
March 18, 2025 at 1:34 PM
We believe this was a necessary step toward a better understanding of causality and will have significant implications on AI.
The moment our conceptual goal was clear, we found the technical tools needed to implement it: Network sheaves and category theory.
🧵 5/9
The moment our conceptual goal was clear, we found the technical tools needed to implement it: Network sheaves and category theory.
🧵 5/9
By stripping causality of its oracular and absolute meaning, the relativity of causal knowledge situates it within a different ontological setting, where truth is not monolithic but emerges inevitably and relatively from a set of relationships.
🧵 4/9
🧵 4/9
March 18, 2025 at 1:34 PM
By stripping causality of its oracular and absolute meaning, the relativity of causal knowledge situates it within a different ontological setting, where truth is not monolithic but emerges inevitably and relatively from a set of relationships.
🧵 4/9
🧵 4/9
We ended up converging on a simple but technically unexplored concept: any causal model is an imperfect and subjective representation of the world, and it cannot be severed from the network of relations the subject is immersed in.
🧵 3/9
🧵 3/9
March 18, 2025 at 1:34 PM
We ended up converging on a simple but technically unexplored concept: any causal model is an imperfect and subjective representation of the world, and it cannot be severed from the network of relations the subject is immersed in.
🧵 3/9
🧵 3/9
One day, Gabriele and I were talking about Grothendieck and his relativism, and we asked ourselves how his approach could be philosophically framed and how it could be used for causal theory.
🧵 2/9
🧵 2/9
March 18, 2025 at 1:34 PM
One day, Gabriele and I were talking about Grothendieck and his relativism, and we asked ourselves how his approach could be philosophically framed and how it could be used for causal theory.
🧵 2/9
🧵 2/9
🔥🌏 According to the @IPCC_CH , over 40% of the global population (about 3.5 billion people) live in contexts of extreme climate vulnerability.
The also IPCC identified 127 risks that affect every aspect of private, social, and economic life of everyone.
Everyone.
🧵 10/10
The also IPCC identified 127 risks that affect every aspect of private, social, and economic life of everyone.
Everyone.
🧵 10/10
January 29, 2025 at 3:37 PM
🔥🌏 According to the @IPCC_CH , over 40% of the global population (about 3.5 billion people) live in contexts of extreme climate vulnerability.
The also IPCC identified 127 risks that affect every aspect of private, social, and economic life of everyone.
Everyone.
🧵 10/10
The also IPCC identified 127 risks that affect every aspect of private, social, and economic life of everyone.
Everyone.
🧵 10/10