“Random Forest = many trees + averaging = better.” If you’ve read even one ensemble methods tutorial, this sentence is familiar to the point of nausea. And even following the most basic data science tutorials, anyone will understand that this is not wrong. What it is, on the other hand, is just dangerously incomplete, because if that were the whole story, the model would just be called “Bagged Trees,” and we would have stopped there. We would take bootstrap samples, train trees, average them, done. No need for the word “Random” in the name at all.But that’s not what happened. When Breiman designed Random Forest in 2001, he deliberately added a second layer of randomness: at every split, every tree only gets to see a random subset of the available features; not all of them but only a random slice.Why? If variance were the only problem, and bagging already reduces it through averaging, what does this extra, seemingly restrictive constraint add? Why deliberately make your trees “more blind”? Why hide existing information from your model that might prove to be significant?The answer hides in one word that practitioners throw around constantly but rarely unpack mathematically: correlation. Specifically, correlation between the predictions of the trees themselves. And once you see the math behind it, the whole design of Random Forest stops looking like a collection of arbitrary hyperparameters and starts looking like a single, elegant argument against a very specific enemy: correlated errors, which averaging alone can never fully eliminate, and which are exactly what stand between bagging and the algorithm’s real potential.That’s what this article is about: why bagging alone has a hard ceiling, what is this ceiling, and how feature subsampling is the mathematically necessary move to break through it.Bias-Variance, a Fast RefresherBefore we deep dive into the trees lets do a quick recap on how prediction error can be decomposed into three pieces:Error = Bias² + Variance + Irreducible NoiseBias: how wrong your model is on average, systematically. A model too simple for the underlying structure (say, a linear model on nonlinear data) will consistently miss the same way. This is underfitting.Variance: how much your model’s predictions swing if you retrain it on a different sample from the same distribution. A model too flexible (a fully grown decision tree) will fit the noise in whatever data it sees, and change dramatically with a slightly different training set. This is overfitting.A single, unconstrained decision tree sits at one extreme of this spectrum: low bias, high variance. It can represent almost any decision boundary (low bias), but it’s wildly sensitive to which exact rows ended up in its training set (high variance), resulting in a situation where if you swap a handful of data points you can get a structurally different tree.This is precisely why decision trees are the ideal raw material for bagging. Bagging’s whole mechanism of averaging many models, is a variance-reduction tool. It does almost nothing for bias. So it makes sense to pair it with a base learner that already has low bias and just needs its variance tamed, rather than, say, bagging a bunch of linear models where bias is the actual problem and averaging won’t touch it.Keep this pairing in mind — bagging attacks variance, not bias — because it’s the assumption the rest of the article stress-tests. The question we’re about to ask is: does bagging actually deliver on that promise fully, or only partially?The Mathematical Core: Discussing the variance computationSuppose you have n predictors and think of each one as a random variable X1,X2,…,XnX_1, X_2, …, X_nX1​,X2​,…,Xn​. In our case XiX_iXi​ is the prediction of tree iii at some fixed test point xxx. The randomness in XiX_iXi​ comes from the fact that tree iii is trained on a random bootstrap sample. If you re-ran the whole training procedure, you would get a slightly different tree, and therefore a slightly different prediction at xxx.Assume, for now, an idealized case:Each XiX_iXi​, has the same variance: Var(Xi)=σ2Var(X_i) = σ^2Var(Xi​)=σ2 for all iii.The XiX_iXi​ are mutually independent.We can form the ensemble prediction by averaging:Xˉ=1n∑i=1nXidisplaystylebar{X} = frac{1}{n}sum_{i=1}^{n}X_iXˉ=n1​i=1∑n​Xi​Deriving the variance of the averageThis is a direct application of how variance propagates through a sum of independent variables. For any two random variables:Var(aX+bY)=a2Var(X)+b2Var(Y)+2ab Cov(X,Y)Var(aX + bY) = a^2Var(X) + b^2Var(Y) + 2ab Cov(X,Y)Var(aX+bY)=a2Var(X)+b2Var(Y)+2ab Cov(X,Y)If XXX and YYY are independent, Covariance will be zero and the cross-term vanishes. Generalizing to nnn independent variables, each scaled by 1/n1/n1/n:Var(Xˉ)=Var(1n∑i=1nXi)=1n2∑i=1nVar(Xi)=σ2nVar(bar{X}) = Varleft( displaystyle frac{1}{n}sum_{i=1}^{n}X_i right) = displaystyle frac{1}{n^2}sum_{i=1}^{n}Var(X_i)= frac{σ^2}{n}Var(Xˉ)=Var(n1​i=1∑n​Xi​)=n21​i=1∑n​Var(Xi​)=nσ2​That’s it. That’s the whole derivation. No cross-terms survive because independence kills every covariance term in the expansion.What this says, physicallyAs n→∞nto inftyn→∞, Var(Xˉ)→0Var(bar{X}) to 0Var(Xˉ)→0. The ensemble’s variance can be driven arbitrarily close to zero, no floor, no limit just by adding more independent trees. This is the exact same logic as averaging nnn independent noisy measurements of a physical quantity: each measurement has its own instrument noise σσσ, but if the noise sources are truly independent (uncorrelated), the standard error of the mean shrinks as σ/ndisplaystyle σ/sqrt{n}σ/n​. Same square-root law, same origin: independence lets fluctuations cancel rather than accumulate.The key idea behind bagging is that, under the assumption of independent trees, averaging more and more trees continuously reduces the ensemble variance, eventually driving it arbitrarily close to zero.The catchAs said before this derivation rests on one assumption that is almost never actually true in Random Forests: independence. The trees are not independent. They’re trained on bootstrap samples drawn from the same underlying dataset, using the same features, often finding the same dominant splits near the top of the tree. That shared structure means Cov(Xi,Xj)≠0Cov(X_i , X_j) neq 0Cov(Xi​,Xj​)=0 and the moment covariance is nonzero, that cross-term we made vanish above comes roaring back into the formula.That’s exactly what the next section confronts head-on: what happens to Var(Xˉ)Var(bar{X})Var(Xˉ) when we drop the independence assumption and let the trees be correlated as they should be in any honest situation of every real Random Forest implementation.The Twist: Trees Are Never Truly IndependentLet’s drop the independence assumption and see what actually happens.Go back to the raw definition of the variance of a sum, without assuming independence this time:Var(Xˉ)=Var(1n∑i=1nXi)=1n2Var(∑i=1nXi)Var(bar{X}) = Varleft( displaystyle frac{1}{n}sum_{i=1}^{n}X_i right) = displaystyle frac{1}{n^2}Varleft( sum_{i=1}^{n}X_i right)Var(Xˉ)=Var(n1​i=1∑n​Xi​)=n21​Var(i=1∑n​Xi​)The variance of a sum, in full generality, expands into a double sum over all pairs (i,j)(i,j)(i,j):Var(∑i=1nXi)=∑i=1n∑j=1nCov(Xi,Xj)displaystyle Varleft( sum_{i=1}^{n}X_i right) = sum_{i=1}^{n}sum_{j=1}^{n}Cov(X_i, X_j)Var(i=1∑n​Xi​)=i=1∑n​j=1∑n​Cov(Xi​,Xj​)Split this double sum into two pieces: the diagonal terms where i=ji=ji=j, and the off-diagonal terms where i≠ji neq ji=j. When i=j,Cov(Xi,Xi)=Var(Xi)=σ2i=j, Cov(X_i,X_i)=Var(X_i)=σ^2i=j,Cov(Xi​,Xi​)=Var(Xi​)=σ2. There are nnn such terms.When i≠ji neq ji=j, each term is Cov(Xi,Xj)Cov(X_i,X_j)Cov(Xi​,Xj​), and there are n2−n=n(n−1)n^2-n=n(n-1)n2−n=n(n−1) such off-diagonal terms.Var(∑i=1nXi)=nσ2⏟diagonal+∑i≠jCov(Xi,Xj)⏟off−diagonaldisplaystyle Varleft( sum_{i=1}^{n}X_i right) = underbrace{nσ^2}_{diagonal} + underbrace{sum_{ineq j}^{}Cov(X_i, X_j)}_{off-diagonal}Var(i=1∑n​Xi​)=diagonalnσ2​​+off−diagonali=j∑​Cov(Xi​,Xj​)​​This is exactly where the earlier derivation cut a corner: independence forced every off-diagonal term to zero. We no longer get to assume that.Introducing ρNow define the (average) pairwise correlation between any two distinct trees:ρ=Corr(Xi,Xj)=Cov(Xi,Xj)σ2⇒Cov(Xi,Xj)=ρσ2ρ = Corr(X_i,X_j)= displaystylefrac{Cov(X_i,X_j)}{σ^2} Rightarrow \ Cov(X_i,X_j) = ρσ^2ρ=Corr(Xi​,Xj​)=σ2Cov(Xi​,Xj​)​⇒Cov(Xi​,Xj​)=ρσ2This is a simplifying assumption — a “mean-field” treatment, exactly like assuming a uniform pairwise interaction instead of tracking every individual pair separately. In reality, some tree pairs are more correlated than others (two trees that both got heavy weight on the same influential outlier row, say), but treating ρ as a single average captures the aggregate effect cleanly, and it’s a very standard move (this is essentially the same simplification Breiman himself used in the original Random Forest paper).With this substitution, the off-diagonal sum becomes:∑i≠jCov(Xi,Xj)=n(n−1)ρσ2displaystylesum_{ineq j}^{}Cov(X_i,X_j) = n(n-1)ρσ^2i=j∑​Cov(Xi​,Xj​)=n(n−1)ρσ2Putting it together we conclude that:Var(Xˉ)=1n2[nσ2+n(n−1)ρσ2]Var(bar{X})= frac{1}{n^2}left[ nσ^2 + n(n-1)ρσ^2 right]Var(Xˉ)=n21​[nσ2+n(n−1)ρσ2]and from the above point the math is pretty simple to derive the final expression for Var(Xˉ)Var(bar{X})Var(Xˉ):Var(Xˉ)=ρσ2+(1−ρ)σ2nVar(bar{X}) = ρσ^2 +displaystyle frac{(1-ρ)σ^2}{n}Var(Xˉ)=ρσ2+n(1−ρ)σ2​Sanity check: setting ρ=0ρ=0ρ=0 the first term vanishes entirely, and you’re left with σ2/nσ^2/nσ2/n which is exactly the independent case we ended up with