The Patenting of Mathematical Methods at the EPO
New EPO Guidelines for Examination
Dr. D. Herrmann (DE), Editorial Committee
Mathematical methods play an important role in many different areas of technology: simulation, design, modelling or control of technical devices or processes, media enhancement or analysis, speech recognition, encryption/decryption of data, DNA analysis and medical applications are only a few examples. Artificial intelligence and machine learning are based on computational models and algorithms for classification, clustering, regression and dimensionality reduction, such as neural networks, genetic algorithms, support vector machines, k-means, kernel regression and discriminant analysis. Such computational models and algorithms are of mathematical nature. Hence, the below also generally applies to such emerging technologies.
According to Art. 52 (2) a), (3) EPC and the established practice of the EPO, mathematical methods as such are not considered to be technical and are thus excluded from patentability. However, this exclusion only applies if a claim is directed to a purely abstract mathematical method, i.e. if the claim does not require any technical means, such as a computer. If the claim is directed to subject-matter involving the use of technical means, then this subject-matter has technical character as a whole and is thus not excluded from patentability under Art. 52 (2), (3) EPC. Once it is established that the claimed subject-matter as a whole is not excluded from patentability and is thus an invention in the sense of Art. 52(1) EPC, the claimed subject-matter is examined with respect to the other legal requirements, in particular novelty and inventive step.
The long-established standard practice of the EPO requires that, in order to involve an inventive step, claimed subject-matter must solve a technical problem with technical means in a way which is not obvious.
With regard to the patentability of mathematical methods, this meant and still means that features of a patent claim which relate to a mathematical method, such as calculations or operations of an algorithm, are analysed to determine if, in the context of the claimed subject-matter, they are of technical character, i.e. if they contribute to producing a technical effect. If they do not make such a technical contribution, they are not taken into account during the assessment of inventive step, in accordance with the examination approach of the widely known COMVIK decision T 641/00 of the EPO Boards of Appeal, and hence cannot support the presence of an inventive step. Normally, the EPO adds such non-technical features to the formulation of the objective technical problem to be solved, which is given to the skilled person as a kind of desired goal when starting from the closest prior art.
When looking at mathematical methods, the particularly relevant question is which criteria a mathematical method-related claim has to fulfil in order for the features of the mathematical method to be recognized as "technical features" that contribute to the technical character of the claimed subject-matter, so that it is to be taken into account when assessing inventive step.
In the revised Guidelines, the EPO appears to have the intention to re-formulate the technical effect requirement by stating that the contribution made by the features of a mathematical method to the technical character of the claimed subject-matter is to be assessed by taking into account whether these features, in context of the claim, fulfil one of the following two alternative requirements:
- the features serve a technical purpose, by its application to a field of technology,
and/or - the features are adapted to a specific technical implementation.
I. "Technical Purpose/Application"
The above first alternative is discussed in this section I. A technical purpose or application may make features relating to a mathematical method technical and hence relevant for the assessment of inventive step. However, the EPO emphasizes in the revised Guidelines that a generic purpose, such as "simulating or controlling a technical system" is not sufficient to confer technical character to a mathematical method, but rather that the technical purpose must be a specific one. Moreover, the mere fact that the mathematical method may possibly serve a technical purpose is not sufficient, either. That is, the claim must be functionally limited to a specific technical purpose, either explicitly or implicitly, which is based on the decision T 1227/05 by Board 3.5.01 (see the headnote and reasons 3.1 therein). This is in line with a general understanding by the EPO, namely that a technical effect must be objectively, reliably and causally linked to a claimed feature (EPO GL 2018, G-II, sections 3.3.2 and 3.7), even though this does not appear to be stated in this exact manner in a decision by the Boards of Appeal of the EPO.
According to the revised EPO Guidelines, this functional limitation to a specific technical purpose could be achieved by establishing a sufficient link between the technical purpose and the mathematical method steps, for example, by specifying how the input and output of the sequence of mathematical steps relates to the technical purpose so that the mathematical method is causally linked to the technical effect.
How this can be done in practice is shown by the case underlying T 1227/05, which is also discussed in the EPO Guidelines (see EPO GL 2018, G-VII, section 5.4.2.4).
