Why There’s No “Best” Strategy (and How to Pick One That Fits You)

October 10, 2025October 10, 2025 ~ Manuel Castañón-Puga

We all love shortcuts. The perfect study hack. The ultimate workout plan. The “best” way to search for answers online. Wolpert and Macready show that this dream has a catch: there’s no single method that wins across every kind of problem. When you average over all possible situations, every strategy performs the same. If one approach excels in some tasks, it must falter in others. Even a random strategy can look just as good—on average—if you judge it across every problem out there.

So what actually works? Match the method to the kind of problem you face. The authors explain this as “alignment.” Think of it like playlists. A gym playlist pumps you up, but it’s awful for falling asleep. In the same way, an algorithm—or any plan—needs to fit the pattern of the task. If you know something about your problems (for example, your homework tends to be practice-with-small-twists, not total curveballs), build your approach around that. Without using what you know, you’re basically picking at random and hoping for luck.

Life also changes while you’re working. Projects shift, goals change, and new information arrives midway. The same “no free lunch” idea still bites in these time-varying situations: after the very first step, no fixed approach dominates across all possible ways things can change. What helps is paying attention to how your world usually shifts. If your schedule becomes busy near exams, use strategies that adapt—such as quick checkpoints and backups—rather than rigid plans that assume nothing will change.

One more practical warning: don’t overhype wins from tiny tests. The authors demonstrate that outperforming another method on a small set of examples doesn’t prove much; it only indicates that you were better in those specific cases. Instead, track results over the kinds of tasks you actually face, and compare to simple baselines. If your fancy routine isn’t clearly better than a plain, honest approach, rethink it. In short, there’s no universal champion. But by learning the shape of your own problems and choosing tactics that match that shape, you turn “no free lunch” into a recipe that works for your everyday life.

Reference:
Wolpert, D. H., & Macready, W. G. (1997). No Free Lunch Theorems for Optimization. In IEEE Transactions on Evolutionary Computation (Vol. 1, Issue 1). doi: 10.1109/4235.585893

Learn Faster with the “Natural” Gradient

October 9, 2025October 10, 2025 ~ Manuel Castañón-Puga

When you’re learning something new, you don’t just step randomly—you look for the path that gets you downhill fastest. Amari explains that many machine-learning models live on curved spaces, so the usual gradient doesn’t actually point straight “down.” The fix is the natural gradient, which adjusts each step to the true shape of the space so updates follow the steepest descent where it really matters. In simple terms, the algorithm stops slipping sideways and starts moving directly toward better settings. This idea originates from information geometry and applies to perceptrons, mixing-matrix problems such as blind source separation, and even linear dynamical systems used for deconvolution, not just toy examples.

Why care? Because using the natural gradient in online learning (updating as each new example arrives) can be as accurate, in the long run, as training with all data at once. Statistically, Amari shows this reaches “Fisher efficiency,” which means the online method eventually matches the gold-standard batch estimator instead of settling for second best. For everyday intuition, think of studying a little every day and still getting the same score as if you’d crammed with the full textbook—provided you study in the smartest direction.

This smarter direction can also dodge the annoying “plateaus” that slow standard backprop training, where progress feels stuck even though you’re doing everything “right.” By respecting the curvature of the model’s parameter space, natural-gradient steps help the learner escape these flat regions more readily, speeding up practical training of neural networks. Amari highlights this benefit while positioning the method across common tasks, from multilayer perceptrons to separating mixed signals, such as voices in a room or unmixing time-smeared audio.

There’s also a tip for tuning your learning rate without guesswork. The paper proposes an adaptive rule that makes big steps when you’re far from the goal and smaller steps as you get close, helping you converge quickly without overshooting. It’s like running on open ground but slowing near the finish line to avoid slipping past it. This adaptive schedule aligns naturally with the natural gradient, offering a practical approach that can be applied in real-world training loops.