before when we assumed tree independency. Good, the general formula correctly reduces to the special case. Lets now examine the limit; does it collapse correctly at the boundary?lim⁡n→∞[ρσ2+(1−ρ)σ2n]=ρσ2displaystylelim_{n to infty } left[ ρσ^2 +displaystyle frac{(1-ρ)σ^2}{n} right] = ρσ^2n→∞lim​[ρσ2+n(1−ρ)σ2​]=ρσ2The second term that carries all the benefit of averaging, and includes nnn vanishes exactly as before. But the first term ρσ2ρσ^2ρσ2, has no nnn in it at all. It was never going to vanish, no matter how large nnn gets.The consequenceYou could add as many trees as you want; tens or hundreds or even millions of them. Still the variance of your ensemble can never drop below ρσ2ρσ^2ρσ2. This is a hard floor, set entirely by how correlated your trees are, not by how many of them you have. Adding more trees only ever attacks the second term. It has zero leverage over the first.This is the mathematical fact that the entire design of Random Forest is built to confront. Next section asks where this ρρρ actually comes from in a real forest — but the diagnosis itself, the existence of this floor, doesn’t depend on any mechanism. It falls straight out of the algebra of correlated averaging, the same way it would for correlated noise in any measurement ensemble.Why ρ Exists, and How Random Forest Breaks ItWe’ve shown that if trees are correlated, averaging can’t save you as variance floors at ρσ2ρσ^2ρσ2. So where does that correlation actually come from?The causeEvery tree sees a different bootstrap sample, but the same underlying dataset. If one feature is a strong predictor (say, “price of a product”), it will win the best-split test at the root of nearly every tree, almost regardless of which rows got sampled because it’s structurally the strongest signal in the data and not an artifact of any particular sample. So trees end up with similar top-level structure, make similar errors in the same regions, and their predictions move together. Bootstrap sampling shuffles rows, but it doesn’t touch which feature dominates leading it to decorrelate noise and not signal.The Random Forest fixRandom Forest attacks this directly: at every single split, each tree is only allowed to consider a random subset of features (typically pdisplaystylesqrt{p}p​​ out of ppp). When the dominant feature isn’t in that subset, the tree is forced to split on something else. Different trees end up built around different features at different points, which breaks the shared structure and because of it, ρρρ drops.That is the whole idea. Bagging randomizes the training rows, which reduces the variance of each individual tree. Random Forest goes one step further by also randomizing the features at every split. This reduces the correlation ρρρ between tree predictions, and it is ρρρ rather than the number of trees nnn that limits how much the ensemble variance can be reducedThe Experiment — What We’re Actually TestingTheory is convincing, but nothing beats seeing the numbers move. So we set up a controlled comparison: build the exact scenario the theory describes, then measure ρ,σ2ρ, σ^2ρ,σ2, and Var(mean) directly, instead of just asserting them.The setup (code at the end of the article)We generate a synthetic population with 30 features, where two features are deliberately made dominant (they carry most of the true predictive signal) while the rest range from weakly informative to pure noise. This mirrors a realistic dataset: a few strong drivers, a handful of secondary ones, and a lot of clutter. It’s exactly the kind of structure that should push plain bagged trees toward high correlation, since every tree has every incentive to split on the same dominant features first.The key methodological choiceThis is where the earlier discussion about conditional vs. unconditional correlation actually matters for the experiment design, not just for the theory. If we trained many trees on bootstrap samples of one fixed training set, we’d be measuring conditional correlation and as we worked out, that correlation is exactly zero for independently-drawn bootstrap samples, no matter how much those samples overlap in content. That’s a mathematical fact, not a subtlety we can sidestep.Breiman’s ρρρ is unconditional: it treats the training set itself as a random draw from the population. So to measure it honestly, each independent “trial” of our experiment has to include a fresh training set, drawn anew from the population, not just fresh bootstrap indices from the same fixed set. All the trees within one trial share that one training-set draw — and that shared draw is the actual, real source of correlation between them.What we do, step by stepRun many independent trials (400 in our case). In each trial: draw a brand-new training set from the population, then train a large batch of trees on bootstrap resamples of it.Do this twice; once where every tree considers all 30 features at every split (plain bagging), and once where every tree only considers a random subset of features at every split (Random Forest, roughly 30≈5–6sqrt{30} ≈ 5–630​≈5–6 features per split). Everything else (the training set draws, the bootstrap sampling, the tree depth) is kept identical between the two, so the only thing that differs is that one design choice.At a fixed set of test points, record every tree’s prediction, in every trial.What we measure from that dataρ: how similarly two different trees behave, at the same test point, across independent trials. Basically, if we reran the whole experiment, would tree A and tree B tend to move together?σ²: how much a single tree’s prediction, at a fixed test point, varies across independent trials.Var(mean) vs. n: for a growing number of trees n, how much does the ensemble’s averaged prediction vary across independent trials?If the theory holds, the third quantity should trace out exactly ρσ2+(1−ρ)σ2/nρσ^2 + (1-ρ)σ^2/nρσ2+(1−ρ)σ2/n falling steeply at first, then flattening out at a floor set by ρρρ, and not by nnn.The ResultsHere’s what came out of running the experiment described above (400 independent trials, up to 120 trees per ensemble):Correlation and individual-tree variance-ρ (correlation)σ2σ^2σ2 (individual tree variance)floor = ρσ2ρσ^2ρσ2Plain bagging0.1369.891.34Random Forest0.04317.420.76Two things jump out immediately.First, ρ drops by roughly 3.2x once feature subsampling is introduced (0.136 → 0.043). Hiding the dominant features from most splits genuinely breaks the shared structure between trees. Rather than repeatedly building nearly identical trees around the same few informative variables, Random Forest encourages diverse tree structures. This diversity reduces the tendency of trees to make the same prediction errors, leading to a much lower inter-tree correlation.Second, and less obvious: Random Forest’s individual trees are actually worse. σ² is roughly double for RF (17.42 vs 9.89); a single Random Forest tree, on its own, is a noisier predictor than a single bagged tree. This makes sense: restricting each split to ~5–6 out of 30 features sometimes forces the tree away from the best available split, making that one tree more erratic. Feature subsampling isn’t a free lunch at the level of a single tree — it’s a trade: individual quality for reduced correlation.Third and more importantly, the asymptotic variance floor ρσ2ρσ^2ρσ2 decreases from 1.34 to 0.76. This demonstrates the key principle behind Random Forest: improving ensemble performance does not require stronger individual trees, but rather a collection of sufficiently accurate trees whose prediction errors are less correlated. Consequently, adding more trees yields a lower limiting ensemble variance than plain bagging.Ensemble variance vs. number of treesn (trees)Bagging: empiricalBagging: theoryRF: empiricalRF: theory19.899.8917.4217.4282.422.412.882.84181.851.821.681.68351.611.591.221.23701.491.460.960.991201.441.410.850.89Two patterns worth sitting with:The theory column and the empirical column track each other closely, all the way through. This isn’t guaranteed — the formula Var(Xˉ)=ρσ2+(1−ρ)σ2nVar(bar{X}) = ρσ^2 +displaystyle frac{(1-ρ)σ^2}{n}Var(Xˉ)=ρσ2+n(1−ρ)σ2​ is a mean-field approximation (a single averaged ρ standing in for many individual pairwise correlations), and it had every opportunity to diverge from what actually happened. It didn’t. The theoretical floor stopped being a symbolic derivation and became a number we can point to and say: this is where it plateaus, and we predicted it.The crossover At n=1, Random Forest starts behind as its lone tree is nearly twice as noisy as bagging’s lone tree (17.42 vs 9.89). But by around n=18, RF has already caught up and overtaken bagging (1.68 vs 1.85). By n=120, RF is sitting at roughly 59% of bagging’s variance (0.85 vs 1.44), despite starting from individually worse building blocks.That crossover is the entire article compressed into one sentence. Averaging alone can’t rescue plain bagging — no matter how many bagged trees you add, you’re stuck above ρσ2≈ρσ² ≈ρσ2≈ 1.34. Random Forest starts from a worse position per tree, but because it decorrelates the ensemble, it keeps improving well past the point where bagging has already flattened out ending up in a completely different neighborhood.All the above can be compressed in the following illustrated image generated by the code in the appendix.The Subtle Point: Worse Trees, Better ForestIt’s worth pausing on something that previous sections numbers already showed, because it’s the detail that surprises people who