Multi-layer transformer models form the backbone of modern deep learning, yet little mathematical work details their benefits and deficiencies as compared with other architectures. This makes it difficult to answer practical and fundamental questions about the transformer architecture: What powers increase with model depth? Can alternative architectures improve efficiency without sacrificing expressivity? Clayton Sanford presents a communication-based theoretical framework for understanding the representational capabilities and limitations of multi-layer transformers. These results imply that parallelizability is a key property of the standard transformer that other architectures cannot easily replicate. Stanford contextualizes these results within the broader conversation about the challenges of developing a principled theory of neural networks and share opinions on how theoretical computer science can remain relevant to their study.

Speaker

Clayton Sanford is a senior research scientist at Google, where he works on distillation and pretraining for Gemini. He has a PhD in computer science from Columbia University and studied machine learning theory with advisors Rocco Servedio and Daniel Hsu. His research focuses on the theoretical capabilities of neural architectures, particularly transformers.

Room Draw 2026 will take place from April 7–9! Be sure to keep an eye out later this semester for the approved regulations and additional details. If you have any questions, please contact the Residential Life team at reslife@g.hmc.edu or reach out to the RALs at ral-l@g.hmc.edu.

HMC Community Conversations offer small-group dialogue (3–5 participants), guided by shared agreements like Listen and Be Curious and Show Respect and Suspend Judgment. This is not a debate—there’s no pressure to persuade or agree. Instead, we’ll listen, reflect and learn from one another.

The topic of conversation for this gathering is “Technology and Relationships.”

While registration isn’t required, it helps us plan. We hope you can join us.

Convergence is the language through which the finite and the infinite converse with each other. This conversation can go both ways: we can understand the infinite by studying the finite (part 1) and the finite by studying the infinite (part 2).

Part 1: We’ll see a situation where the finite accurately describes the infinite. I’ll introduce a classical model of opinion dynamics that’s difficult to analyze. It turns out this model can be thought of as the limit of a family of models as a certain parameter approaches infinity. We’re able to show that our model captures important dynamics of the “infinite” model — for finite parameter values!

Part 2: We’ll see how dynamics on infinite networks tell us about dynamics on finite networks. Studying large networks of interacting agents can be challenging. A convenient strategy is to use infinitely large networks (the “continuum limit”). We do this with functions called graphons which are the limits of sequences of graphs. Under suitable conditions, the solutions of the graphon continuum limit model converge to the solutions of the equivalent models on finite-size networks.

Do you feel like you have to choose between applied or theoretical math? Between loving graph theory or differential equations? After this talk, I hope you’ll see that with convergence we can bridge the gaps.

We gather every other Friday to talk and reflect as one community on the readings from John Fugalsang’s book Separation of Church and Hate.

We welcome you to bring your lunch and join us in talking about topics that stood out to you regarding the reading(s).

The Office of Human Resources is excited to welcome employees back to Breakfast Connections, a monthly gathering that provides a welcoming space to connect with HR, share feedback and engage in open conversations about workplace experiences.

The Office of Human Resources continues the Spring Learning Series in partnership with Optum, featuring the theme “How to Create a Healthy Workplace.” These monthly, live, instructor-led virtual sessions (via WebEx) are designed to help you bring energy, motivation and meaning into your professional and personal life through engaging and practical topics. Each session will be recorded so you can revisit the content at your convenience.

Join us for an engaging career panel discussion exploring how data science is transforming the future of human health. Hear from professionals working across academia and industry as they share their career paths, discuss how they apply technical and analytical skills to real-world health challenges and offer advice for students interested in this rapidly growing field. This event will provide insight into the many ways data science can make a meaningful impact on human wellbeing.

Speakers: Nadia Abuelezam ’09, math bio (Michigan State University),
Christine Lee ’11, math bio (Brightside Health),
Kyle Suver ’18, CS/math (Modern Health),
Kenneth Mitchell ’24, math CS bio (Axiom Bio)

In collaboration with the Innovation Accelerator Lab for Emerging Health Technologies and the Innovation Accelerator Lab for Data Science and Social Impact

At Harvey Mudd, students learn to become highly competent scientists and engineers, but beyond that they learn skills for analyzing the world around them, seeing things from different perspectives and breaking down the underlying systems that exist in many diverse contexts. Although many students will go on to work in more traditional technical industries, the skills learned at Mudd can be applied to many different pursuits: art, policy, business and more. Through the lens of video games, Israel Jones will discuss ways that systems thinking can be brought to bear in fields we would traditionally consider less “technical,” such as the arts. Jones will go through broad problem spaces in the industry as well as incredibly specific problems that he’s tackled in his own work, discussing the ways a technically trained perspective can provide solutions to non-technical problems.