I.1 The Decision T 1227/05
The purpose of the patent application underlying this decision was to simulate or model the performance of a circuit under the influence of a 1/f noise and the proposed solution was based on the notion that 1/f noise can be simulated by feeding suitable random numbers into the circuit model.
An appeal was lodged against the examining division's decision to refuse the application with a claim directed to a method with mathematical steps for simulating a circuit subject to 1/f noise on the grounds that the simulation method according to claim 1, as it then stood, constituted a mental act or mathematical method as such and was therefore excluded from patentability under Article 52(2) EPC as a non-invention.
In an annex to summons, the Board remarked that a computer-implemented embodiment of the method would overcome the non-invention objection (Art. 52 (2), (3) EPC). The inventive step assessment though could only consider features which contributed to the technical character of the simulation method. So what particularly needed to be examined was whether the mathematical formulae in the independent claims could contribute to a technical character.
In simplified terms, claim 1 of this case was the following (see EPO GL 2018, G-VII, section 5.4.2.4 and section III of T 1227/05):
A computer-implemented method for the numerical simulation of (the performance of) an electronic circuit subject to 1/f noise, wherein:
(a) the circuit is described by a model featuring input channels, noise input channels and output channels;
(b) the performance of the input channels and the output channels is described by a system of stochastic differential equations;
(c) an output vector is calculated for an input vector present on the input channels and for a noise vector y of 1/f-distributed random numbers present on the noise input channels; and
(d) the noise vector y is generated by the following steps:
(d1) setting the number n of random numbers to be generated;
(d2) generating a vector x of length n of Gaussian-distributed random numbers;
(d3) generating the vector y by multiplying the vector x with a matrix L defined according to equation E1*.
Equation E1 was explicitly specified in the claim.
As background information (see EPO GL 2018, G-VII, 5.4.2.4), this claim is directed to a method carried out by a computer for the numerical simulation of (the performance of) an electronic circuit subject to 1/f noise, which is one of the main sources of noise in electronic circuits. Features (a)-(c) specify the mathematical model used in the numerical simulation. It involves a noise vector y of 1/f-distributed random numbers, i.e. random numbers having a particular statistical property typical of real (physical) 1/f noise. Steps (d1)-(d3) define the mathematical algorithm used for generating these random numbers. According to the description, this mathematical algorithm is particularly efficient in terms of computation time and storage resources required to generate the random numbers needed for the simulation.
The Board was also convinced that the claimed features relating to the mathematical method would allow for a resource-efficient simulation. The Board commented, however, that a technical advantage cannot be acknowledged based on the mere observation that a claimed method runs faster than a "conceivable" reference method. As it would always be possible to conceive of a slower reference method, a mere speed comparison would not a suitable criterion for distinguishing between technical and non-technical procedural steps (reasons 3.2.5). This comment by the Board is controversial and obviously hard to digest by software programmers.
The Board argued that beyond its implementation, a procedural step may contribute to the technical character of a method only to the extent that it serves an adequately defined technical purpose of the method (reasons 3.1).
In this context, the Board noted that the metaspecification of an (undefined) technical purpose (simulation of a "technical system") would not be considered adequate. However, the board was persuaded that the above underlined purpose of the method, namely simulation of a circuit subject to 1/f noise, constitutes an adequately defined technical purpose for a computer-implemented method, provided that the method is functionally limited to that technical purpose (see reasons 3.1 and headnote). In the case of this decision, the stated purpose - simulation of a circuit subject to 1/f noise - was established in the further steps of the claimed method. On the basis of the physical and mathematical derivation specified in the description, it was verifiable that the random numbers generated according to the claims actually introduce 1/f noise into the circuit simulation. The board was therefore persuaded that the independent method claims are, beyond the mere purpose limitation, functionally limited to the numerical simulation of a noise-affected circuit (reasons 3.1.2).
As the algorithm defined by steps (d1)-(d3) requires less computer resources than other known algorithms, in the context of the claimed method being functionally limited to the numerical simulation of a noise-affected circuit, this results directly in a reduction of the computer resources required for the claimed technical purpose, namely the numerical simulation of an electronic circuit subject to 1/f noise, which is the achieved technical effect. According to the Guidelines (see EPO GL 2018, G-VII, section 5.4.2.4), one should note that if the claim were not limited to the numerical simulation of an electronic circuit subject to 1/f noise, the mathematical algorithm defined by steps (d1)-(d3) may not be considered serving any technical purpose and may thus not be considered to contribute to the technical character of the claim, because requiring less computer resources than another mathematical algorithm being on its own not sufficient in this respect according to the above comment by the Board in T 1227/05 (reasons 3.2.5).