have used Random Forest for years without digging into why it works: a single Random Forest tree is a strictly worse predictor than a single bagged tree, and yet the Random Forest ensemble ends up strictly better.This isn’t a contradiction but the entire point, once you separate two things that are easy to conflate:Individual quality (how good is one tree, on its own): bagging wins here. σ² = 9.89 for bagging vs 17.42 for RF. Clearly, a bagged tree, seeing all 30 features at every split, simply makes better individual decisions.Ensemble quality (how good is the average of many trees): RF wins here, and not narrowly as at n=120, RF’s ensemble variance is 0.85 vs bagging’s 1.44, roughly 41% lower.The mechanism connecting these is entirely about ρρρ, not σ2σ^2σ2. Feature subsampling doesn’t make trees better — if anything, it makes each one a bit worse, since it’s occasionally forced away from the strongest available split. What it buys is independence between the mistakes different trees make. And because the ensemble variance formula weights ρρρ so heavily (recall: ρρρ survives untouched as n→∞nto inftyn→∞, while σ2σ^2σ2’s contribution shrinks toward zero), a small sacrifice in individual quality can purchase a much larger reduction in shared error.This is a genuinely counter-intuitive trade for anyone used to thinking “better base learner → better ensemble.” For Random Forest specifically, the opposite can hold: a slightly worse base learner, if it’s less correlated with its peers, produces a meaningfully better ensemble. It’s the same logic behind why a portfolio of mediocre, uncorrelated bets can outperform a portfolio of excellent, highly correlated ones; diversification has real value, and it can outweigh individual quality once you’re combining many things.Practical Takeaway: max_features Isn’t a DetailIf there’s one parameter in sklearn.ensemble.RandomForestRegressor (or RandomForestClassifier) that gets set once to ‘sqrt’ and never touched again, it’s max_features. The results above suggest that’s often leaving something on the table.The tradeoff, made concretemax_features controls exactly the quantity this whole article has been about: how many features each split can see, which directly trades off σ2σ²σ2 against ρρρ.Too high (close to, or equal to, all features — i.e. plain bagging): every tree gravitates toward the same dominant features, and you hit the floor early. Adding more trees past that point burns compute for essentially nothing.Too low (e.g. 1 feature per split): trees become so restricted they’re barely better than random guessing at each split, and the floor, while lower in ρρρ terms, can end up higher in absolute Var(mean) terms because σ2σ²σ2 has grown faster than ρρρ shrank.Somewhere between these two extremes is a sweet spot — and where it sits depends on the data, specifically on how many features are genuinely dominant versus how many carry real, if secondary, signal.The one-line mental model to carry forwardmax_features isn’t a randomness dial you set and forget — it’s the lever that decides where your forest sits on the σ2−ρσ² – ρσ2−ρ tradeoff. Tune it the way you would tune any bias-variance knob: by checking what it does to your actual validation error, not by trusting the default because it’s the default.AppendixHere you can find the code I built and used for the analysis. Feel free to execute and reproduce my results or experiment with different parameters. (Estimated time of run ~ 7 mins)”””Bagging vs Random Forest: measuring rho (tree correlation) and thevariance floor Var(mean) = rho*sigma^2 + (1-rho)*sigma^2/n.KEY METHODOLOGICAL POINT:With a FIXED training set, if each tree’s bootstrap sample is drawnindependently, tree predictions are mathematically INDEPENDENT (rho = 0exactly) — this follows from a basic probability fact: if A and B areindependent random variables, then g(A) and h(B) are independent for anyfunctions g, h, even g = h. This holds no matter how nonlinear ordiscontinuous the tree-fitting function is, and despite the fact thatany two bootstrap samples will typically overlap heavily in content –overlap in realized values does not imply statistical dependence.The correlation rho in Breiman’s formula is UNCONDITIONAL: it requiresthe training set itself to be random (drawn from the population) acrossrepeats. All trees in a repeat share that one training-set draw, which isthe actual common source of dependence. So each independent “repeat” ofthis experiment must redraw the training set fresh, not just thebootstrap indices.”””import numpy as npfrom sklearn.tree import DecisionTreeRegressorimport matplotlib.pyplot as pltimport timeRNG_GLOBAL = np.random.default_rng(0)# —————————————————————–# Data-generating process: a couple of DOMINANT features, several# weaker informative features, and pure noise features.# —————————————————————–N_TRAIN = 400N_FEATURES = 30TRUE_COEF = np.zeros(N_FEATURES)TRUE_COEF[0] = 4.0TRUE_COEF[1] = 2.5TRUE_COEF[2:8] = 0.5NOISE_SCALE = 1.5X_PROBE = RNG_GLOBAL.normal(size=(25, N_FEATURES)) # fixed evaluation pointsdef run_repeats(max_features, R, n_max, seed0, max_depth=5): “””R independent repeats. Each repeat: draw a FRESH training set from the population, then train n_max trees on bootstrap resamples of it (with the given max_features policy). Returns predictions at the fixed probe points, shape (R, n_max, n_probe). “”” preds = np.empty((R, n_max, X_PROBE.shape[0])) for r in range(R): rng = np.random.default_rng(seed0 + r) X_train = rng.normal(size=(N_TRAIN, N_FEATURES)) y_train = X_train @ TRUE_COEF + rng.normal(scale=NOISE_SCALE, size=N_TRAIN) for t in range(n_max): idx = rng.integers(0, N_TRAIN, size=N_TRAIN) # bootstrap rows Xb, yb = X_train[idx], y_train[idx] tree = DecisionTreeRegressor( max_features=max_features, # None = bagging, ‘sqrt’ = RF max_depth=max_depth, random_state=rng.integers(0, 1_000_000), ) tree.fit(Xb, yb) preds[r, t, :] = tree.predict(X_PROBE) return predsdef pairwise_rho(preds, n_slots=10): “””Average pairwise correlation between distinct tree ‘slots’, across independent repeats, at fixed test points (unconditional rho, per Breiman’s definition). “”” slots = preds[:, :n_slots, :] rhos = [] for k in range(slots.shape[2]): mat = slots[:, :, k] corr = np.corrcoef(mat, rowvar=False) off = corr.sum() – np.trace(corr) n_pairs = n_slots * (n_slots – 1) rhos.append(off / n_pairs) return float(np.nanmean(rhos))def individual_tree_variance(preds): return float(preds[:, 0, :].var(axis=0).mean())def empirical_var_of_mean(preds, n_values): out = [] for n in n_values: cum_mean = preds[:, :n, :].mean(axis=1) # (R, n_probe) var_per_point = cum_mean.var(axis=0) out.append(float(var_per_point.mean())) return np.array(out)# —————————————————————–# Run the experiment# —————————————————————–R = 400 # independent repeats (reduce to ~100 for a faster run)N_MAX = 120 # max ensemble size probedN_VALUES = np.array([1, 2, 3, 5, 8, 12, 18, 25, 35, 50, 70, 90, 120])t0 = time.time()preds_bag = run_repeats(max_features=None, R=R, n_max=N_MAX, seed0=10_000)t1 = time.time()print(f”Bagging: {t1-t0:.1f}s”)preds_rf = run_repeats(max_features=”sqrt”, R=R, n_max=N_MAX, seed0=50_000)t2 = time.time()print(f”RF: {t2-t1:.1f}s”)rho_bag = pairwise_rho(preds_bag)rho_rf = pairwise_rho(preds_rf)sigma2_bag = individual_tree_variance(preds_bag)sigma2_rf = individual_tree_variance(preds_rf)floor_bag = rho_bag * sigma2_bagfloor_rf = rho_rf * sigma2_rfvar_bag = empirical_var_of_mean(preds_bag, N_VALUES)var_rf = empirical_var_of_mean(preds_rf, N_VALUES)print(f”nrho: bagging={rho_bag:.4f} RF={rho_rf:.4f}”)print(f”sigma^2: bagging={sigma2_bag:.3f} RF={sigma2_rf:.3f}”)print(f”floor: bagging={floor_bag:.3f} RF={floor_rf:.3f}”)print(f”n{‘n’: >5} {‘bag_emp’: >10} {‘bag_theory’: >11} {‘rf_emp’: >10} {‘rf_theory’: >11}”)for n, vb, vr in zip(N_VALUES, var_bag, var_rf): tb = rho_bag * sigma2_bag + (1 – rho_bag) * sigma2_bag / n tr = rho_rf * sigma2_rf + (1 – rho_rf) * sigma2_rf / n print(f”{n: >5} {vb: >10.3f} {tb: >11.3f} {vr: >10.3f} {tr: >11.3f}”)# —————————————————————–# Plot# —————————————————————–fig, ax = plt.subplots(figsize=(9, 6))n_smooth = np.linspace(1, N_VALUES.max(), 300)theory_bag = rho_bag*sigma2_bag + (1-rho_bag)*sigma2_bag/n_smooththeory_rf = rho_rf*sigma2_rf + (1-rho_rf)*sigma2_rf/n_smoothax.plot(N_VALUES, var_bag, “o”, color=”#d62728″, label=”Plain bagging (empirical)”, markersize=6, zorder=5)ax.plot(n_smooth, theory_bag, “–“, color=”#d62728″, alpha=0.6, label=f”Bagging theory (rho={rho_bag:.3f})”)ax.axhline(floor_bag, color=”#d62728″, linestyle=”:”, alpha=0.5, linewidth=1.5)ax.plot(N_VALUES, var_rf, “s”, color=”#1f77b4″, label=”Random Forest (empirical)”, markersize=6, zorder=5)ax.plot(n_smooth, theory_rf, “–“, color=”#1f77b4″, alpha=0.6, label=f”RF theory (rho={rho_rf:.3f})”)ax.axhline(floor_rf, color=”#1f77b4″, linestyle=”:”, alpha=0.5, linewidth=1.5)ax.text(N_VALUES.max()*0.65, floor_bag+0.05, f”bagging floor = rho*sigma^2 = {floor_bag:.2f}”, color=”#d62728″, fontsize=9)ax.text(N_VALUES.max()*0.65, floor_rf+0.05, f”RF floor = rho*sigma^2 = {floor_rf:.2f}”, color=”#1f77b4″, fontsize=9)ax.set_xlabel(“Number of trees (n)”, fontsize=12)ax.set_ylabel(“Var(ensemble mean prediction)”, fontsize=12)ax.set_title(“Bagging plateaus early; Random Forest keeps improvingn” “(empirical points vs. theoretical Var(mean) = rho*sigma^2 + (1-rho)*sigma^2/n)”, fontsize=12)ax.legend(fontsize=9, loc=”upper right”)ax.set_ylim(bottom=0)ax.grid(alpha=0.3)plt.tight_layout()plt.show()References:Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32.