Speaker

Israel Jones ’19 is a gameplay engineer and technical designer at Secret Door. He majored in CS/math with a concentration in literature and media studies. In his senior year, he realized he felt called to creative pursuits but still had a love for math and programming. He then went on to pursue his master’s in interactive media at USC, where he identified more clearly how he could stand at the crossroads of work that is both artistically fulfilling and technically challenging. He has now spent four years sitting in an office doing that. Outside of work he also does choir, improv and student mentoring. If you want, he could even mentor you!

“From Signal to Strategy: Integrating Molecular Biomarkers in Clinical Trials to Accelerate Drug Development in Transplant”

This guest lecture by Houston Gilbert, head of program strategy and biometrics at Biogen, is for the Bio160 Molecular Immunology class. It is sponsored by the Innovation Accelerator Laboratory for Emerging Health Technology and is open to all health tech-interested students.

Human Resources is excited to introduce a new learning series: The HR Compass – Chart Your Course. This series is intended to empower every staff member to spark innovation, influence outcomes, harness digital tools, build resilience, take accountability, coach for growth and navigate change with clarity and confidence across Harvey Mudd.

The “Leverage Coaching” session will help staff members use coach‑approach questions and active listening to unlock ideas, develop skills and accelerate performance.

Advance registration is required to attend the live virtual session. Access information will be shared with registered participants prior to the session.

The Cabinet is hosting informal coffee breaks in spring 2026 for students, faculty and staff. These coffee breaks will be attended by most of the Cabinet team and will provide an opportunity for the community to share ideas, express concerns and highlight successes.

All are welcome to stop by as schedules allow.

The Office of Human Resources invites you to join us in celebrating Administrative Professionals Day as we recognize and thank our administrative professionals for their dedication, expertise and invaluable contributions.

HMC Community Conversations offer small-group dialogue (3–5 participants), guided by shared agreements like Listen and Be Curious and Show Respect and Suspend Judgment. This is not a debate—there’s no pressure to persuade or agree. Instead, we’ll listen, reflect and learn from one another.

The topic of conversation for this gathering is “News in the Modern World.”

While registration isn’t required, it helps us plan. We hope you can join us.

During the Spring semester, President Nembhard’s office hours are open to all students, faculty and staff. These sessions provide an opportunity to discuss projects, ideas for the College, the strategic plan, issues affecting the community and other topics.

To request a meeting, please choose a preferred slot on the Doodle. Submitting a request does not guarantee an appointment, and a member of the President’s Office will follow up to confirm next steps.

Please note:
• Groups should be limited to no more than five people.
• Requests are reviewed and confirmed on a first-come, first-served basis and are subject to change.

“Coloring Graphs with a q-Twist: From Chromatic Polynomials to Polyhedral Geometry”

Abstract

How many ways can you color the vertices of a graph so that no two connected vertices share the same color? This classic question is answered by the chromatic polynomial, a fundamental tool in combinatorics that counts “proper colorings.” Meléndez introduces a new “weighted” version of this concept: the q-chromatic polynomial. Instead of simply counting colorings, this invariant assigns weights to them, producing a richer algebraic/combinatorial object that recovers the classical chromatic polynomial when q=1.

A key theme of the talk is the connection between graph coloring and polyhedral geometry. Meléndez will explain how proper colorings can be interpreted as lattice points inside geometric objects called polytopes, and how tools from polyhedral geometry (such as Ehrhart theory) help us understand these polynomials. This perspective leads to new formulas, structural insights, and a concrete bridge between combinatorics and geometry.

No background necessay, just a willingness to stare at graphs and polytopes.

We gather every other Friday to talk and reflect as one community on the readings from John Fugalsang’s book Separation of Church and Hate.

We welcome you to bring your lunch and join us in talking about topics that stood out to you regarding the reading(s).

Please join us for a career panel sponsored by the Innovation Accelerator Lab for Emerging Health Technology. This panel includes Elizabeth Johansen ’01, Katherine Partington ’21 and Mikayla Mann ’25. This fantastic group will talk about careers in health through the lens of design, technological development, consulting, start ups and more.

Alumni and students who are in biotech, biomedical, pharmaceutical, and all areas associated are invited to this casual reception, hosted by Matina Donaldson-Matasci (professor of biology) and Steven Santana ’06 (professor of engineering). We aim to grow the network and connections of all who are in and interested in the field of biotech.