Interestingly, the Board also noted that while the invention may be preceded by a mental or mathematical act, the claimed result must not be equated with this act. The above claim would rather relate to a simulation method that cannot be performed by purely mental or mathematical means, not to the thought process that led to that simulation method (reasons 3.2.1).
Moreover, the Board made important observations with regard to simulation (and design or model) software, which, especially today, are generally applicable to the patenting of mathematical methods.
The Board noted that a simulation performs technical functions typical of modern engineering work. It provides for realistic prediction of the performance of a designed apparatus, such as a circuit, and thereby ideally allows it to be developed so accurately that a prototype's chances of success can be assessed before it is built. The technical significance of this result increases with the speed of the simulation method, as this enables a wide range of designs to be virtually tested and examined for suitability before the expensive apparatus fabrication process starts. Without technical support, advance testing and/or qualified selection from many designs would not be possible, or at least not in reasonable time (see reasons 3.2.2, headnote). Such simulation methods could also not be denied a technical effect merely on the ground that they do not yet incorporate the physical end product (see headnote).
For these above reasons, in the Board's view, all steps relevant to circuit simulation - and that includes the mathematically expressed claim features - contribute to the technical character of the claimed simulation method and have to be taken into account when assessing inventive step, in particular non-obviousness (reasons 3.2.4 and 4).
On the one hand, the decision T 1227/05 has been confirmed in several decisions by the EPO Boards of Appeal, such as T 1784/06 and T 988/12.
The application underlying T 988/12 related to a method for simulating and analyzing one or more scenarios for a 4G broadband service to be deployed and the decision emphasized that this purpose would cover both business scenarios and technical scenarios and would thus be an inadequately defined technical purpose which does not necessarily render technical the features relating to the simulation.
On the other hand, several decisions questioned whether it is sufficient that the technical purpose be "adequately defined" and the claim limited to that purpose, as T 1227/05 appears to suggest. Such doubts were expressed in T 1630/11 (point 7.1 of the reasons), T 1265/09 (point 1.13 of the reasons, penultimate paragraph) and T 531/09 (point 3 of the reasons). In this context, it is, however, important to note that T 1227/05 does not appear to suggest that a mere technical purpose limitation in the claim suffices. Rather, the claimed operations must credibly lead to the claimed technical purpose. In case of T 1630/11, however, this question was left open because the Board considered that the technical purpose of the claimed simulation was in any case not adequately defined. Claim 1 was concerned with simulation only insofar as it specified the execution of a multi-processor specification developed as a graphical program. According to the Board, the claim was not concerned with the "simulation" of any specific such processor, nor any specific class of processors.
Patent practitioners can therefore conclude from decision T 1227/5 and the discussion in the EPO Guidelines that method claims directed to a mathematical method should contain an adequately defined technical purpose and that the mathematical method is to be functionally limited to that purpose. By this functional limitation to the technical purpose, the features relating to mathematical method contribute to the technical character of the claimed subject-matter and become relevant for the assessment of inventive step.
I.2 Examples in the EPO Guidelines for Technical Purposes/Applications
In the revised Guidelines, the EPO provides a list of examples of technical applications providing such technical purposes for the features relating to the mathematical method:
- controlling a specific technical system or process, e.g. an X-ray apparatus or a steel cooling process;
- determining from measurements a required number of passes of a compaction machine to achieve a desired material density;
- digital audio, image or video enhancement or analysis, e.g. de-noising, detecting persons in a digital image, estimating the quality of a transmitted digital audio signal;
- separation of sources in speech signals; speech recognition, e.g. mapping a speech input to a text output;
- encoding data for reliable and/or efficient transmission or storage (and corresponding decoding), e.g. error-correction coding of data for transmission over a noisy channel, compression of audio, image, video or sensor data;
- encrypting/decrypting or signing electronic communications; generating keys in an RSA cryptographic system;
- optimizing load distribution in a computer network;
- determining the energy expenditure of a subject by processing data obtained from physiological sensors; deriving the body temperature of a subject from data obtained from an ear temperature detector;
- providing a genotype estimate based on an analysis of DNA samples, as well as providing a confidence interval for this estimate so as to quantify its reliability;
- providing a medical diagnosis by an automated system processing physiological measurements;
- simulating the behavior of an adequately defined class of technical items, or specific technical processes, under technically relevant conditions
The revised EPO Guidelines emphasize that whether a technical purpose is served by the mathematical method is primarily determined by the direct technical relevance of the results it provides.