It’s a glorious day in Kirkland, Washington, an affluent Seattle suburb on the eastern shore of Lake Washington. The temperature is in the mid-80s, and the sky is incapable of being any more blue. The view from the Gates Ventures conference room overlooks the Carillon Point Marina, where a flotilla of expensive boats bob in the water, and across the lake to the Olympic Mountains that define the horizon. It’s gorgeous. And vaguely terrifying.  Because if the scene is placid, the messenger is not. Seated across from me at a conference room table, Bill Gates is rocking back and forth in his chair, totally animated. And the more he has to say—about the threats of terror or economic collapse or just losing control of our AI systems—the more agitated I find myself becoming, too.  The philanthropist and former Microsoft CEO says he has been growing increasingly alarmed by the rate of change at which AI technology is advancing, especially since guardrails are not keeping pace. In a new essay published today, Gates argues that we have passed the points where multiple potential dangers should have been checked. “We’ve crossed the threshold in terms of [AI’s] bio-capabilities, cyber-capabilities, psychosocial capabilities, job-market-destruction capabilities, and even the lack of control,” he said in an interview with MIT Technology Review about his new memo. “I’m just stunned at the lack of concern and discussion outside of the industry.” In an effort to wake the world up to what he sees as a rapidly growing societal disrupter, the 70-year-old tech titan has begun sounding the alarm as a “shrill voice,” both publicly with his new essay (the first of multiple he plans on the topic) and in meetings with the press, and privately in conversations with industry, government, and civil society leaders. 
And while Gates is calling attention to a number of issues, his warnings about the bio-capabilities of the current frontier models are especially chilling. “Any model that can make novel molecules should be monitored,” he says. “I view bioterrorism risk, versus a natural pandemic, as about 50 times more scary, more likely than a natural pandemic risk.” In addition to the cautionary notes, he also advances some novel ideas for moving society forward. Among them are the concepts of human-reserved jobs, and taxes on robots and tokens. (A robot tax is a longtime notion of his.) The former would preserve some societally agreed-upon jobs for human beings, which he notes may vary from one nation to another. The latter is a tax that sets aside money earned from AI usage that replaces human work. 
And to be sure, there is also a hint of optimism. Gates is bullish on the ways AI will continue to transform agriculture and health care and education, for example, or the ways in which it can help us navigate bureaucracy. And, he argues, eventually we do get to abundance. But first? Turbulence. And lots of it.  MIT Technology Review sat down with the billionaire philanthropist to talk about the road that lies ahead, its dangers, and how it could someday take us to a better place.  The following interview has been edited for length and to improve clarity and readability. Mat Honan / MIT Technology Review: Thanks for doing this. I don’t know if you had something you wanted to open with, or I can just jump in.  Bill Gates: You know, one good question I’ve had is: Why am I speaking out now? MIT Technology Review: Literally, my first question! Bill Gates: It’s really two things. One is that we’ve crossed the thresholds in terms of the bio-capabilities, cyber-capabilities, psychosocial capabilities, job-market-destruction capabilities, and even the lack of control; we’re seeing signs of difficulties there. And all these years, people have said, “Okay, when we get close to these thresholds, we’ll really figure out how to let only good people use it, or how to not let it do these things, and maybe that’s when we won’t let people copy models.” And I’m in a state of shock that we’ve crossed these thresholds.  So the fact that we’ve gotten past these is one reason, and the second is that I’m just stunned at the lack of concern and discussion outside of the industry. Within the industry, it’s complicated because the industry doesn’t like criticizing itself, or players like criticizing each other. Some companies are hiring fewer entry-level workers, which you’d have to call a pretty modest signal. But it’s going to happen, and not in any long time frame—because the things that hold people back in terms of capabilities and reliability, all those things are being solved. And so for a substantial part of the white-collar market, you have very low-cost substitution. And then you can have an opinion on how quickly robotics come along. We’re not there yet, but it is stunning the progress being made there—a little bit more in China than in the US, but somewhat in both.

MIT Technology Review: You talked about all of this happening so much faster than the internet revolution did, than some of these previous technological revolutions did. What type of timescale are you talking about? You pointed to the thresholds that we’ve crossed. In your view, have we already passed some sort of tipping point where there’s going to be this inevitable change?  Bill Gates: The past definitely is very misleading on this, and a lot of people lean on that. “Hey, no previous technology resulted in a net jobs reduction,” and they’re right. And I’ve given that speech.  But with any credibility that I have, this time is different. When you can replace human cognition for an extremely high percentage of jobs across every industry in the same time frame at modest cost, relative to human labor costs, and your error rates … will probably be lower than human rates. The past is just very misleading. The current economic statistics are very misleading. “If you’re worried about AI, going to a data center protest is not the most effective way to start the debate about how we minimize these bad things.” Bill Gates And to the degree there’s any expression of concern at all, it’s like, “Hey, don’t build data centers.” Well, you can stop every data center in the United States and it won’t change any of the issues that I’m talking about. Data centers will be built globally. If you’re worried about AI, going to a data center protest is not the most effective way to start the debate about how we minimize these bad things. Just like yelling at an oil company executive is not the way to solve climate change.  MIT Technology Review: You talk about the benefits of AI in your essay as well as the costs. How are you thinking about balancing that message? And are you hoping people get a little worried when they read it? Bill Gates: They’d better! I didn’t expect to be the shrillest voice saying society broadly is not paying attention to this, but I think that’s necessary.  So yes, I’m super concerned that the negatives will be a lot bigger. The positives are real. The Gates Foundation, the way we’re innovating in vaccines and drugs, it’s incredible how we’re using those tools. We’re part of a big public-domain effort to gather data into both protein-level and cell-level modeling, and we fund Biomni at Stanford [a biotech AI agent for research].  We don’t yet have a way of interacting with the government bureaucracy improved through AI. AIs are very good at bureaucracy, complex regulatory things. “I want to go to small claims court; help me do this.”
The [Gates] Foundation spun off a group called NextLadder, which is a lot about that low-income-family scenario that I put in the essay. What benefits are there? What training programs are available? “I’ve been evicted.” “I’m getting out of jail.” “I’ve got to declare bankruptcy.” It’s super complicated, and with no ability to hire lots of advisors to help with those things, AI should be a fantastic agent for somebody who’s got economic challenges and needs to find government or nongovernment help.  MIT Technology Review: Some of what you’re talking about is AI becoming more intelligent than humans. There seems to be a lot of certainty in tech circles, especially, that it’s going to go further than where we are, and I wonder how close you think we are to it not just being this interface that we can use to access and analyze, and run complicated problems, but becoming something more than that—where AI is making the decisions, looking for the thing to analyze, coming up with the research.