Reference:
Amari, S. (1998). Natural Gradient Works Efficiently in Learning. Neural Computation, 10(2), 251–276. https://doi.org/10.1162/089976698300017746

How Tech Can Read the Room—and Make Your Experience Better

April 21, 2025October 10, 2025 ~ Manuel Castañón-Puga

Ever felt like a game, app, or museum exhibit “just gets you” and reacts at the right moment? Rosales et al. explain a simple idea behind that feeling: measure how you’re interacting, then use that to adapt what you see. They lean on a classic set of eight clues about your behavior—presence, interactivity, control, feedback, creativity, productivity, communication, and adaptation—to describe your “level of interaction.” Think of them as vibes the system watches for: Are you engaged? Are you trying new things? Are you getting responses when you press buttons? These signals help the system learn what to show next, so you don’t get bored or lost.

To test this in real life, the team visited an interactive science museum in Tijuana, where people—especially children and teenagers—play to learn. They tracked everyday details, such as how long someone stayed, where they moved, whether they read information labels, and if they returned to the same spot. That may sound small, but together, those bits tell a story about attention and curiosity, helping designers make labels clearer, stations easier to use, and activities more enjoyable. Imagine a driving or flight station that notices you’re stuck and gives a quick tip, or speeds things up when you’re clearly nailing it—that’s the goal.

Under the hood, Rosales et al. use a fuzzy logic system—don’t worry, it’s just math that handles “in-between” values instead of only yes/no. Each of the eight clues gets a score between 0 and 1, and the system groups those scores into levels from “very bad” up to “excellent.” Then it determines your overall interaction level, ranging from 0 to 5, much like a skill tier in a game. If your level is near the next tier, it nudges you upward and updates its knowledge of you for the next step. In plain terms, the exhibit watches what you do, estimates your current mood, and adapts so you can keep learning without zoning out.

Does it work? They tried it with data from 500 visitors. The team split the group in half—one half to set up the tool and the other half to test it—and compared the system’s calls with human judgments. The results were close most of the time, with about 76% accuracy, which is decent for a first pass. For everyday life, that means smarter exhibits, apps, and games that can sense when to give you hints, when to challenge you, and when to switch things up. It’s the same idea you can use yourself: notice your own signals—am I engaged, getting feedback, learning something new?—and tweak your setup, whether that’s changing a study app’s difficulty, turning on captions, or picking a different mode in a game. Small cues add up to a better experience.

Suggested by Gayesky and Williams’ level idea and brought to life by Rosales et al., this approach is about meeting you where you are and moving with you. The more systems pay attention to those eight everyday clues—and the more they adjust in the moment—the more tech feels like a helpful guide, rather than a hurdle. Next time a tool feels smooth and responsive, there’s a good chance it’s quietly reading the room and adapting to keep you in the zone.

Reference:
Rosales, R., Ramírez-Ramírez, M., Osuna-Millán, N., Castañón-Puga, M., Flores-Parra, J. M., & Quezada, M. (2019). A fuzzy inference system as a tool to measure levels of interaction. In Advances in Intelligent Systems and Computing (Vol. 931). https://doi.org/10.1007/978-3-030-16184-2_52

How Rumors Actually Travel in Your Group Chats

November 25, 2024October 10, 2025 ~ Manuel Castañón-Puga

Think of your friends as dots and the relationships between you as lines. That picture—a network—can tell us a great deal about how a message travels. Raya-Díaz and colleagues explain that we can describe who’s connected to whom with something called an adjacency matrix, which is just a grid that marks a 1 when two people are linked and 0 when they aren’t. From that grid, you can spot who knows lots of people (their “degree”) and even find “hubs,” those super-connected folks who shrink distances in a network and speed things up. In simple terms, if a rumor hits a hub, it can quickly jump to many others.

But not all groups look the same. One shape the authors use is the “barbell” network: two tightly connected friend groups, separated by a thin path—perhaps that one person who belongs to both circles. In this setup, what happens to a rumor depends a lot on the people sitting on the bridge between the two sides. If the bridging person doesn’t pass things on, one whole half may never hear the news. That’s why “betweenness centrality”—basically, how often someone sits on the shortest route between others—matters so much for real communication. The higher your betweenness, the more you act like a hallway everyone has to walk through.