The revised EPO Guidelines also again remind that a technical nature of the data or parameters used for a mathematical method does not necessarily imply that the mathematical method contributes to the technical character of the claimed subject-matter (T 2035/11, T 1029/06, T 1161/04).
However, the revised EPO Guidelines also state that, in the context of computer-aided design of a specific technical object (product, system or process), the determination of a technical parameter which is intrinsically linked to the functioning of the technical object, where the determination is based on technical considerations, is a technical purpose (T 471/05, T 625/11).
According to an example provided by the revised EPO Guidelines, in a computer-implemented method of designing an optical system, the use of a particular formula for determining technical parameters, such as refractive indices and magnification factors, for given input conditions so as to obtain optimal optical performance makes a technical contribution. As another example, determining by iterative computer simulations the maximum value that an operating parameter of a nuclear reactor may take without risking rupture of a sleeve due to stress makes a technical contribution.
In contrast, where the computer-aided determination of the technical parameters depends on decisions to be taken by a human user and the technical considerations for taking such decisions are not specified in the claim, a technical effect of improved design cannot be acknowledged since such an effect would not be causally linked to the claim features (T 835/10).
According to other examples provided by the revised EPO Guidelines, if a computer-implemented method results merely in an abstract model of a product, system or process, e.g. a set of equations, this per se is not considered to be a technical effect, even if the modelled product, system or process is technical (T 49/99, T 42/09). For example, a logical data model for a family of product configurations has no inherent technical character, and a method merely specifying how to proceed to arrive at such a logical data model would not make a technical contribution beyond its computer-implementation. Likewise, a method merely specifying how to describe a multi-processor system in a graphical modelling environment does not make a technical contribution beyond its computer-implementation.
I.3 T 0489/14 - Referral to the Enlarged Board of Appeal (G 1/19)
In the case underlying T 0489/14, the claims of the main request were directed to a computer-implemented method of modelling pedestrian movement in an environment, wherein the environment was not further specified, and the claim was focused on operations of simulating movement of pedestrians through the environment.
On the one hand, the Board tended to consider the features relating to the simulation as mental acts, and thus as non-technical features, and the computer implementation of the simulation as the only technical aspect of the claimed method, which would, however, render the claimed subject-matter obvious over a general-purpose computer (see reasons 5 to 8, 12 and 17). In particular, the Board argued that a technical effect would require a direct link of the simulation with physical reality, such as a change in or a measurement of a physical entity (reasons 11 and 23).
On the other hand, the Board also acknowledged the findings of T 1227/05 and concluded that the features relating to the simulation would be technical if one followed T 1227/05 (see reasons 13 to 15 of T 0489/14).
However, the Board was not fully convinced by the reasoning provided in T 1227/05, which is outlined in section I.1 above, and considered the computer-implemented simulation as a tool to only assist the engineer's cognitive process of verifying a design of a circuit, which, in the Board's view would be a fundamentally non-technical process. Further, the Board focused in T 0489/14 a lot on the argument, that a computer-implemented simulation method would provide a greater speed for the testing of designs, when arguing that any computer algorithm would be faster than a mental execution (see reasons 15).
Overall, the Board concluded that both,the question of patentability of simulation methods would be a point of law of fundamental importance and the Board's intended deviation from the interpretation and explanations of the EPC given by T 1227/05 would justify a referral of the following questions to the Enlarged Board of Appeal, which is presently pending under the case number G 1/19:
- In the assessment of inventive step, can the computer-implemented simulation of a technical system or process solve a technical problem by producing a technical effect which goes beyond the simulation's implementation on a computer, if the computer-implemented simulation is claimed as such?