Bill Gates: Well, you can go to the peak and say, “What about mathematics or physics?” There are definitely some jobs, like Warren Buffett’s, where from age 13 he engaged in reinforcement learning about the value of businesses, and over 80 years later he has a lot of implicit knowledge. We don’t know how to create a Warren Buffett investor, because it’s very implicit. We didn’t record everything he learned, so we don’t have that track available. So there are jobs where the complex implicit judgment about how you work with people to get things done, there are people working to encode that into the models. Certainly, that collaborative stuff is really not there yet. But you could say 50% of the job market is doing jobs that aren’t “a lifetime of experience” type jobs. You know, telesales, telesupport, the accounting department. When you close the books at the end of the month, which revenue should be in, not in? This customer got a bad thing. What discount should we give them? How do we show that? It’s well defined.  Any job that’s well defined, the AI is cheaper and better. Yes, people have seen cases where it was implemented wrong. The data wasn’t right. So, say it takes a couple years for people to realize that such a high percentage of white-collar jobs are achievable by paying an AI a lot less money. And so the discussion about okay, when do mathematicians not even understand the new things that are coming up? That’s interesting for people like us. And okay, MIT Technology Review, you should write about that. But in terms of the broad job market, we passed the threshold that for a swath of white-collar jobs, including almost every entry-level job, the AI is cheaper—properly implemented. And so, I’m telling you we’ve crossed the bioterrorism threshold, we’ve crossed the cyberattack threshold, we’ve crossed the job market threshold, we’ve crossed the psychosocial dependence threshold, and there are hints that we may be crossing the control threshold.  Ryan Greenblatt talking to Dwarkesh [Patel] about how [reinforcement learning] (RL) creates perverse incentives that have led to this cheating and collaboration between various AIs, I think is very instructive. Ryan, who’s ensconced in this issue, is going, “Wow, RL is really doing some things that our explicit instructions are not rich enough [to prevent].” And what’s that going to lead to? That’s a problem I always thought was way out there. I expected a lot of loud voices as we even got close to the [threshold of] can a nontechnical person do a cyberattack just using AI. We’re there! 
On the bio thing, I claim any model that can make novel molecules should be monitored. It can’t be copyable into a dark place where you get rid of the monitoring logic. I claim the US should say any model that can make new molecules is subject to that monitoring. I claim we should approach China and say, “Hey, let’s agree on this. What’s the downside?” You know, how big is the bioterrorism market? It’s not very big, and the benefits are gigantic. We also need to improve surveillance. I view bioterrorism risk versus a natural pandemic as about 50 times more scary, more likely than a natural pandemic risk. And who’s speaking out to say that those things should be monitored? Who’s upping the surveillance work?  “Any model that can make novel molecules should be monitored.” Bill Gates So who are the experts in government? A long time ago, government was very involved as technology would progress because they were the cutting-edge buyer of jets or rockets or whatever. Here, they’re not that important of a leading-edge market. That’s been true of the digital revolution, and it’s true of the AI revolution. So the depth of knowledge in the government isn’t necessarily super-strong, because they are not the cutting-edge buyer or even the big R&D funder. AI research is not government-grants funded. MIT Technology Review: Yeah, I know you’ve been talking to people in government. Are there people who you think understand the urgency? Are there people who you feel like are positioned to take a leadership role? Are there people who you feel like understand and are trying to push things? Bill Gates: I hope this doesn’t become a partisan issue, where one party completely ignores all these problems and the other party gets involved. I’d like to have a common base that these are problems, and then each party can have slightly different responses to it. 
That will require not a substantial increase in the size of the bureaucracy, but it’ll require upping the AI expertise in the government. It’ll require some collaboration with industry—certainly on the cyber front they know, and they’re very, very worried. And they worry: Should we speak publicly? Because in a way, that could highlight the riskiness.  There’s these perverse things, both in cyber and bio. But we’re past any reasonable threshold.  I believe in monitoring. Now, some people can say that won’t work or that there’s some drawback to it, but I welcome their ideas. This memo is not, “hey, here’s the solution.” It’s got robot taxes, human reserve. And I’ll do a bio memo. That one I’ll do before the end of the year—it really talks through all the different things, building on what I know from the Foundation and my work on pandemics.  Globally, we are better prepared for a pandemic, even in the US— which is normally the leader on these global things, and people are very unused to the US not being a cooperative, friendly leader on global problems. I do think we can go back to doing better at that. And we have to with AI, including working with China on defining these thresholds, like biomonitoring. MIT Technology Review: I want to make sure that I get to ask you about these two ideas that you brought up. One is human-reserved jobs, and the other is the robot and token tax. Let’s start with that second one, actually. Talk to me about how a robot and token tax might work. Bill Gates: Well, you can say 50% of your revenue from a token tax is paid to the government, and the government has that money to help people who lose their job because of AI. Now, people say that will slow the AI industry down. And should some token uses not be subject to the tax? Is there really a separation between AIs that help with invention versus AIs that do job substitution? If somebody can tell me how to tell the AI “no job substitution,”—I mean, does Asimov’s third law that you do no harm mean you don’t take my job away? I don’t know. I’d have to ask Asimov what he meant.  So what is the source of revenue for whatever safety-net enhancement we need to do? The government already owns part of the profits just through the corporate profit tax. I don’t think you need to use shares. You can just raise the corporate profit tax back to where it was, or you could say certain industries pay a higher corporate profit tax than other industries. The federal government owns a part of the profit pool of all companies in the United States. And that’s without voting shares or deciding when to sell shares—that’s crazy stuff in my view. A token tax is a sales tax, value-added tax, vertically oriented like an alcohol, tobacco, or luxury-type tax.  If people have other ideas for raising the money to improve the safety net, or if they don’t think we need to improve the safety net, hopefully this shrill paper starts that debate. I think the safety net will need more resources, a lot more resources, and I believe that the token tax is key to that.  Robots, it’ll be some mix of banning them, which is kind of human-reserved, and taxing them. They’re not here yet, but in some ways, when you cross that threshold, you cross it all at once. As soon as the robot’s good enough to work in a factory, it’s probably good enough to cook food, clean rooms, go to construction sites, take all the warehouse jobs. You cross the threshold, and boom, that’s almost 30% of the job market. Then you’re saying, “Oh my God, what is our policy about this?” Because the robot’s cheaper. “We’ve got to get through a very tumultuous period.” Bill Gates MIT Technology Review: I believe previously you have been skeptical of UBI [universal basic income]?  Bill Gates: Well, we’re not rich enough to afford UBI. MIT Technology Review: But do you think that we should be moving toward something like that now? Have you reconsidered that? Bill Gates: You have the period of turmoil, which is the next 10 to 20 years, and then you have some steady state, I hope, where people grow up knowing that society is so rich that regarding food and services, we really do have some level of abundance. But we’re not there. You’ve got winners and losers at this point. Houses are not going to get cheap really quickly. Education, because of the way we think of it as credential, it’s not going to get cheap really quickly.  We’ve got to get through a very tumultuous period. So yes, eventually you have abundance, but we’re at least a decade away from that.  MIT Technology Review: On to human-reserved jobs. I thought that was really interesting, and it was a new concept to me. You don’t advocate for which jobs to be human-reserved. But I would love to know more on how you’re thinking about it. In my mind, you hear about the dignity of work, because people like to work. People get so much value out of work that has nothing to do with compensation, and I wonder how you square that with the notion that only some jobs are special enough that we just want people doing them.  