The team modeled a classroom to show this in action. Each student had a few simple traits: the number of connections they had (degree), how close they were to everyone else, whether they were on those in-between routes (betweenness), and—crucially—whether they chose to cooperate by passing the message along. One student initially received the rumor; after that, its spread depended on two factors: their willingness to share and the degree of betweenness of the neighbors they spoke to. When the “bridge” students cooperated, the message flowed to both sides; when they didn’t, it stalled, even if plenty of people on each side were chatty. You’ve seen this in everyday life: a club hears about an event only if the one friend who’s in both the club and your class actually tells them.

So what can you do with this? First, notice the bridges in your world—the friend who hops between group chats, the classmate in multiple circles, the teammate who also runs student council. If you want something to spread fast (a study guide, a show, a fundraiser), talk to them early. If you want to keep something confidential, be cautious about sharing it with people who belong to different groups. And remember, spreading isn’t automatic; it’s a choice. In the authors’ simulations, flipping cooperation on or off at the bridge changed everything—proof that a single person can shape what the whole network knows. That awareness helps you share more effectively, avoid misinformation, and ensure the right people actually hear what matters.

Reference:
Raya-Díaz, K., Gaxiola-Pacheco, C., Castañón-Puga, M., Palafox, L. E., & Rosales Cisneros, R. (2018). Influence of the Betweenness Centrality to Characterize the Behavior of Communication in a Group. In Computer Science and Engineering Theory and Applications, Studies in Systems, Decision and Control (Vol. 143, pp. 89–101). https://doi.org/10.1007/978-3-319-74060-7_5

Smart Predictions, Simple Rules: How “Fuzzy” Agents Learn the Forex Mood

November 4, 2024October 10, 2025 ~ Manuel Castañón-Puga

We all make decisions with shades of “maybe.” That’s the idea behind the system described by Hernandez-Aguila et al.: using fuzzy logic combined with a team of simple “agents” (think: virtual traders) to predict currency prices. Each agent follows clear rules and, importantly, can express doubt. This “intuitionistic” fuzzy logic allows a rule to not only indicate how much something is true, but also how much it isn’t—and how uncertain we are—so the model remains human-readable instead of a black box.

Here’s the twist that feels very real-life: the agents don’t have to act all the time. They use “specialization” thresholds to determine when market conditions resemble situations they are familiar with. If the match is weak, they sit out—just like you might skip riding a scooter on a rainy day. These thresholds coordinate the team: agents avoid trades where they’d likely do poorly, and the model only speaks up when it recognizes a strong pattern. In practice, the system ranks how strongly each input fits an agent’s rules and picks a cut-off (a depth level) that triggers action only in the most familiar scenarios.

Why bother with “fuzzy” in the first place? Because real data is messy. Instead of forcing a yes/no, fuzzy sets allow us to say “somewhat high” or “very low,” then convert many such shades into an output. Intuitionistic fuzzy sets go further by tracking non-membership and “hesitancy,” which captures doubt—useful for markets that change mood quickly. This combo keeps rules readable (“if the trend is high, then buy is high”) while acknowledging uncertainty, such as when you plan to study more when your focus feels “medium” and you’re unsure it’ll last.

Does it work? The authors tested their approach on major currency pairs and compared it with deep learning and other popular methods. Their errors (measured by mean absolute error) were in the same ballpark as those of state-of-the-art models, and using specialized agents helped performance. They also assessed the real-world impact by comparing their specialized models to a simple “buy and hold” approach over many years; their models performed better in terms of revenue. The takeaway for daily life is simple: clear, interpretable rules that know when to act—and when to pause—can rival the complexity of black boxes. Try adopting that mindset in your own decisions: define simple rules, acknowledge uncertainty, and act only when the pattern aligns.

Reference:
Hernandez-Aguila, A., Garcia-Valdez, M., Merelo-Guervos, J. J., Castanon-Puga, M., & Lopez, O. C. (2021). Using Fuzzy Inference Systems for the Creation of Forex Market Predictive Models. IEEE Access, 9, 69391–69404. https://doi.org/10.1109/ACCESS.2021.3077910