- If the answer to the first question is yes, what are the relevant criteria for assessing whether a computer-implemented simulation claimed as such solves a technical problem? In particular, is it a sufficient condition that the simulation is based, at least in part, on technical principles underlying the simulated system or process?
- What are the answers to the first and second questions if the computer-implemented simulation is claimed as part of a design process, in particular for verifying a design?
It will be highly important for the patent practice, as well as interesting from the legal point of view, to follow how the Enlarged Board will view the referral as such, the argumentation provided in T 0489/14 (especially in relation to T 1227/05), and the above posed questions.
II. "Technical Implementations"
The above second alternative is discussed in this section II. The revised EPO Guidelines continue with outlining an alternative path according to which a mathematical method may also contribute to the technical character of the invention independently of any technical application when the claim is directed to a specific technical implementation of the mathematical method and the mathematical method is particularly adapted for that implementation in that its design is motivated by technical considerations of the internal functioning of the computer, which is based on T 1358/09 by Board 3.5.07 (see reasons 5 therein). According to the single example provided by the revised Guidelines, the adaptation of a polynomial reduction algorithm to exploit word-size shifts matched to the word size of the computer hardware is based on such technical considerations and can contribute to producing the technical effect of an efficient hardware implementation of said algorithm.
II.1 The Decision T 1358/09
The invention of the application underlying this decision is concerned with the computerized classification of text documents. This is done by first building a "classification model" and then classifying documents using this classification model. The classification model is built on the basis of a set of documents which have been previously classified into a number of predefined classes. In particular, once the classification model has been built, an unclassified document is classified by representing it as a vector in the same vector space and determining the subspace to which the vector belongs. The document is then classified into the class corresponding to this subspace (T 1316/09, reasons 3).
The Board argued that classification of text documents would certainly be useful, as it may help to locate text documents with a relevant cognitive content, but in the Board's view this does not qualify as a technical purpose in the sense of section I above. Whether two text documents in respect of their textual content belong to the same "class" of documents would not a technical issue and the Board also referred to the decision T 1316/09, which held that methods of text classification per se did not produce a relevant technical effect or provide a technical solution to any technical problem.
In T 1358/09, the Board agreed with the appellant in that a human being would not apply the claimed classification method to perform the task of classifying text documents. The Board further accepted that the proposed computerized method may be faster than classification methods known from the prior art.
Interestingly, the Board emphasized that not all efficiency aspects of an algorithm are by definition without relevance for the question of whether the algorithm provides a technical contribution. In this context, this decision specifies the above (see section I) mentioned statements made in reasons 3.2.5 of decision T 1227/05. If an algorithm is particularly suitable for being performed on a computer in that the algorithm design was motivated by technical considerations of the internal functioning of the computer, it may arguably be considered to provide a technical contribution to the invention and the Board also referred to the decision T 258/03 (reasons 5.8), which refers to decision T 769/92 (headnote I). However, such technical considerations would have to go beyond merely finding a computer algorithm to carry out some procedure and the Board also referred to the decision G 3/08 (reasons 13.5 and 13.5.1), which commented on decisions T 769/92 and T 258/03.
In the present case, T 1358/09, the Board considers that no such technical considerations would be present. According to the Board, the claimed algorithm would not go beyond a particular mathematical formulation of the task of classifying documents. The aim of this formulation would clearly be to enable a computer to carry out this task, but no further consideration of the internal functioning of a computer could be recognized by the Board.
Important for patent practitioners is also the observation by the Board according to which it would be an inherent property of deterministic algorithms to provide reliable and objective results and that the mere fact that an algorithm leads to reproducible results would not imply that it makes a technical contribution (reasons 5.6).
According to the Board, the only implementation features specified in the claim of this case are references to the method being "computerized" and the text documents being "digitally represented in a computer". However, the Board found that these technical implementations of the mathematical algorithm would be obvious.
The decision T 1358/09 was supported by other decisions, such as T 2418/12 and T 22/12, wherein the latter rephrased the above condition by stating that if the design of an algorithm were motivated by a problem related to the internal workings of the computer, e.g. if it were adapted to a particular computer architecture, it could, arguably, be considered as technical (reasons 2.8).
