Baran Hashemi

Tnx Kyle 🤜

We got accepted at #NeurIPS2025. I am very happy that I could merge my knowledge of Mathematics with AI to create sth new and useful for the community. ☺️

The paper: arxiv.org/abs/2505.17190
The code: github.com/Baran-phys/T...

Current AI research vibes:
- Let’s use LLM to do a baby science/math, after it doesn’t work, headline: LLM is bad at the baby math task —> guaranteed virality 😒
- Meanwhile, you develope a novel (non-LLM) method to solve this issue, report success on a deep math problem
—> naa, not enough drama🤦🏻

Another new result from the #NeurIPS rebuttal/discussion phase, our Tropical Transformer achieves much better length OOD performance across all algorithmic tasks, while being 3x-9x faster at inference and using 20% fewer parameters than the Universal Transformer (UT) models.

Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms Dynamic programming (DP) algorithms for combinatorial optimization problems work with taking maximization, minimization, and classical addition in their recursion algorithms. The associated value functions correspond to convex polyhedra in the max plus semiring. Existing Neural Algorithmic Reasoning models, however, rely on softmax-normalized dot-product attention where the smooth exponential weighting blurs these sharp polyhedral structures and collapses when evaluated on out-of-distribution (OOD) settings. We introduce Tropical attention, a novel attention function that operates natively in the max-plus semiring of tropical geometry. We prove that Tropical attention can approximate tropical circuits of DP-type combinatorial algorithms. We then propose that using Tropical transformers enhances empirical OOD performance in both length generalization and value generalization, on algorithmic reasoning tasks, surpassing softmax baselines while remaining stable under adversarial attacks. We also present adversarial-attack generalization as a third axis for Neural Algorithmic Reasoning benchmarking. Our results demonstrate that Tropical attention restores the sharp, scale-invariant reasoning absent from softmax.

During #NeurIPS rebuttal, we have evaluated🌴Tropical Transformer on the Long Range Arena (LRA), achieving highly competitive results, placing 2nd🥈 overall in average accuracy.
Check out our paper: arxiv.org/abs/2505.17190
Our code: github.com/Baran-phys/T...

Cool. Will definitely do 👍

Interesting. I was not aware of aware if the challenges in the video subfield. But that makes sense given the context. We will definitely explore those benchmarks in the future. Thanks for the suggestions.

Tnx. We did not test yet on any other benshmarks. You mean algorithmic or language type benchmarks?

Interesting. I was not aware of this study. However, we did not just used tropical operations, we tried to simulate a concrete tropical circuit and do the message passing in the tropical space with the Generalized Hilbert metric as the kernel.

7/ Our message ✍️
Better reasoning might come not from bigger models, but from choosing the right algebra/geometry 🌴.
@petar-v.bsky.social @jalonso.bsky.social
#TropicalGeometry #NeuralAlgorithmicReasoning #AI4Math

6/ We also show that each Tropical attention head can function as a tropical gate in a tropical circuit, simulating any max-plus circuit.

5/ We benchmarked on 11 canonical combinatorial tasks. Tropical attention beat vanilla & adaptive softmax attention on all three OOD axes, Length, value and Adversarial attack generalization:

4/ Tropical Attention runs each head natively in max-plus. Result:
Strong OOD length generalization with sharp attention maps even in several algorithmic tasks, including the notorious Quickselect algorithm (Another settlement for the challenge identified by @mgalkin.bsky.social )

Image by Cowdery and Challas, featured in June 2009 Mathematics Magazine

3/ In the Tropical (max + ) geometry, “addition” is max, “multiplication” is +. Many algorithms already live here, carving exact polyhedral decision boundaries --> so why force them through exponential probabilities?
Let's ditch softmax, embrace the tropical semiring 🤯🍹.

Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms Dynamic programming (DP) algorithms for combinatorial optimization problems work with taking maximization, minimization, and classical addition in their recursion algorithms. The associated value func...

2/ We introduce Tropical Attention -- the first Neural Algorithmic reasoner that operates in the Tropical semiring, achieving SOTA OOD performance on executing several combinatorial algorithms
arxiv.org/abs/2505.17190

🧵 Tropical Attention --> Softmax is out, Tropical max-plus is in 🦾
1/ 🔥Ever experinced softmax attention fade as sequences grow?
That blur is why many attention mechanisms stumble on algorithmic and reasoning tasks. Well, we have a Algebraic Geometric Tropical solution 🌴

I'm speaking about AI for enumerative geometry at the CMSA New Technologies in Mathematics seminar, on Wednesday.

If you think of DyT as an Activation function, it will be exactly a sub-family of our learnable Dynamic Range Activator (DRA) activation function, when (a,c)=0:

openreview.net/forum?id=4X9...

Call Paper Submission Entrance The workshop uses OpenReview as the review platform. For detailed submission guidelines, please see below.

🔥Big News! The 2nd AI for Math Workshop is coming back to #ICML2025 and we’re back with the theme of exploring the frontiers of AI for mathematical reasoning, problem solving, discovery!

🫵 Calling all pioneers in AI4Math:
📜 Submit your exciting work:
sites.google.com/view/ai4math...

Beautiful indeed!

Dark Energy Survey: implications for cosmological expansion models from the final DES Baryon Acoustic Oscillation and Supernova data The Dark Energy Survey (DES) recently released the final results of its two principal probes of the expansion history: Type Ia Supernovae (SNe) and Baryonic Acoustic Oscillations (BAO). In this paper,...

The DESI survey @desisurvey.bsky.social suggests the universe is *not* maximally boring! Statistical significance is not quite there yet, but a new result is a bit stronger than their previous indication that dark energy might be varying with time. (cont.)

arxiv.org/abs/2503.06712

For the ICLR Camera-ready version:

openreview.net/forum?id=4X9...

Tnx. The probing methods were both linear and non-linear over the conjectural form of the large-genus asymptotic form of the intersections. If the model actually learned the underlying math, it must have internalized the parameters of the asymptotic formula. We found that this was the case.

Can Transformers Do Enumerative Geometry? We introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of $\psi$-class intersection numbers on the moduli space of curves....

🚀 Curious how Transformers understand Enumerative Geometry or model recursive functions with factorial blow-up?
I'll be presenting our results, openreview.net/forum?id=4X9..., at the Math4AI/AI4Math Workshop @mpiMathSci! 🔥
📅 Registration is open until Feb 28
🔗 www.mis.mpg.de/events/serie...
#AI4Math

Can Transformers Do Enumerative Geometry? How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work...

I am extremely happy to announce that our paper
Can Transformers Do Enumerative Geometry? (arxiv.org/abs/2408.14915) has been accepted to the
@iclr-conf.bsky.social!!
Congrats to my collaborators Alessandro Giacchetto at ETH Züruch and Roderic G. Corominas at Harvard.
#ICLR2025 #AI4Math #ORIGINS