Bill Gates: I’ve never seen the concept of human reserve before. You know, maybe if we dig into the literature, we’ll find it. But pre-AI, it’s kind of a dumb idea because there was infinite demand. And yeah, some people like textile workers were caught, and so how do you do benefits or retraining? But technology’s been a net [job] creator, and so now, for the first time, we have to say, what about childcare? What about food preparation in the house? I’m reading this book, Annie Bot, where this guy has this robot in his house, and it just shows how weird it is. It’s his sexual partner and sort of his mate, but sort of not. Very strange.  I know that people like watching people play baseball, and the fact that the robots can play better won’t take away from it. So you know people are paying $10 billion to buy sports teams that are not going to be worthless in the age of AI. Maybe that’s right. My friend Vinod [Khosla] just did that. It’s actually hard to get above like 30% or 40% [of jobs replaced by AI]. If you could get to 50% then you could say: Okay, early retirement, shorter workweek for lots of people. You know, you might get there. But if you’re more down in the 10% to 15% range, then that is an utterly different society. So this would be radical to say [for example] childcare is not done by robots. There are definitely some professions that I didn’t write the formula for, and when I do the full memo on it, I’ll try to. In education, you clearly want AI to be there as this kind of tutor that immediately tells you what your homework results are and can challenge you, and it’s very personalized. That’s super-good. But I still think you want a teacher—or will choose to have a teacher who’s talking with you about your motivation, and organizing kids into different groups where they’re socially working on problems together. Likewise, in health care, with talking to the patient being the point of escalation for mental-health care. But you really want the AI involved, because it’s there 24 hours a day with a perfect memory. And there’s Limbic, the UK company (that actually was just visiting the Foundation) that does mental health stuff. And in many cases, patients prefer Limbic. And there’s a nursing AI called Hippocratic.  You know, is there a preference for a human taxi driver or Waymo? Most people I know, sadly (or maybe not sadly, who knows?) prefer to ride a Waymo. So it’s going to be hard to get a consensus. It can be country by country, but then you have to change your import policies to do the equivalent of what the EU calls the carbon border adjustment mechanism (CBAM). You have to sort of CBAM your human reserves, so you tariff up things you’re doing without robots. You could have human reserve for two reasons. One, you want it to be human reserve forever; it’s a humanity thing, sort of like the pope talks about. Or just for a transition period, that 53-year-old truck driver or machine tool person, telling him to go do childcare may not work perfectly. So you say, okay, for a decade, he’s human-reserved.  MIT Technology Review: Almost like a UK smoking ban, but in reverse.  Bill Gates: And who pays for that? Do you incentivize employers not to let people go? Well, they are going to be subject to competition from startups that are pure AI startups. I mean, people vaunt this notion that maybe there’ll be a single-person billion-dollar company, which wow, there’s some job substitution taking place there.  MIT Technology Review: In the memo you say that if it was realistic to get people to slow down, you would be advocating for them to slow down. Obviously you’re talking with [Microsoft CEO] Satya Nadella, but I’ve heard that you speak with other CEOs at some of these AI companies. What makes you think it’s not realistic to get them to slow down on technology development while we catch up with some of these bigger societal questions? Bill Gates: You can’t count on an industry to self-regulate. You can’t. It’s kind of a crazy idea. I am very lucky. I know Sam [Altman of OpenAI] and Greg [Brockman of OpenAI] and Mustafa [Suleyman of Microsoft] and Demis [Hassabis of Google DeepMind]. They’re great people, and in private, they’re concerned. I don’t talk to Elon much, but I know from his public comments he’s concerned. Although now he’s kind of a “what the hell, we’ll see what happens” guy. But look at the origin stories of these companies. OpenAI is created partly because Elon’s afraid that Google won’t manage AI properly, and he wants it to be one that’s broadly available and managed in a pro-humanity way. Then OpenAI has this “if it gets good enough we’ll shut it off” thing—as though they’re the only one, and that they can just go bury it. In the Infinity Machine [a biography of Demis Hassabis], [Sebastian] Mallaby talks about how Demis and Mustafa [Suleyman] were negotiating with Google management to have some special governance for the DeepMind technology, so that if it got to some cyber threshold, maybe they’d hold back in a non–purely capitalistic way. So everyone’s concerned about these negative effects, and everyone said that when we got to these thresholds, that we would do things. We’re crossing the thresholds, and we have voluntary review, and our discussions with China about, well, “we’re going to ban nothing. So are you going to ban nothing? Okay, let’s do that together.”  You have to say what you’re willing to do. And yes, the industry, a little bit, is saying, hey, our PR stories have got to improve, and you know anybody who’s talking smack should just leave, because all of us have decided to say nice things because we’re trying to raise trillions. And anyway, there’s the Chinese. There are win-win ways for China and the US to work together, even aside from AI. But the one that’s by far most important to work together on is AI. But first, you have to show what you’re willing to do domestically. You don’t even have to do it. You have to say what you’re planning to do—and then I have no reason to think the Chinese won’t go along, that models that create the molecules have to be monitored. Why would they be against that? I agree it’s not a perfect thing. You’ve got to do all the other things, but the fact that that’s not even being discussed—it’s a crazy world. I don’t get it. It’s weird to think I’m alive at a time, and I’m calling the alarm stronger than other people. Who the hell am I? But that’s the situation I feel I’m in. MIT Technology Review: For most of my life you’ve been seen as a very effective messenger, and someone who people pay a lot of attention to, which I’m sure is why you’re speaking of it now. And yet also, in recent years—and I know you’ve expressed regrets about the associations with Epstein—there are also things, just bananas kind of stuff, related to conspiracies around the Covid vaccine that aren’t your fault or in your control. But it makes me wonder if you think you can still be an effective messenger and how you think about this message and your legacy. Bill Gates: Well, I’m not big on legacy, but you know, people criticized me during the antitrust trial, and I maybe could have handled some things there better. Definitely, that’s the post–Source Code book [the first volume of his autobiography] that I get to go through that. You know, my first marriage didn’t succeed. I certainly made huge mistakes there. You know that is a negative mark against me. Spending time with Epstein—deeply foolish, risked the Foundation’s reputation, which is absolutely key to its doing its work. I had a chance in front of Congress to answer every question they asked and say, “Hey, this was a mistake.” I wasn’t social, never met any woman, except you know there were women he had with him, and made it black-and-white clear what I did do and what I didn’t do.  You know, I’m a billionaire. I made my money off of technology. Maybe that last one actually cuts in my favor, that it’s so unusual for me to attack innovation that unless it’s the right policy and safeguards are put in place, it will be a net negative to humanity. And we’re not paying attention to that in terms of a broad discussion the way that is absolutely required. So yeah, I’m an imperfect messenger. I’ve chosen, to the degree that I have access to politicians and world leaders, that my main message since 2008 has been to help the poorest in the world. You know, let’s eradicate malaria. Let’s buy vaccines for children. So, when I’ve seen Trump or Xi or Macron or—I haven’t met Burnham yet, but I will in a month—I want my voice to be mostly about that, you know, foreign aid and research and reducing child death.  My voice about AI concerns—they’re related in terms of accelerating the good, but may even crowd out, a little bit, the time I have to talk about global health, foreign aid, saving lives, and some of the problems we’re having. But I’m going to use my ability to give interviews or to see political leaders or talk broadly about minimizing these negatives. You know, just the awareness. I’m not sure how many people know that we crossed all these thresholds that we said we’d do something about, and it’s only this year that we did. In the last quarter, last year, I was stunned at the coding. Claude code, the context buffer, the agentic approach, just the model underneath. We crossed a huge threshold for coding, but then it was only months after that I realized that it was not only a coding threshold; it was a massive cyberattack threshold. And you know what happened as a result of that? Not much.  So yes, I’m an imperfect messenger. You know, let’s find the perfect messenger, and I’ll share all my thoughts with that person. (I’m being a tiny bit sarcastic, because I’m not sure there is a perfect messenger.) You’ve got to really, right now, you’ve got to understand the technology and the slope it’s on, and you have to know something about cyber or bio or psychosocial. People should be able to get that. I don’t know why they’re not more concerned. 