Overall, it appears to be more difficult to fulfil the requirement of the "technical implementations", because advantages of algorithms normally reside in the particular coding involved which, however, can and should usually be executed in the same manner by any computer, which may be one reason, why the Guidelines are quite silent on examples for this requirement.
III. Parallels with Federal Court of Justice Case Law in Germany
The above trend of the EPO Boards of Appeal appear to be in harmony with the decision of the Federal Court of Justice in Germany (X ZB 1/15 - Flugzeugstand, 2015) on the subject of mathematical methods.
The matter at the heart of the decision of the Federal Court of Justice concerned the refusal of a German patent application, whose independent claim was claiming a method for determining a state of an airplane. The state was a position, a velocity and an attitude of the airplane. The independent claim further specified several mathematical operations including determining a number of measured values relating to the state of the airplane and processing the measured values in a particular manner using a Kalman-Filter to estimate the state of the airplane. The crucial aspect of the invention was the selection and computing of the data, which were fed to the Kalman-Filter, wherein the Kalman-filter was advantageously fed by a smaller number of values, because this reduces the time needed for data processing.
The Court starts the analysis with the well-accepted requirement that features of a mathematical method, as any other claimed features, must contribute to a technical solution of a specific technical problem to be patentable (see headnote a) and reasons III.1 to III.2.a)). The Court also noted that technical activity involves working with natural forces, wherein laws of nature are usually described by mathematical methods. According to the Court, the application of such mathematical methods for achieving a specific technical success or result would be technical and a mathematical method could only be considered non-technical if, in context of the claimed subject-matter, the method did not relate to any purposely applied natural forces (see headnote b) and reasons III.2.b)).
The Court found that the claimed mathematical operations, which were not disclosed in the prior art, would sufficiently relate to purposely applied natural forces, because the increased speed in data processing obtained by these features would serve the purpose to more reliably estimate the state of the airplane and would hence directly affect the functioning of the system which is used to estimate the state of the airplane (see headnote c) and reasoning III.3.a)). In this context, the Court also emphasized that an inventive step must not be denied based only on the reason that no advantage can be identified, i.e. that the invention is a mere alternative compared to the prior art (see headnote d) and reasons III.3.b)).
Therefore, the Federal Court of Justice in Germany also looked at the advantages provided by the mathematical operations and whether these advantages directly translated to a technical effect, here a different functioning of the technical system which estimates a state of an airplane. While the terminologies used by the Federal Court of Justice in Germany and the Boards of Appeal of the EPO for their assessments of technical contributions of mathematical methods are different, the Court and the Boards, as exemplified by T 1227/05, are imposing quite similar requirements on claim language for features of mathematical methods to be considered technical, and hence relevant for the assessment of inventive step.
IV. Conclusions
In summary, if a mathematical method does not serve a technical purpose and if the claimed technical implementation does not go beyond a generic technical implementation, the mathematical method is to be expected to not contribute to the technical character of the invention (EPO GL 2018, section 3.3).
Thus, patent practitioners should adapt their drafting of claims which contain features relating to a mathematical method by either incorporating an adequately defined technical purpose or by incorporating an adaptation of the mathematical method to a specific technical implementation (like a "fingerprint" of the underlying hardware in the mathematical method). For an adequately defined technical purpose, it may not suffice to merely include the purpose limitation relating to simulating a (specific) technical device, but rather the stated purpose should also be established in the further steps of the claimed method, so that a functional limitation to this technical purpose is credible. An advantage associated within the mathematical method may then arguably directly result in a technical effect.
The revised Guidelines indicate a specifying, or even tightening, of the criteria applied by the EPO that features relating to a mathematical method must fulfil in order to be treated as a technical feature and hence relevant for the assessment of the inventive step. Even though the employed terminology is different, the case law by the Boards of Appeal, which led to these revisions of the Guidelines, and the decisions by the Federal Court of Justice in Germany formulate similar criteria for the patenting of mathematical methods. The basis of these criteria is now at stake due to the referral G 1/19 pending at the Enlarged Board of Appeal of the EPO. In case G 1/19 leads to a stricter legal view deviating from T 1227/05, then applicants might consider filing less patent applications about computer-implemented simulation or design methods with the EPO and might prefer to choose the GPTO instead.