Why most of the agents are just flowcharts in disguise, and what to build instead.I wrote most of this at an airport several months ago and then left it in drafts. The noise has only gotten louder since, so here it is.A few months ago, on our way back from a client workshop, we were discussing the scope of what constitutes Agentic AI and all of us quoted examples from our experience. There was a discussion on why automation can’t solve it and how most of the agentic AI use cases are nothing but glorified automation. The question was, “Give me one real use case for an agent. Not a demo. Not automation. A real one. Because everything I have seen so far, I could have built with a workflow engine and a model call.”We all had been in agentic AI conversations for months at that point. We had architected these systems. We had pitched them. And still, sitting there with a tea and twenty minutes at our hand to spend, we had to think long enough to give an example that survived thirty seconds of scrutiny.That bothered me enough to write it down.The test I reached for firstMy instinct was to define agentic by the shape of the work.Does the task require the system to make decisions mid-execution that could not have been anticipated at the start? If yes, agent. If no, automation.I thought of an example from aviation maintenance, because that is where I had spent the previous six months.An A320 aircraft lands with an ECAM warning, AIR PACK 1 FAULT.What automation does: triggers a checklist, notifies the duty engineer, maybe pulls the MEL reference. Done.What traditional ML does: predicts probability of component failure from historical fault patterns, produces a confidence score. The engineer still decides.What I think an agent would do: it starts with the ECAM(a message in the cockpit systems of the aircraft) message, queries the CFDS(a centralised fault display system)for fault history and finds Pack 1 has thrown the same fault three times in six weeks. That changes the picture, so it pulls the TSM (troubleshooting manual) identifies four candidate root causes. It checks AMOS(a database used in aviation all over the world) for parts on hand and finds that two of those four need a Flow Control Valve, which is not at that station. It then checks which causes are deferrable under MEL(minimum equipment list, the minimum an aircraft needs to have to be air worthy), finds one deferrable under Category C(one of many categories)for ten days, looks at the aircraft’s next ten rotations to understand the operational cost of deferring, and drafts a recommendation: defer under Cat C, order the FCV(valve) for arrival before day eight, flag for deep inspection at the next base maintenance slot.Nobody pre-programmed that decision tree. The plan emerged from the process rather than preceding it.I still was not convinced with myself. And on reflection, I believe, I was right.Why that example failsBecause you can draw that flowchart.CFDS, then TSM, then AMOS, then MEL, then rotations. It is a complicated flowchart with branches, but a competent engineer could have specified it in advance. Complexity is not the same as open-endedness. A tree with two hundred branches is still a tree.This is the mistake almost every agentic pitch deck makes, mine included. We show something intricate and expect the intricacy to be self-evidently agentic. It is not. Intricacy is just a bigger flowchart, and flowcharts have a technology already, and it is cheaper, faster and far more reliable than any LLM you will put in that slot.So where is the actual line?Known unknowns versus unknown unknownsHere is the distinction I have settled on, and it is narrower than most people in this market are willing to admit.Automation handles known unknowns. You do not know whether the part is in stock, but you know that stock is a thing you need to check.Agents handle unknown unknowns. You do not know what you need to check, and you will only find out by looking.Take a use case that genuinely breaks automation: due diligence on an acquisition. The instruction is one line. Identify material risks in this target.No one can draw that flowchart upfront. The agent reads three thousand pages of contracts and notices an unusual indemnity clause in a supplier agreement. That clause references a regulatory filing, so it goes and fetches the filing. The filing hints at an informal environmental inquiry that appears nowhere in the data room. It then goes looking through news archives and court records to size the exposure and surfaces it as a risk that was never on anyone’s checklist.Nobody knew to look for that. The agent found a thread and pulled it. You cannot enumerate what you do not know exists.A second one, closer to the consumer world. A brand has a moisturiser generating complaints. Sentiment analysis flags them and a rule routes them to a team. Fine, that is automation and it works.The agentic version notices that the complaints cluster in humid climates, in summer months, and disproportionately from one retail chain. Nobody asked it to look at that intersection. It hypothesises a cold chain or formulation stability issue, pulls batch numbers, cross references manufacturing and logistics logs, and raises a possible recall exposure before a human has connected any of those dots.That property, where discovery changes direction in a way you could not have mapped, is the whole thing. Everything else is scaffolding.Why real examples are so hard to findThis is the part that took me longest to understand, and I think it is the most useful idea here. There could be gaps but still I want to crystallise the information.Enterprises have spent years deliberately engineering open-ended state out of their processes.That was rational. Human judgment is expensive, inconsistent and does not scale. So organisations built SOPs for every scenario, approval hierarchies with fixed triggers, rule based systems in ERP, CRM and WMS, and workflows where every decision point had a predetermined answer. A purchase order above fifty thousand goes to the CFO. Always. Not because that is the smartest possible rule, but because it is auditable and it scales.The goal was to make processes repeatable without requiring thinking.But when you remove ambiguity from a process, you also remove its ability to deal with anything the designers did not anticipate. So enterprises invented a pressure valve: the exception queue. Anything that does not fit gets escalated to a human. That human applies judgment. If the same exception recurs enough times, someone writes a new rule and it gets absorbed back into the process.Humans were the agents all along. They were sitting at the edges of the process, absorbing the unknown unknowns, and the org chart pretended that was not happening.So when a leadership team sits in a room and asks “where do we use agents”, they look at their core processes, find them fully specified, and conclude there is nothing here. Of course there is nothing there. They spent five decades making sure of it.The opportunity is not in the core. It is at the boundary, where the structured process meets messy reality. Where a supplier stops behaving the way the ERP expects. Where a customer complaint does not fit any category. Where a regulatory change quietly invalidates three workflows at once.So you want to start an agentic journeyThis is the question I get most often now, usually after someone’s board has asked them what their agentic strategy is. Here is what I would actually tell them.Image by authorStart from the exception queue, not from the use case list. Do not run an ideation workshop. Go find where your experienced people are spending their judgment today. Look at what gets escalated, what sits in someone’s inbox for two days, what requires a phone call to a colleague who “knows how this works.” That is your map. Those escalations are the fossil record of open-ended state in your organisation.Assume your bottleneck is access, not intelligence. Almost nobody fails because the model was not smart enough. They fail because the agent could not reach the data, or the document store had no usable metadata, or the source of truth for supplier terms turned out to be four spreadsheets on a shared drive. An agent’s ceiling is the set of things it can actually see and do. Budget accordingly, and be honest that a good part of your first year is plumbing. Had you have a good AI strategy, your agentic strategy will be much easier.Decide the autonomy level explicitly, and write it down. There are three modes: Recommend only, Act with approval, Act and report. Most enterprise use cases should live at recommend stage far longer than the anyone suggests, and there is no shame in that. A system that assembles the evidence dossier and hands it to a human is already removing the expensive part of the work.Build the evaluation harness before you build the agent. This is the discipline gap I see most often. If you cannot tell whether the agent reasoned well on a case, you cannot deploy it, you cannot improve it, and you certainly cannot defend it in an audit. Curate fifty real historical cases with known outcomes before you write a line of orchestration code. The golden set of QnA is what I see missing in most of agentic orchestrations, your system doesn’t need to pass all the cases that are in your golden set but at least it will guide you towards your point A and if you know where your point A is, then only you can go to point B.Change what governance is measuring. Deterministic systems are governed by asking, “was the rule followed”. Agentic systems have to be governed by asking “was the reasoning sound, was it within bounds, and can we reconstruct it.” That is a different control framework and your risk function will need to be brought along early, not shown a finished system.Pick a first domain where being wrong is recoverable. Not because agents are unreliable, but because you are going to learn things about your own data and processes that you would rather learn without a regulatory consequence attached.The uncomfortable part: greenfield is easier than retrofitThis one surprises people, and it runs against how most transformation programmes are structured.It is significantly easier to build an agentic system from scratch than to make an existing application or process agentic.The reason follows directly from everything above. An existing enterprise process has already had its ambiguity engineered out. That was the entire point of building it. So when you go to “make it agentic”, you find there is nothing left for an agent to do except execute a sequence of steps that a workflow engine performs more cheaply, more predictably and with better logging. You end up wrapping a language model around a deterministic process and paying more money for less determinism. I have watched teams do this and then wonder why the business case will not close.Retrofit also drags along everything the original system was designed for. Schemas built for transactions rather than reasoning. Permission models built for named human users rather than service identities acting on behalf of someone. Audit trails that assume a fixed path through the process. SLAs that assume a fixed number of steps. Interfaces that were designed to be clicked, not called. None of that is unsolvable, but it is where the calendar goes.Greenfield teams are not smarter. They simply have less to unlearn. They get to design the process around the properties an agent is good at: open state, iterative discovery, tool access, judgment under incomplete information.The practical middle path, and this is what is recommended: do not try to agentify the process. Leave the deterministic core exactly where it is, because it works. Agentify the exceptions that fall out of it. That is where the open-ended state already lives, that is where your expensive people are already spending their time, and it means you are adding a capability rather than replacing a working system with a probabilistic version of itself.And is automation the first step of an agentic journey?Sort of, but not in the way people mean it.Automation is not stage one of a maturity curve that ends in agents. They are not the same thing at different levels of sophistication. But automation is a prerequisite, in a specific and important sense: your automations become the tools your agents call. Every reliable API, every clean integration, every well defined action you have already built is something an agent can now use as a hand.An agent without solid automation underneath it is a very expensive intern with no hands. It can reason beautifully about what should happen and then do nothing about it.So the organisations best positioned for this are not the ones that skipped process automation to chase agents. They are the ones that did the boring integration work for a decade and now have something worth reasoning over.Where I have landedMost of what we see and term as agentic is automation with a better narrator. That is not a scandal. Automation is genuinely valuable and there is nothing wrong with selling it, as long as we call it what it is.The remaining part is real and it is genuinely new, because it addresses a category of work that no previous technology could touch. The work at the edges. The exception queue. The unknown unknowns that we quietly staffed with experienced humans and hoped for the best.That is the part worth building in the realms of agentic.The spirited discussion ended there at the tea shop but was there in my mind and thus, I wanted to crystallise my thoughts here.If you are working through this in your own organisation, I would be curious to hear where you have found genuine open-ended state, and where you concluded it was automation after all.

Whether you’re a first-time author or a TDS veteran, welcome to our formatting guide! As of August 2026, we launched our bespoke author platform to replace the WordPress site we’d previously used. You can expect a much easier, more intuitive, and more streamlined drafting experience here, but in case you’d like some guidance on how to upload your work to TDS, you’re in the right place.Table of contentsEssential ElementsAdding the contents of your articleTextHeadingsListsBlockquoteSeparatorTableCode and GitHub GistsMath notationsImagesVideo optionsSocial embedsLink embedsTable of ContentsHow can I ask for help with my draft?Essential ElementsWhenever you’d like to start a new article draft, look for the + New Article button on the top-right corner of the page. You’ll immediately see a pop-up modal inviting you to add key details about your work, like the title, subtitle, main category, and tags. If you’re not sure about some of these, that’s fine — the only required field at this stage is the article’s title. And you can always edit these details later if you’d like.Once you click on the Create Article button you’ll reach the editor screen. The other required element to think about now is the featured image. Look to the sidebar to find the options for choosing or creating one.If you’ve created a custom image for your article, fantastic — click on Upload image and choose it from your computer. If you’ve already uploaded your image to to your media library, or decided to repurpose an image from an older article, pick Choose from library and select the image you want.You also have the option to generate your image using AI directly from your draft using — you guessed it — the Generate with AI button. Click on it and a new modal will appear.Just type in your prompt — feel free to be as descriptive and specific as you want — and click Generate. After a few seconds you’ll see several options to choose from. If you ever need some additional guidance on choosing a featured image, or want to refresh your memory around our guidelines, here’s a FAQ that covers the topic.Adding the contents of your articleWith the essential elements out of the way, it’s time to actually upload your article. Our streamlined UI will get your draft ready for review with minimal hassle. To add regular text, simply start typing. To add any other kind of content or media, always start with the / key. A block menu will pop up, showing all the available content types you can add.Use the up and down arroes to scroll through the list, choose the block you want at that point in your article, and go from there. Let’s take a closer look at your options.TextSelf-explanatory! Just type in or paste your written content. Whenever you start a new paragraph, it’s set to text by default, so you don’t actually need to use the / key (unless you really want to).To add special styling to any part of your text, highlight the relevant portion and you’ll see a menu pop up:You can choose between bold, italic, underline, strikethrough, abd inline code. This is also where you’ll find the link button and alignmnet options. The text box symbol is where you should go if you want to leave a comment for our editors. Click on it, write your comment, tag someone specific from our team if you’d like (using the @ symbol), and click on Comment to submit it. Tip: to find all your comments in one neat space, look to your sidebar, and click on the Threads tab.HeadingsCreating a clear structural hierarchy within your article helps both readers and search engines navigate your content. Add a new heading whenever you start a new section, and choose the right one depending on its position within your article. When you type /heading you’ll see six levels available. Always start new sections with H2, and go down the hierarchy from there: for example, Section 1 in H2, Section 1.1 in H3, Section 1.11 in H4, etc. Please don’t use H1 headings in the body of the article.ListsYou have the option to create both bulleted and numbered lists, depending on your needs — just choose the right block from the list and you’re good to go. Tip: use the tab button to nest a secondary list within your primary list.BlockquoteChoose the blockquote block to highlight specific points or ideas, or when you’re quoting longer passages from external sources. Using blockquotes sparingly can be very effective, but don’t overdo it — just like bold or italicized text, they can quickly become distracting.SeparatorSometimes, a heading might feel insufficient for creating a visual break between or within sections.In those cases, use the Separator block — just make sure you select the Dotted style, which is the one we chose as our default on TDS. (If for some reason you absolutely need to use a different style of separator, that’s probably ok. Just leave us a comment explaining your choice.)TableTables are great for comparing benchmark results, product features, and more. The Table block makes creating sleek tables very easy.The + buttons below and to the right of the table will add rows and columns, respectively. The other settings in the pop-up menu allow you to toggle the header row and column, align the table vertically, delete rows and columns, and delete the table entirely.Code and GitHub GistsMany TDS articles include code — sometimes lots of code. The text block we covered above gives you access to inline code styling, however that’s not a practical solution for more than, say, a short snippet. You have two great options to choose from:Code blockChoose a code block when you’d like to input code directly into the draft and choose a language-specific syntax highlighting for it. Just paste your code into the block — then, either keep it in Auto mode and our site will choose the most appropriate highlights for it, or scroll down the list of available programming languages and choose the relevant one.If the block only contains outputs, natural-language prompts, etc., rather than working code, just pick Markdown, which will keep it in plaintext.GitHub GistsYou also have the option of embedding GitHub Gists directly into your draft, which can be useful if you’re bringing your work over from a repo. All you need to do is paste the URL of your gist (make sure it starts with gist.github.com) and click on Embed — it will magically appear in your draft and in the final article.Math notationsOne of the biggest upgrades of our bespoke editor is how easy it is to add equations, formulas, and any other math symbol-heavy content. Here, too, you have two options to choose from.Inline MathGo with the Inline Math block when you need to insert mathematical symbols or notations in the midst of your running text — just type it into the input box, check the preview below it to make sure everything looks good, click Save, and you’re done.Block MathFor longer and more complex mathy stuff, opt for Block Math — this is where you can truly work your LaTeX magic. Once again, use the preview below the input box to make sure all the sigmas and deltas are in the right spot.ImagesFor charts, plots, screenshots, animations, and so on, use the Image block. You have several options here: uploading, using an image already in your media library, adding via URL, or generating one using our built-in AI tool. Go wild! (Ok, not too wild, please.)Once you’re image is in, you can click on it and a settings popup will appear. This is where you can control its dimensions and alignment, add an alt and a title, and delete it if you decided not to use it.The most important setting here is the caption — the second symbol from the left. This is where we ask all authors to add sourcing and licensing information for all their images, including those they generated with AI and/or created themselves. Tip: if your article contains numerous images, and you created all or most of them, you can avoid adding an annoying number of captions by adding a note along the lines of “All images, unless otherwise noted, are by the author.” Then you only have to add captions to the ones you’ve sourced from third parties.Video optionsLooking to add a a live demo, a lecture you gave, or the song your audio ML project is referring to? Easy — just embed it using either the YouTube, Vimeo, or DailyMotion embed blocks. They all work the same way: choose the right block, paste the URL of the video you’d like to add, and click Embed. The result is a natively embedded, controllable video player:[embedded content] Social embedsThe best way to include content from social media in your articles is embedding them — the formatting is already optimized for our site, and you avoid running into thorny copyright issues, since you’re essentially re-sharing the original post. Beyond the video embeds we mentioned in the previous subsection, you can also embed tweets and Reddit posts following the exact same process: choose the block, paste the URL, click Embed, and presto!Link embedsUse the Link embed block to create styled embedded links to other URLs. Choose the block, paste the link to the page in question, and click Embed.Table of ContentsFor a final bit of magic, you can automatically generate a clickable table of contents of your article by adding the… Table of Contents block! It works by collecting all your headings and subheadings into a TOC format, so giving your thoughts to the internal structure of your article will pay off here.To create it, just add the Table of Contents block wherever you’d like it to appear — for example, after a quick intro (and, ideally, before your first heading).Tip: TOCs are optional; they usually work best in longer pieces and deep dives, and can feel a bit superfluous in a short, code-heavy article, for example.How can I ask for help with my draft?If this guide hasn’t addressed the question you had or an issue you ran into, no worries — you can reach out to use directly from your draft. Just highlight any word(s), click on the comment symbol, and tag one of our team members with the @ symbol. (If it’s a longer question and you prefer to email us, you can — find us at publication@towardsdatascience.com.)

For Rupert Young ’95, SM ’95, his career in data science and cybersecurity began when his grandfather gifted him thousands of stamps: He built intricate databases to catalogue them, displaying the “precise eye” for detail and nuance that his MIT application essay said would make him a good engineer. Young is now chief product officer of ­MaxMind, whose work with IP-address location data and fraud prevention has made it a go-to resource. Streaming companies, security vendors, merchants, and ad-network providers use its signature tool, GeoIP, to determine how and where users are accessing services. This information makes it possible to ensure retail sites are using the correct currency, flag suspicious bank logins, and more. Young’s passion for engineering was shaped by internships, and he has paid it forward by volunteering at his children’s California high school and trying to keep up with what “the next generation of engineers are tinkering with.” The next generation of product innovation at MaxMind excites him too. “Working with my team to try to find patterns in data and solve challenging problems—to me, there’s no greater joy,” he says. Read more at www.technologyreview.com/alumni-profiles.

When remotely operated vehicles settle on the seafloor or dig through a sand bed, they can kick up clouds of sediment that onboard cameras struggle to see through. Often, the only thing to do is wait until the dust settles. But a new system developed by Amy Phung, SM ’23, PhD ’26, and her advisor Richard Camilli, SM ’00, PhD ’03, of the Woods Hole Oceanographic Institution (WHOI), offers a solution.  In this technique, the vehicle first uses sonar to quickly map its surroundings. That technology doesn’t provide detailed resolution, but it works equally well in cloudy and clear water. And it allows a vehicle to safely get close enough to specific objects for cameras to visualize them more carefully. To speed up the processing so the mapping can be done in real time, the researchers combined the sonar tech with an image-­matching algorithm developed by researchers in France that quickly estimates the relative depth of each pixel in a 2D scene. “An analogy would be if you were to go into a china shop in the dark, and try to pick your way around to find a specific coffee mug without knocking things over,” Camilli says of their new technique. “This would allow you to do that.” He and Phung say applications could include scientific exploration, underwater construction and maintenance, and handling of unexploded undersea mines.